understanding and exploiting commodity...
TRANSCRIPT
IN DEGREE PROJECT TECHNOLOGY,FIRST CYCLE, 15 CREDITS
, STOCKHOLM SWEDEN 2017
Understanding and Exploiting commodity currenciesA Study using time series Regression
DYLAN DEHOKY
EDWARD SIKORSKI
KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ENGINEERING SCIENCES
Understanding and Exploiting commodity currencies A Study using time series Regression DYLAN DEHOKY EDWARD SIKORSKI Degree Projects in Applied Mathematics and Industrial Economics Degree Programme in Industrial Engineering and Management KTH Royal Institute of Technology year 2017 Supervisors at KTH: Henrik Hult, Pontus Braunerhjelm Examiner at KTH: Henrik Hult
TRITA-MAT-K 2017:04 ISRN-KTH/MAT/K--17/04--SE Royal Institute of Technology School of Engineering Sciences KTH SCI SE-100 44 Stockholm, Sweden URL: www.kth.se/sci
Abstract
This thesis within Industrial Economics and Applied Mathematics examines theterm commodity currency. The thesis delves into analysing the characteristicsand consequences of such a currency through a macroeconomic perspective whilediscussing previous studies within the matter. The applied mathematical statis-tics section audits the correlation between the currency and the commodities ofthe exporting country through a time series regression. The regression is basedon the currency as the dependent variable and the commodities represent thecovariates. Furthermore, a trading strategy is developed to see if a profit canbe made on the foreign exchange market when looking at the commodity pricemovements.
Key words: Commodity currencies, regression analysis, time series regression,Dutch disease and trading strategy
Att forsta och utnyttja ravaruvalutorEn statistisk analys baserat pa tidsserieregression
Sammanfattning
Det har kandidatexamensarbetet ar skrivet inom industriell ekonomi och tillampadmatematik och granskar termen ravaruvaluta (commodity currency). Upp-satsen analyserar, utifran ett makroekonomiskt perspektiv, karaktarsdragenoch konsekvenserna av en sadan valuta, samtidigt som den diskuterar tidigarestudier inom amnet. Delen inom tillampad matematik undersoker korrelationenmellan valutan och ravarorna som landet exporterar genom en tidsserieregres-sion. Regressionen ar baserad pa valutan som responsvariabel samtidigt somravarorna representerar kovariaterna. Den fardiga modellen anvands sedan i enhandelsstrategi som forsoker forutspa vaxelkursens rorelser genom att titta paravarornas rorelser.
Preface
This Bachelor’s thesis was written in the spring of 2017 by Edward Sikorski andDylan Dehoky, during their five-year master’s degree program within IndustrialEngineering and Management at KTH Royal Institute of Technology. The the-sis combines both aspects from industrial economics and applied mathematicalstatistics. These aspects were integrated into one report, although the economi-cal and mathematical theories were separated under section 2 and 3 respectively.
We would also like to take the opportunity to thank Joel Berhane, Sara Alexis,Graziella El-Ghorayeb, and Dalill Arafat for their never-withering belief in us.Lastly, we would like to express our appreciation to our supervisors Henrik Hultand Pontus Braunerhjelm for allowing us to write this thesis together, despiteEdward being on the other side of the globe.
Contents
1 Background 11.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Research Question and Problem Statement . . . . . . . . . . . . 21.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Previous Research . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Theoretical Background 42.1 Understanding Exchange Rates . . . . . . . . . . . . . . . . . . . 4
2.1.1 Floating or pegged? . . . . . . . . . . . . . . . . . . . . . 42.1.2 Nominal exchange rate (NER) . . . . . . . . . . . . . . . 52.1.3 Real exchange rate (RER) . . . . . . . . . . . . . . . . . . 52.1.4 Overshooting . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.5 Purchasing power parity (PPP) . . . . . . . . . . . . . . . 62.1.6 PPP puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.7 Factors influencing the exchange rate . . . . . . . . . . . . 7
2.2 Commodity Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Supply and demand . . . . . . . . . . . . . . . . . . . . . 8
2.3 Commodity Currencies . . . . . . . . . . . . . . . . . . . . . . . . 92.3.1 Commodity currencies through PPP . . . . . . . . . . . . 92.3.2 Consequences of a commodity currency . . . . . . . . . . 10
2.4 Dutch Disease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4.1 Historical events . . . . . . . . . . . . . . . . . . . . . . . 112.4.2 Consequences . . . . . . . . . . . . . . . . . . . . . . . . . 112.4.3 Other theories . . . . . . . . . . . . . . . . . . . . . . . . 122.4.4 Mitigation of the phenomenon . . . . . . . . . . . . . . . 13
3 Mathematical Theory 143.1 Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . 143.2 Ordinary Least Squares . . . . . . . . . . . . . . . . . . . . . . . 14
3.2.1 Key assumptions . . . . . . . . . . . . . . . . . . . . . . . 153.2.2 Lagged variables . . . . . . . . . . . . . . . . . . . . . . . 153.2.3 Interpretation of the coefficents . . . . . . . . . . . . . . . 153.2.4 Logarithmic transformation of variables . . . . . . . . . . 16
3.3 Time Series Regression . . . . . . . . . . . . . . . . . . . . . . . . 163.3.1 Similarity measure . . . . . . . . . . . . . . . . . . . . . . 173.3.2 The Autoregressive model . . . . . . . . . . . . . . . . . . 18
3.4 Validating the Model . . . . . . . . . . . . . . . . . . . . . . . . . 183.4.1 Hypothesis testing . . . . . . . . . . . . . . . . . . . . . . 183.4.2 F-test statistics and t-test . . . . . . . . . . . . . . . . . . 193.4.3 p-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4.4 R2 and Adjusted R2 . . . . . . . . . . . . . . . . . . . . . 203.4.5 Akaike Information Criterion . . . . . . . . . . . . . . . . 20
3.5 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5.1 Heteroscedasticity . . . . . . . . . . . . . . . . . . . . . . 21
3.5.2 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . 223.5.3 Endogenity . . . . . . . . . . . . . . . . . . . . . . . . . . 233.5.4 Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.5.5 Autocorrelation and cross-correlation . . . . . . . . . . . . 243.5.6 Spurious regression . . . . . . . . . . . . . . . . . . . . . . 25
4 Method 274.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Literature Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3 Choice of Country . . . . . . . . . . . . . . . . . . . . . . . . . . 284.4 The Regression Model . . . . . . . . . . . . . . . . . . . . . . . . 294.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5 Results 335.1 Preliminary analysis of the data and unit root analysis . . . . . . 335.2 Cointegration analysis . . . . . . . . . . . . . . . . . . . . . . . . 355.3 Regressions without lag . . . . . . . . . . . . . . . . . . . . . . . 365.4 Regressions with lag . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.4.1 Smoothed data . . . . . . . . . . . . . . . . . . . . . . . . 405.5 Analysis of models . . . . . . . . . . . . . . . . . . . . . . . . . . 425.6 Trading results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6 Discussion 49
7 Further Research 53
8 References 54
9 Appendices 589.1 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589.2 Regression outputs . . . . . . . . . . . . . . . . . . . . . . . . . . 679.3 Nominal Commodity Prices . . . . . . . . . . . . . . . . . . . . . 68
1 Background
The relationship between macroeconomic fundamentals and the real exchangerate is among the more controversial in the field of international macroeco-nomics. Attempts to model the behaviour of the real exchange rate empiricallyhas repeatedly proven to be unsuccessful. This was most noticeably demon-strated by Meese and Rogoff [1983], where they found a random walk modelperforming as well as any of their models in predicting the exchange rate. Thisrandom walk contradicts the Purchasing Power Theory, which claims that ex-change rates should converge towards an equilibrium level, such that price lev-els are equal once converted to a common currency [Rogoff, 1996]. Voices havebeen raised that real shocks in macroeconomic fundamentals could prove tobe decisive in resolving these empirical puzzles. However, what these priceshocks might be, or how to identify and measure them remains to be answered[Chen & Rogoff, 2012].
In contrast, commodity prices have generally been shown to drive real exchangerates in major commodity-exporting countries, giving birth to the term ”com-modity currencies”. One of the first people to discover the correlation betweena commodity exporting country and its currency was Paul Krugman [1980], ashe observed how oil prices affected different exchange rates. More extensive re-search was made, and economists could confirm the correlation. In 2003, Cashinlooked at currencies among developing countries and saw that the correlationwas not as robust as with developed countries. The reasons to this was thatinflation and capital controls in developing countries in turmoil are constantlyfluctuating [Cashin et al. , 2003].
There are several commodity currencies, but studies have shown that the Cana-dian dollars (oil), Australian dollars (gold) and New Zealand dollars (agricul-tural products, e.g. wheat) are the three currencies among developed countrieswith high correlation to their commodities [Chen & Rogoff, 2002]. Other cur-rencies worth mentioning are the South African Rand (metals, e.g. platinum),Norwegian Krone (oil) and Brazilian Real (oil, soybeans, iron). When the priceof a commodity rises, the cost of goods sold increases, thus, resulting in an in-crease of the price. Consequently, this raises inflation. The response to a risein inflation is a rise in interest rates, in order to strengthen the currency. Inessence, appreciation of commodity prices results in a strengthened currency.
However, macroeconomic problems arise along with a commodity currency. TheDutch disease is such an implication, which in simple terms regards how a natu-ral resource boom can cause other sectors, often manufacturing, to experience adecline. The term was coined in the journal The Economist in 1977, describingthe decline in The Netherlands’ manufacturing sector following the discovery ofoil in the country. This is as the increased commodity export drives up the valueof the currency, making the other sectors less competitive on the internationalmarket.
1
Another complication that a commodity currency bears is the sensitivity tofluctuations in the price of the commodity. In the case of developing countries,where a commodity is their main source of income, a fall in the price of theircommodity can have dire consequences. For instance, 60% of Mali’s export isgold, leaving them vulnerable to fluctuations in gold prices [OEC, 2015].
However, despite considerable research having been conducted in the field, themajority of the literature concerning the relationship between commodity pricesand exchange rates focus on a longer time horizon. This begs the question, froman investors point of view, whether there exists a relationship over a shorter timeperiod.
Hence, this thesis differs from previous studies in the field by seeking to concludewhether there exists a relationship between the nominal exchange rate, insteadof the real exchange rate, and commodity prices in selected major commoditycurrencies on a short term.
1.1 Aim
This thesis aims to assess the short-term relationship between nominal exchangerates and commodities in countries where the majority of the total export con-stitutes of one, or a few, commodities. It further aims to examine, both from amacroeconomic and statistical point of view, the reasons behind the results.
1.2 Research Question and Problem Statement
The aim culminates in the following two problem statements:
• Is there a short-term relationship between commodity prices and nominalexchange rates?
• Is it possible to profit from this relationship?
An Ordinary Least Squares (OLS) estimation will be used for one country,using data from January 2009 until December 2016, to give a robust empiricalunderpinning to these questions. The OLS method will be defined and discussedin the section Mathematical Theory.
1.3 Limitations
The individual commodity currency selected was the Australian dollar. Thecurrency was selected as Australia is a commodity exporting country, with over60% of its export consisting of commodities. Furthermore, Australia was specif-ically interesting whilst looking at previous studies within the subject. A moredetailed explanation can be found under the section Method. Lastly, data be-tween 2009-01-02 until 2016-12-30 was examined, as data for earlier periods oftime were not found for all the commodities.
2
1.4 Previous Research
In one of the most cited studies in the field, Meese and Rogoff [1983] attemptedto compare a variety of structural exchange rate models based on their out-of-sample accuracy. They found that their models failed to forecast countryexchange rates more accurately than a random walk model. Even though thestructural models based their predictions on actual realized values, they failedto improve on the random walk model.
One of the first to study the correlation in developed countries (Australia,Canada and New Zealand) between prices of their primary commodities andthe real exchange rates were Chen and Rogoff [2002]. They found, especiallyfor Australia and New Zeeland, that the price of their commodity exports hada strong influence on their real exchange rates. These results were of a magni-tude in line with predictions of standard theoretical models. Despite this, therewas still a purchasing power parity puzzle (PPP puzzle) in the residual whenadjusting for commodity price shocks.
Another study conducted in 2003 by Cashin et al. examined the co-movementbetween real exchange rates in 58 commodity exporting countries and the pricesof their commodity exports. They showed a long-run relationship in two-fifthsof the countries under study.
Beine et al. [2012], Sachs Warner [2001] and Coudert et al. [2008] all studiedthe correlation between commodity currencies and their consequences.
Bjørnland and Hungnes [2004] studied the PPP puzzle and showed that once youaccount for the interest rate differential in the real exchange rate relationship,any deviations from the purchasing power parity are explained for. The studyexamined Norway, which has oil as its primary commodity, where it constitutesa majority of Norway’s exports. The results are in contrast to previous studieswhere the PPP puzzle has not been found to hold in the long run. Bjørnlandand Hungnes, therefore, claim to have solved the PPP puzzle.
The mentioned reports were studied in order to gain a deeper insight into thedynamics of the currencies. Valuable insight was gained by studying their work,as it helped with the structuring of the problem and mathematical model. Thedifferentiating factor in this thesis compared to previous research will be themathematical model. This thesis examined the correlation by using daily prices,whilst all prior research used monthly prices.
3
2 Theoretical Background
This section will discuss the economic theory behind a commodity currency, andwhat the consequences can be. Different models will be explained, in order togive the reader a deeper insight into commodity pricing and the dynamics ofit. A detailed description of the Dutch disease will give a better understandingof the consequences of a commodity currency, and also how to prevent majoreconomical implications for a nation.
2.1 Understanding Exchange Rates
The exchange rate is the rate at which a currency can be exchanged for another[Krugman & Wells, 2013]. It can also be regarded as the price at which curren-cies trade, or the value of one currency in relation to another. These currenciesare traded on the foreign exchange (FX) market, where traders can buy andsell currencies. The exchange rate is determined by the supply and demand ofa currency and its corresponding equilibrium point. Thus, when the quantityof a currency demanded in the FX market is equal to the supplied quantity, theequilibrium exchange rate has been reached.
2.1.1 Floating or pegged?
A government can choose between different exchange rate regimes in governingtoward the exchange rate. It can either implement a fixed or floating exchangerate. [Krugman & Wells, 2013]
A fixed exchange rate means that the rate is pegged to some other cur-rency, usually the US dollar. An early implementation of the fixed exchangerate was the Bretton-Woods system. It was a result of the financial instabil-ity in the world after World War II. The system was a monetary policy thattied countries’ currencies to the US dollar, which was backed by gold. Thepurpose of this agreement was to end reoccurring and drastic devaluations ofcurrencies in order to gain competitive advantages in the exports market. Thesystem was abruptly discontinued in the so-called ”Nixon shock” in 1971, asthe United States could no longer guarantee the value of the dollar to the goldprice. [Keylor, 2001]
A modern example of a fixed exchange rate would be the Hong Kong dollar.Hong Kong has an official policy where the Hong Kong dollar (HKD) has a setexchange rate of 7.80 HKD per USD. However, there might emerge a problem inwhere the fixed value may not be the natural equilibrium exchange rate betweenthe two currencies on the foreign exchange market. Instead, the HK dollar mayeither be above or below the target exchange rate. To keep the rate fixed incase of depreciation, the government of Hong Kong has different options. Oneway is for the government to carry out an exchange market intervention, buyingits own currency on the FX market, thus, soaking up the surplus of its own
4
currency. This requires the government of Hong Kong to have an FX reserve ofUS dollars to exchange for HK dollars. If the exchange rate is above the targetlevel the government can use the same principle in the reverse direction, sellingHK dollars and buying US dollars. [Krugman & Wells, 2013]
In contrast, a floating exchange rate is when the government lets the marketforces set the exchange rate based on supply and demand. A majority of thecountries in the world employ a floating exchange rate regime.
2.1.2 Nominal exchange rate (NER)
The nominal exchange rate is the price of a currency in terms of another cur-rency, and is the rate that is usually displayed at currency exchanges. Theyare often quoted in the form of currency pairs. For example, the quotationEUR/USD 1.36 means that 1 euro will buy 1.36 US dollars and 1.36 will thusbe the nominal rate from the dollar holder’s perspective, while being 0.735 fromthe euro holder’s perspective. An exchange rate has a base currency and acounter currency. In our example, the euro is the base currency and the USdollar is the counter currency.
2.1.3 Real exchange rate (RER)
The nominal exchange rate does not necessarily paint the whole picture. Itmight be of interest to know what can be bought with a certain currency, whichis where the real exchange rate comes in. It tries to measure the value of acountry’s goods against those of another country, or a set of countries, at thecurrent nominal exchange rate. In general, the RER between two countries isdefined as the product of the nominal exchange rate multiplied and the ratio ofprices between the countries. The prices are measured by using a broad basketof goods. These baskets take the form of the indices of the aggregate price levelsin the countries being compared - such as the consumer price index - makingthe RER an index number that can be benchmarked through time. The formulafor the RER is as follows,
RER = ePYPX
(1)
where e is the exchange rate of currency X in currency Y . PY and PX are theindices of the aggregate price levels in each country. [Krugman & Wells, 2013]
However, researchers, policymakers and economists are normally more inter-ested in the real effective exchange rate (REER). The REER is the averageof the bilateral RER:s between the country and the countries it trades with. It isweighted by the respective trade shares of each trading country. The REER of acountry can be in equilibrium even though being overvalued compared to sometrading partners, as long as it is undervalued relative to others. The REER canbe used in assessing whether a currency is misvalued, and if so by how much.
5
This is done by analysing the REER series over time. If the exchange rates arein equilibrium the REERs should be unchanged over time.
However, fluctuations in the REER does not necessarily imply an underlyingmisalignment. This is due to consumption patterns, cost for transportation,trade policies and tariffs having the ability to change faster than the marketbaskets that economists construct. Therefore, not all large REER deviationsshould be interpreted as misalignments, but at the same time, not all deviationsthat are not misalignment’s can be attributed to the above-mentioned factors.Indeed, some REER adjustments are especially smooth, indicating that otherfactors may be at play. Some of these, especially in higher-productivity coun-tries, can be derived from technological progress which leads to lower productioncosts on tradables, and thus, lower prices. The international competition leadsto lower international prices on said tradables. Yet, theory and data support thenotion that the main part of REER variations is due to fluctuations in the pricesof non-tradables relative to those of tradables. This is particularly common indeveloping countries. [Catao, 2007]
2.1.4 Overshooting
Overshooting is a term used to describe why exchange rates, in most cases,are more volatile than expected. The phenomenon, called the Dornbusch Over-shooting Model, is named after Rudi Dornbusch who introduced the modelin his famous paper ”Expectations and Exchange Rate Dynamics”, in 1976.The model argues that exchange rates will temporarily overreact to alterationsin monetary policies, in compensation of rigid prices in the economy. Conse-quently, there will be a higher volatility in the exchange rate as a result ofovershooting and the following corrections. [Dornbusch, 1976]
In this thesis, our mathematical model does not account for overshooting. Thisis as our model looks at how changes in commodity prices affect the exchangerate, excluding changes in monetary policies.
2.1.5 Purchasing power parity (PPP)
First formulated during the sixteenth century in Spain by scholars of the Univer-sity of Salamanca, the Purchasing Power Parity (PPP) is closely related to thetheory of the real exchange rate. It states that exchange rates should convergetowards an equilibrium level, such that price levels are equal once converted toa common currency [Rogoff, 1996]. It is used to compare different currencies byusing a broad market basket of goods and services [Krugman & Wells, 2013].The currencies are at par when mentioned market basket of goods is priced thesame after adjusting for the exchange rate.
For the sake of simplicity, it will be demonstrated in terms of a single prod-uct - the Big Mac sold by McDonald’s Corporation. The Big Mac is a good
6
example since it is widely available in many countries and almost identical re-gardless of which McDonald’s restaurant in the world you order it from. If thereal exchange rate was equal to 1 the price would be the same in the US asin France if sold on the same market. That would be the case if, in using thequotation used before, a Big Mac would cost $1.36 in the US and 1 euro inFrance. However, if the price of the Big Mac would be higher than 1 euro inFrance it would suggest that the euro was overvalued, putting pressure on themarket and the nominal exchange rate to adjust. This is due to there being anopportunity to exchange euros to dollars in order to buy Big Macs in the US andselling them in France, much according to the law of one price. In practice, it isprobably not much to gain in importing or exporting Big Macs, the same can-not be said about tradable commodities, and some of the ingredients in the BigMac can be regarded as such. Furthermore, although there exist many majorobstacles in reality - such as transportation costs, tariffs, trade barriers - curren-cies that diverge in RER face pressure to adapt due to the arbitrage opportunity.
Suppose, for example, that a basket of goods and services that costs $100 inthe United States costs 1,000 pesos in Mexico. Then the purchasing power par-ity is 10 pesos per U.S. dollars: at that exchange rate, 1,000 pesos = $100, sothe market basket costs the same amount in both countries. Calculations ofpurchasing power parities are usually made by estimating the cost of buyingbroad market baskets containing many goods and services — everything fromautomobiles and groceries to housing and telephone calls.
2.1.6 PPP puzzle
The concept of PPP was revived in the during the 1970s. Since then, the theory’svalidity has been highly debated among economists and scholars, making itthe PPP puzzle. Even though the theory claims that any deviations shouldonly be minimal or momentary, empirical work supporting the PPP was weak[Taylor & Taylor, 2004]. Indeed, while few economists view the PPP seriouslyin the short-term, most regard the PPP, or a variant of it, as an anchor forlong-term real exchange rates. This is as real exchange rates go extremelyslowly towards PPP, as deviations from the equilibrium decrease by 15% peryear. The long-term believers argue that there are frictions in the internationaltrade goods market, which as previously mentioned are transportation costs,tariffs, etc. [Rogoff, 1996].
2.1.7 Factors influencing the exchange rate
Inflation and interest rates are two important factors that can both appre-ciate and depreciate the exchange rate. The two factors work hand in hand, ascentral banks use the interest rate to steer inflation. High interest rates usuallyattract foreign investment, which leads to an increased demand for a country’scurrency (and an increased exchange rate). Nonetheless, central banks are care-ful as high interest rates raises inflation, which appreciates the currency. On the
7
other hand, low interest rates boost economic growth and consumer spending,although it does not attract foreign investments. Hence, inflation and interestrates are difficult to manage, while having a great influence on a country’s cur-rency. [Krugman & Wells, 2013]
In order to afford financing of public sector projects and governmental fund-ing, countries usually take on debt. Public debt may stimulate the domesticeconomy, however, large public deficits make countries less attractive to foreigninvestments. This is due to the fact that debt stimulates inflation, thus de-preciating the real exchange rate. Consequently, a high inflation will make itdifficult for the country to pay off their debt with their cheaper real currency.[Beningo & Lopez-Salido, 2004]
Terms of trade is another explanation for a rise in the exchange rate. It is theratio of a country’s import and its export. Essentially, it measures how much aneconomy can import per unit of exported goods. A banal exemplification wouldbe if a country were to only export oil, while also only importing wheat. Theterms of trade would simply be the price of oil divided by the price of wheat[Reinsdorf, 2009]. An appreciation in the prices of exported goods would in-crease the country’s terms of trade, while a rise in the prices of imported goodswould lower it. Research conducted by Coudert et al [2008] confirmed the linkbetween the REER and the commodity terms of trade. In the long run, theprice elasticity between the two terms was found to be 0.5. In simpler terms, a10% appreciation in terms of trade implies a 5% rise of the REER.
Political stability is an important factor that investors seek in a currency.A country with such stability will draw investments away from countries thatare in a less optimal situation. Political turmoil, elections and other politicalsituations can cause a movement of capital to more stable currencies.
2.2 Commodity Pricing
Whether if it is the manufacturing industry or the service industries, commodi-ties are omnipresent. Commodities are essential for the entire economy as awhole. Therefore, it is important to understand the characteristics of a com-modity and its pricing.
2.2.1 Supply and demand
According to basic microeconomic theory, supply and demand are the two fac-tors that determine the price. A decrease in demand or increase in supply lowersthe price of the commodity. Vice versa, an increase in demand or decrease insupply raises the price [Krugman & Wells, 2013]. The supply and demand of aproduct can be changed by various different factors. The finding of a new sourceof the resource would alter the supply, while the demand would be affected if asubstitute product emerges.
8
Economists attempt to predict commodity price movements by looking at lead-ing indicators. Interest rates and inflation are leading economic indicators,and are commonly used to predict movements. Within commodity pricing,potential leading indicators would be investments, government spending, con-sumption and net exports [Krugman & Wells, 2013]. However, what differs acommodity currency from the rest is the impact that the commodities have onthe currency, which lessens the impact of the other economic factors.
2.3 Commodity Currencies
Firstly, it is worth mentioning that there is no precise definition of a commoditycurrency. Currently, the definition of a commodity currency is when a country’sexport is heavily dependent on one or more commodities. In other words, thereis no set percentage of the country’s export that has to consist of commodities forit to be defined as a commodity currency. The currencies are most common indeveloping countries, although they do also exist in developed nations. Chen andRogoff [2002] studied the commodity currencies of three developed countries:Canada, Australia and New Zealand. The results showed that commodity priceshad a strong influence on the REER. However, the impact of the commoditywas less for the Canadian dollar, as Canada’s export was more diversified thanthe other two countries.
2.3.1 Commodity currencies through PPP
As mentioned in the section PPP Puzzle, there has been an ambiguity regardingthe PPP. In 1976, Professor Dornbusch’s overshooting model showed clearly thatinflation and monetary instability could not explain the entire truth of the per-sistent exchange rate volatility. The standard monetary models failed to graspthe whole situation, as they were unable to explain the slow rate at which devia-tions from the PPP seemed to die out, even though the real exchange rates werevolatile. In essence, shocks in taste, technology or other similar factors could notaccount for the short-term fluctuations in exchange rates. Thereupon, Rogofffound a potential solution to the PPP puzzle by examining commodity curren-cies. Commodities could provide a shock that is both volatile, persistent andreoccurring. [Chen & Rogoff, 2002]
In 2002, Chen and Rogoff claimed that their univariate regressions suggestedthat the missing shock was the volatile commodity prices. By examining threecommodity-exporting developed countries, they could identify that commoditiesexplained a significant contribution to the PPP puzzle. However, the introduc-tion of commodities did not resuscitate the monetary approach to the exchangerate, despite being a dependable explanatory factor. Consequently, a year later,Cashin et al proved the same result in a third of the 58 countries they examined.[Cashin et al. , 2003]
9
Bjørnland and Hungnes examined the PPP puzzle and introduced an interestrate differential in their calculations. They noticed that the differential causedthe correlation between commodities and currencies to decrease, which was tobe expected. However, they detected that adjustments to shocks from the equi-librium took maximum a year on average, which argues for the validity of PPP[Bjørnland & Hungnes, 2005]. Consequently, they argue that the puzzle hasbeen solved for the commodity currency, if taking the interest rate into account.
2.3.2 Consequences of a commodity currency
The consequences of a commodity currency are that if the commodity experi-ences a decline in price, the income from exporting that commodity decreasesalong with the price. Hence, the dependence of a single commodity bears heavyrisk. Canada and its reliance on oil is a great example. During 2015, oil prices fell38%, resulting in the Canadian oil industry to post losses of 11 billion Canadiandollars. In 2016, the same trend continued [Murillo, 2016]. As the oil pricesdipped below 30 USD per barrel in 2016, Bank of Canada governor StephenPoloz stated that the drop in oil prices have caused a 50 billion Canadian dollarcut to Canada’s national income. This equates to $1500 a year per capita forthe nation [Kirby et al. , 2016]. Another consequence of having a commoditycurrency could be the Dutch disease.
2.4 Dutch Disease
The Dutch disease is an economic phenomenon first described by economists W.Max Corden and J. Peter Neary in 1982, published in the Economic Journal.The phenomenon describes the negative effects that follow a large increase in thevalue of the country’s natural resources, which causes a decline in other partsof the economy. It affects three sectors: the non-tradable sector, the boom-ing (tradable) sector, and the lagging sector. The non-tradable sector includesservices (i.e. labour), while the booming sector represents the newly-found ex-traction of natural resources (oil, gold, diamonds, etc). The lagging sector isusually a reference to manufacturing or agriculture, in other words, industrieswith heavy use of labour. [Corden & Neary, 1982]
Initially, the Dutch disease begins with a new found source of natural resourcesor increases in commodity prices, which causes the revenues of the boomingsector to increase rapidly. Consequently, the real exchange rate of the countryappreciates. This appreciation of the exchange rate impedes other sectors, astheir exports become more expensive for other countries to buy. Also, importsfor these sectors become cheaper, resulting in those sectors being less competi-tive. This is in line with what we described for a commodity currency.
What the Dutch disease specifically addresses is that a resource boom has twomain consequences for the non-tradable sector. Firstly, the resource boom in-creases demand for labour, causing production to shift from the lagging to the
10
booming sector. This alteration is called direct-deindustrialization.
The second development is called the indirect-deindustrialization, or the ”spend-ing effect”. It is a result of the extra revenue gained by the resource sector, whichraises demand for labour in the non-tradable sector at the expense of the lag-ging sector. The increased demand within the non-tradable sector raises theprices within non-tradables. However, the prices in the tradable sector are un-changed, as they are set on the international market. This causes the REER toappreciate. The indirect-deindustrialization occurs if there is no labour mobilitybetween sectors, as it obstructs the alteration in the supply of services to shiftin demand. Hence, if such a mobility exists it allows the supply of services toadjust. Consequently, workers can move between sectors, which forces all sec-tors to increase wages. As previously mentioned, the result is that the tradablesector can not raise their prices to mitigate the pay rise, resulting in a declinein manufacturing output and employment. [Corden & Neary, 1982]
2.4.1 Historical events
In 1959, large gas reserves were discovered in the Netherlands, causing Dutchexports to soar. As per the definition of the disease, the booming sector thrivedwhile another sector lagged. Moreover, between 1970 to 1977, there was a risein unemployment from 1.1% to 5.1% and corporate investment was crashing.The sudden boom of gas exports raised the value of the Dutch currency, makingother sectors less attractive on international markets. Moreover, the gas extrac-tion industry generated few jobs, while also being a capital-intensive sector. Tohinder the Dutch currency from appreciating rapidly, the Dutch central bankimplemented low interest rates. In turn, this removed future economic potentialin the country as investments vanished. [Kiev, 2014]
In modern time, there have been several cases of potential Dutch diseases. Mostof the cases involve developing countries, such as Burundi, Tanzania and PapuaNew Guinea. More renown cases of the Dutch disease in developed countrieswould be the rise of oil prices in 2014 and the impact on Canada. The risein the price of the commodity, as Canada exploited their oil sands, led to anovervalued Canadian dollar. Consequently, this lowered competitiveness in themanufacturing sector. [Tencer, 2014]
2.4.2 Consequences
The consequences of the Dutch diseases are similarly considered to have a greatimpact on a country’s economy. To continue on the case of the appreciation ofoil prices and Canada, the consequences were a profitable oil extraction methodand a contracted manufacturing sector [Beine et al. , 2012]. However, it is no-table that the oil price fall in 2015-2016 eased the concerns of Dutch diseasein Canada. This ease was at the expense of the Canadian economy, as theCanadian export income lost $50 billion dollars. Hence, it is not entirely clear
11
whether which consequence has the greatest impact.
Overborrowing is a potential effect of the Dutch disease. A prosperity ofresources along with high commodity prices can allow countries to use theirresources to borrow capital to finance large investments. However, when pricesplunge, countries are left with huge unsustainable debts while their resource haslost in value.
Volatility is usually high for commodities, as the supply elasticity for theseresources usually are low. In turn, if the commodities’ volatility is low and agreat portion of the export income derives from commodity exports, it will drivethe volatility of the real exchange rate. Empirical work has shown that there isa detrimental impact on economic performance. [Loayza et al. , 2007]
Lastly, declined GDP growth is caused by the abundance of resources. Stud-ies by Sachs and Warner [2001] show that a finding of natural resources has anegative impact on GDP growth. They state that a 10% increase in the ratioof national resources to GDP can lower the GDP growth by 0.4-0.7%. Addi-tionally, they found that it reduced manufacturing export growth. However,Lederman and Xu [2015] argue that these findings are not entirely conclusive asthey do not take all factors into consideration. They claim that the the findingsdo not have grounded economic theory to back their measure of natural resourceabundance. Instead, Lederman and Xu used another approach by examiningthe net exports of natural resources per worker, and could thus find a positiveeffect on growth.
2.4.3 Other theories
There are theories that conflict with the Dutch disease. The main contradic-tory theory would be the Balassa-Samuelson (B-S) hypothesis which is an-other explanation for the appreciation of the REER. The effect tends to occurin developing economies, as they begin using their land, labour and capital ina more efficient manner. A rise in productivity gives way to wage growth inboth the tradable goods and the non-tradable goods sectors. This wage rise al-lows citizens to consume more goods and services, which in turn push up pricesand consequently inflation. According to the B-S hypothesis, high productiv-ity growth in the tradable sector relative to the non-tradable sector causes anappreciation of the REER, due to increased inflation. The larger the differ-ence in productivity growth between the sectors, the faster the REER rises.[Druzic & Tica, 2006]
These theories are viable, as it can be difficult to identify a lagging sectorwith the Dutch disease, and as there could be various other factors causingthe lagging sector to decline.
12
2.4.4 Mitigation of the phenomenon
Fiscal policy, i.e. how a government can adjust its tax rates and spending lev-els to influence its nation’s economy, is a way to reduce the impact of the Dutchdisease. Researchers analysed the natural resource boom during the 1970s and1980s, and concluded that spending levels should have been adjusted more cau-tiously to the sharp rises in income [Gelb & Associates, 1988]. The reason whyfiscal policy is an important instrument way to deal with the Dutch diseaseis mainly because it can constrain the spending effect while smoothing expen-ditures to reduce the volatility. Governments can save the revenue abroad insovereign wealth funds and thus reduce aggregate spending. A lot of commoditydependent countries have adopted this fiscal policy, for instance the followingsovereign wealth funds have the purpose of mitigating the Dutch disease: StateOil Fund of Azerbaijan, Stabilization Fund of the Russian Federation, Govern-ment Pension Fund in Norway and the Australian Government Future Fund.However, all countries cannot adopt this policy. Developing countries can not af-ford to keep revenues abroad during a longer time, as factors such as health careand education require funds. The need to allay poverty stands as more impor-tant than any macroeconomic implication. Lastly, within the government’s fiscalpolicy, a strategy to avoid appreciation of the REER is to increase saving in theeconomy. This would decrease large capital inflows which increases the REER.This would be achieved by running a budget surplus. [van Wijnbergen, 2008]
The ”permanent income approach” is an important benchmark for fiscal policy.It can only be applied to expendable resources, and proposes to first calculatethe net present value of the net future revenues from these resources. Then,it proposes to calculate the constant real amount or annuity that received inperpetuity, would yield the same net present value. The method recommendsto restrict government spending using the expendable natural resource revenuesto this annuity, and saving the rest of the revenues overseas. Further downthe road, when the natural resources have run out or depreciated in value, thegovernment is able to withdraw the financial assets and continue spending onthe same annuity level. [van Wijnbergen, 2008]
Another way to curb the Dutch disease is to revise the country’s spending poli-cies. As mentioned, the non-tradable sector declines during the phenomenon.However, by investing funds in the sector, ensures that productivity in the sec-tor improves which is important. Alleviating the pressure from the non-tradablesector could be a structural way to respond to the Dutch disease. Moreover, apolicy that would stimulate demand for imports, which would increase the termsof trade, would diminish demand pressure and also any future implication. In-vestments in transport, logistics, infrastructure and education could mitigatethe adverse effects of a natural resource boom. It could benefit the productivitywhile also help fight poverty. However, as mentioned earlier, it is important toensure that there are enough funds for public projects with the sole purpose ofassuaging poverty in low income countries.
13
3 Mathematical Theory
Regression analysis is used as a statistical tool. The main purpose is to estimatethe relationship between a section of covariates and a dependent variable. Thiswill be explained further in the section.
3.1 Multiple Linear Regression
The definition of a multiple linear regression model is given by:
yi =
k∑j=0
xijβj + ei, i = 1, ..., n, (2)
where yi are observations of the dependent random variable. The value of yidepends on the covariates, xij and the residual or error term ei. The beta’s,βj , also called the coefficients, are the terms to be determined from running theregression. Lastly, there are k explanatory variables and n observations. Themodel can also be written with matrix notation as follows
~Y = X~β + ~e (3)
with the following vectors
~Y =
y1...yn
, ~β =
β0...βk
~e =
e1...en
and the matrix
X =
1 x1,1 ... x1,k1 x2,1 ... x2,k...
.... . .
...1 xn,1 · · · xn,k
[Lang, 2016]
3.2 Ordinary Least Squares
The Ordinary Least Squares (OLS) method is commonly used to conduct amultiple linear regression on a set of a data. The method calculates the valueof α and β from equation 2, by minimizing the sum of the squared residuals.The residuals are squared in order to remove the possibility that positive andnegative residuals cancel each other out. There are some requirements for themethod to be successful, which will be explained further in the subsection below.
14
3.2.1 Key assumptions
In order for the Ordinary Least Squares (OLS) estimator to show relevant re-sults; the following assumptions are made:
1. The dependent variable is a linear function of the covariates and the resid-ual.
2. The expected value of the residual is equal to zero E[ei] = 0.
3. Perfect multicollinearity is nonexistent, as the covariates are linearly in-dependent.
4. The residuals have variance V [ei|X] 6= Iσ2, and are uncorrelated, Cov(ei, ej) =0, for i 6= j.
Under violation of these assumptions, the model would need altering. Themethod of modification will be described in a different subsection in the chapternamed Errors. [Kennedy, 2008]
3.2.2 Lagged variables
In general, regression analysis is considered timeless, as it does not take timeinto account. Further, in regression the dependent y-variable is influenced byprior y-values. This can be overcome by using lagged dependent variables. Theaim of lagged variables is to provide more accurate coefficient estimates. Thesemodels, so-called partial adjustment models, are formulated as following:
Yt = β0 + β1Yt−1 + β2X1t + . . .+ βnXnt + et. (4)
Moreover, independent variables, xi, are possible to lag. However, this oftenincrease the level of difficulty noticeably. Also, the contribution to the modelis only a fraction of the level of difficulty. Another effect that previous studieshave shown is that estimated lagged effects can irritate the bias and lead tofurther collinearity between covariates [McKinnish, 2002].
3.2.3 Interpretation of the coefficents
Ceteris paribus means ”other factors being equal”, and is a key notion in causalanalysis. It is used in order to screen out factors that may influence the relationof interest, by holding all other factors that may influence this relationshipfixed. For example, lets assume one would like to investigate the change ofdemand of a certain good after a price change, while holding all other factorsthat may influence the change of demand fixed. These factors could be income,individual tastes, price of substitute goods, etc. If these factors are not heldfixed, the causal effect of a price change of the goods will be impossible tomeasure. [Kennedy, 2008]
15
3.2.4 Logarithmic transformation of variables
Not all models follow a linear model, thus, requiring a transformation of vari-ables to be implemented. There are various different transformations, such asthe power transformation or the logarithmic transformations. Choosing thecorrect transformation is often difficult since it is hard to know the true modelof the observed values on beforehand. However, in this thesis, the logarithmictransformation was used.
Regarding the logarithmic transformation, there are three different ways in-volving logarithms: the log-linear, linear-log and log-log model. This thesisuses the log-linear transformation, i.e.
log(yi) = xiβi + ei (5)
The logarithmic transformation is used when there exists a non-linear relation-ship between the dependent and independent variables. Also, the transforma-tion can be used when dealing with a highly skewed variable that has to betransformed into a more appropriate one. Also, logarithmic transformationshave a variance reducing effect. [Aneuryn-Evans & Deaton, 1980]
3.3 Time Series Regression
The cross-sectional data described above differs from time series data. The mostobvious difference is temporal ordering, which means that one must recognizethat the past can affect the future, but the future cannot affect the past. Thus,time series data can be of great use, as this is how the stochastic process of acommodity’s price fluctuates. However, one has to be cautious when conductingthe time series regression. The correlation between the independent and depen-dent variable can distort the OLS large sample properties. [Woolridge, 2009]
There are six assumptions for time series regression, namely:
1 Linear in parametersThis implies that the stochastic process (xt1, ..., xtk, yt): t = 1, 2, ... , nfollows the linear model:
yt = β0 + β1xt1 + ...βkxtk + ut (6)
where ut is the term of error. n represents the number of observations.
2 No perfect collinearityNo covariate is constant, or a perfect linear combination of the othercovariates.
3 Zero conditional meanAt each t, the expected value of ut, given that all the explanatory variablesfor all time periods are available, is equal to zero.
E[ut|X] = 0, t = 0, 1, 2, ..., n (7)
16
4 No serial correlationThe errors at two different times are uncorrelated, conditioned on X.
Corr[ut, us|X] = 0 (8)
5 HomoscedacityConditional on X, the variance ut is the same for all times t.
V ar[ut|X] = σ2, t = 1, 2, ..., n (9)
6 NormalityThe errors ut are independent of X and identical and independently dis-tributed random variables with a normal distribution with mean 0 andvariance σ2.
3.3.1 Similarity measure
To study the linear relationship between two time series and the sample cor-relation, equation (31), can be used. An alternative measure of the similaritybetween two time series is based on the Euclidean metric, defined as follows,
DXY =1
T
T∑t=1
(xt − yt)2 (10)
By expanding the square on the right hand side, familiar quantities can beextracted from the compact form in equation (10)
DXY =1
T
T∑t=1
(xt − yt)2
=1
T
T∑t=1
[(xt − x)− (yt − y) + (x− y)]2
=1
T
T∑t=1
(xt − x)2 +1
T
T∑t=1
(yt − y)2
+ (x− y)2 − 2
T
T∑t=1
(xt − x)(yt − y)
(11)
where x and y are the sample means of the respective series. The two firstterms are the sample variance of each series, while the last is sample covariance(compare to equation (31)). Dividing both sides of the equation with the squareroot of the sample variance turns the third term into equation (32). Comparedto the simple cross-correlation, this measure also takes the variance of each seriesinto account, as well as the difference in their means. Note that the measurein equation (10) is sensitive to the scaling of the variables but can be madeinvariant by using a modified measure, calculated using the terms on the righthand side equation (11), divided by the appropriate terms.
17
3.3.2 The Autoregressive model
The AR(p) model is defined as
Xt = c+
p∑i=1
φiXt−i + εt (12)
where c is a constant, φ1, . . . , φp are the parameters of the model and εt isa zero-mean white noise process. The simplest instance of this process is theAR(1) process, given by
Xt = c+ φXt−1 + εt (13)
For this process, the mean and variance are given by
E(Xt) =c
1− φ, V ar(Xt) =
σ2ε
1− φ2(14)
In particular, if c = 0 then the mean of the process is zero. The autocovarianceof the AR(1) process is given by
Cov(Xt+h, Xt) =σ2ε
1− φ2φ|h| (15)
From the expression for the variance in equation (14), the autocorrelation iseasily obtained as
Corr(Xt+h, Xt) =Cov(Xt+h, Xt)
V ar(Xt)= φ|h| (16)
The parameters of the model can be estimated using OLS.
3.4 Validating the Model
The validation of a model is necessary before it can be used. The methodof validating a model is by using statistical tests and theories, which will bedescribed in the subsections below.
3.4.1 Hypothesis testing
Hypothesis testing is used to study a set of parameters, allowing conclusions tobe made. There are three steps in testing a hypothesis. [Uriel, 2013].
1. Formulate a null hypothesis H0 specifying a value to βj , and an alternativehypothesis H1.
2. Compose a test statistic with a known distribution under the assumptionthat H0 is valid.
3. From this test statistic, rule whether to reject H0 or not.
18
3.4.2 F-test statistics and t-test
The F-test is suited for more rigid models. It tests model relevance of severalcoefficients at once, in other words the hypotheses:
H0: βi = 0 for i > 1H1: βi 6= 0 for i > 1
The following expression is the F-variable and its distribution.
F =n− k − 1
r
( |e∗|2|e|2
− 1)∈ F(r, n− k − 1). (17)
The null hypothesis, H0 is rejected if F is larger than the distribution on theright hand side of equation 17, proving that the model is significant. Further, erepresents the residual from the unrestricted model. e∗ symbolizes the residualfrom the restricted model, where r is the amount of β:s that are set to be equalto zero. n is the amount of observations while k represents the amount of pa-rameters in the model. [Lang, 2016, p.10]
An alternative method to the F-test, is the t-test that is relevant when thereis only a single restriction to the model. Also, it tests whether the β-value issignificant. In the same null hypothesis as mentioned above, the test statisticshould follow a t-distribution. The t-distribution can be seen as the following:
t =βi − βiSE(βi)
∼ tn−k, (18)
βi represents the estimation of one of the covariates. βi is a constant, whileSE(βi) is the sampled standard error of βi. The t is t-distributed with n−k−1degrees of freedom.
3.4.3 p-value
The before-mentioned F-test is essential in generating the p-value, that is givenby:
p = Pr(F > X), (19)
X is a F (r, n− k − 1) distributed random variable, while F is the test statistic.The null hypothesis is accepted if the p-value is greater than the predeterminedsignificance level α. [Lang, 2016, p.10] In this thesis, α = 5% will be used asthe significance level.
19
3.4.4 R2 and Adjusted R2
The coefficient of determination, i.e. R2, measures the ”goodness of fit” meaninghow well the model fits the data points. R2 has a range between [0, 1], wherevalue 1 implies that the model can to 100 per cent explain the variability of theobservations around the mean. The formula for R2 is the following:
R2 = 1−∑i(yi − yi)2∑i(yi − y)2
. (20)
The adjusted R2 takes into account the downside of the regular R2. This down-side is that R2 increases when adding more dependent variables, regardless ifthey have any explanatory power [Lang, 2016, p.8-9]. In the equation below, itis visible that the adjusted R2 is altered by the degree of freedoms, resulting ina lower value than the ordinary R2.
R2 = 1− n− 1
n− k − 1·
∑i
(yi − yi)2∑i
(yi − yi)2(21)
3.4.5 Akaike Information Criterion
An information criterion can be used when choosing between similar models.The Akaike Information Criterion test (AIC) is a widely adopted tool, whichuses the equation below. [Lang, 2016, p.22]
− 2 ∗ ln(L) + 2k (22)
In the equation above, k represents the amount of covariates, the residualsand n the sample size. L is the maximized value of the likelihood function.[Lang, 2016]. The AIC allows us to perform model selection, by comparing thecalculated AIC value for the proposed model. The best model, in the sense thatit minimises the information loss relative to the true data-generating model, isthe one with the smallest value for the AIC. As the true model is not known,the AIC is an estimate of the information loss.
3.5 Errors
The estimator will give inconsistent results if the key assumptions of the Ordi-nary Least Squares (OLS) model are breached. Consequently, the model wouldneed altering. This section will present the different kinds of violation, alongwith different methods of reducing their effect.
20
3.5.1 Heteroscedasticity
Homoscedaticity is one of the key assumptions of the OLS, and heteroscedaticityviolates it. It occurs when the residuals do not have constant variance, i.e.
V ar(ei) = σ2i , (23)
Under this violation, the error term is heteroscedastic and requires modificationin order to fulfill the assumption of homoscedaticity. Otherwise the standarddeviations of the coefficient estimates will be incompatible, rendering the F-testinvalid. This would result in inconsistent estimates. [Lang, 2016, p.16]
Different techniques to mitigate heteroscedaticity will be presented below.
Reformulate the ModelThe best way to remove heteroscedacity is by reformulating the model. Thiscan either by done by adding covariates or transforming the variables in themodel. This thesis looks at specific covariates’ correlation with the dependentvariable, and utilizes transformation of variables.
Breusch-Pagan testThe Breusch-Pagan test is used to test for conditional heteroscedaticity. Themethod involves testing if the estimated variance V ar(e) is dependent of the co-variates in the model. If the estimated variance is dependent on the covariates,the model is heteroscedastic.
As previously mentioned, an assumption for homoscedaticity is that E[e2i ] =σ2i , which implies that the variance is not dependent on the covariates. In order
to conduct the Breusch-Pagan test, the variance of the model is needed, whichcan be obtained by taking the average of all squared terms of error e2. Further,a regression is conducted on e2 as a dependent variable with the covariate X.
e2 = βX + u (24)
where u is the model’s term of error. Moving on, one can test H0 (homoscedas-tic model) against H1 (heteroscedastic model) with use of a F-test. If the F-testcan prove that the variables are jointly significant, then one can reject H0, prov-ing that the model is homoscedastic. [Woolridge, 2009]
Residual vs FittedA useful method to identify heteroscedaticity is by using plots. The plot iscomposed by seeing how residuals on the y-axis fit along with the estimatedresponses on the opposite axis. If the points are in the vicinity of the zero line,it proves homoscedastic data.
21
White’s consistent variance estimator
Cov[β] = (XtX)−1XtD(ei2)X(XtX)−1 (25)
whereD(ei2) is a diagonal nxn-matrix with the diagonal elements ei, i = 1, 2, . . . , n.
When employing White’s method, the standard errors are estimated from theequation above, and the regression is still implemented using the OLS method.The standard error of the i:th diagonal element can be written as:√
Cov[β] =√
(XtX)−1s2 (26)
where s2 = |e2|n−k−1 [White, 1980]
3.5.2 Multicollinearity
Multicollinearity results in difficulties in identifying the effects of the explana-tory variables on the dependent variable. This issue emerges when two or morecovariates are approximately linearly dependent. Furthermore, the variances ofthe regression coefficients are contrasting large under multicollinearity, whichresults in incorrect estimate points.
To avoid this error, the covariates have to be selected carefully. For exam-ple, including dummy variables for all conceivable cases can naturally lead tolinear dependence causing multicollinearity. As multicollinearity causes highvariances of regression coefficients, a method to identify this error is by inves-tigating covariates variances. A commonly used method is by examining theVariance Inflation Factor (VIF). It is defined as:
V IF =1
1−R2i
(27)
This factor displays how much the variance of the i:th covariate has increasedas a result of multicollinearity. A VIF > 10 indicates that multicollinearity isevident. [Lang, 2016, p.55]
However, there are ways to compensate for large VIF values. One way to reducethis variance is by gathering additional data for the regression, as this results ina decreased variance. This is as the standard error of the coefficients dependson the amount of observations, seen in the following formula.
SE(βi) =
√σ2
(n− 1)V (xi)· 1√
1−R2i
, (28)
22
3.5.3 Endogenity
Endogeneity emerges if the residual is correlated with one or more of the co-variates. The key assumption that the expected value of the error term is equalto zero is thus breached, causing the OLS estimator to emit inconsistent values.This subsection will go through common causes of this error.
SimultaneityThe emergence of simultaneity is caused when a covariate is affected by thedependent variable, while also influencing the dependent variable. This is acommon problem in demand and supply models.
Missing relevant covariatesThe exclusion of a relevant covariate leads to the effect being transferred to theresidual instead. This causes endogeneity, since the residual is correlated withone (or more) of the previously included covariates. Hence, it is highly impor-tant to select as many compatible covariates as possible, before performing theregression.
Sample selection biasSample selection bias arises when the sample of data is not randomly selected.Consequently, the residual explains an attribute that is not considered in theregression model.
Measurement errorsMeasurement errors is the difference between the actual results and the mea-sured ones. This causes endogeneity as the covariates are incorrect, resultingin making the independent variables stochastic. Subsequently, the independentvariables become correlated with the residual. [Lang, 2016]
3.5.4 Normality
Plots are useful to examine if residuals meet the normality assumption, ex-plained in section Plots and tests are useful tools to evaluate if residuals inregression models meet the normality assumption explained under section Keyassumptions. This thesis will use Quantile-quantile plots (Q-Q) to assess ifresiduals are normally distributed.
Quantile-Quantile plots
By plotting the quantiles of the two variables x and y, it is visible to see if thetwo variables come from an identical distribution. The plot will follow a straightline with slope 1 if they have identical distribution. Furthermore, it is possibleto identify if y is a linear function of the predictor variable x, as the plottedvalues follow a straight line.
23
A good estimate of the regression model is essential for the Q-Q plot to beaccurate. The Q-Q plot is also useful for identifying outliers, skewness, heavytails and bimodality [Gnanadesikan & Wilk, 1968]. Since normality is a keyassumption for the OLS, it is of extreme importance that the OLS-estimatorproduces valid estimates.
3.5.5 Autocorrelation and cross-correlation
Autocorrelation implies that adjacent observations are correlated, meaning thatthe values at different times are co-dependent. Autocorrelation is typically un-desirable, as it means that the computation of correlations between data pointsis done adequately.
The auto-correlation of a stochastic process is the correlation between valuesat different times. Thus the function contains two different points in time, t ands. Then, Xt is the output value by the process at time t. The definition of theautocorrelation between time t and s is then:
R(s, t) =E[(Xt − µt)(Xs − µs)]
σtσs(29)
where µX and σX are stationary values of the mean and standard deviation ofthe process Xt.
The cross-correlation function is used to find the lag where the overlap be-tween two functions is the greatest. The function is as follows:
ρXY (τ) =E[(Xt − µX)(Yt+τ − µY )]
σXσY(30)
where the values µX and σX are same values as in the equation above. Theprocess Yt has the same characteristics as Xt.
The sample cross covariance function is a calculation of the covariance betweentwo different time series, xt and yt at the different lags k = 0,±1,±2, .... Thiscalculation is done by estimating the cross covariance at the different lags using:
cxy(k) =
{1T
∑T−kt=1 (xt − x)(yt+k − x), k = 0, 1, 2, ...
1T
∑T−kt=1 (yt − y)(xt+k − x), k = 0,−1,−2, ...
(31)
where x and y are the sample means of the time series. The sample cross-correlation is now obtained from equation (31) by dividing with the square rootof the sample variances,
rxy(k) =cxy(k)√
cxx(0)√cyy(0)
, k = 0,±1,±2... (32)
24
Durbin-Watson test
Durbin-Watson is a commonly used method to test for autocorrelation. Thetest statistics is as follows:
d =
∑Tt=2(et − et−1)2∑T
t=1 e2t
, (33)
In the formula above,t is the time of the observation, while T is the number ofobservations. et is the residual of the observation at time t. The parameter dranges between [0, 4], where a value d = 2 entails no autocorrelation. When dlies between zero and one, it implies a positive autocorrelation. Meanwhile, avalue between three and four suggests a negative autocorrelation. In general, ad-value > 2 could result in an underestimation of the relevance of a covariate.[Durbin & Watson, 1951].
3.5.6 Spurious regression
Imagine a scenario where the regression of y on x proves to be a significant rela-tionship. However, after introducing another dependent variable z, the partialeffect of x on y diminishes to zero. This is the so-called spurious regression,which is a term that describes a scenario where two variables are correlatedthrough a third variable. To exemplify this, the following simple regression isused:
yt = β0 + β1xt (34)
which outputs an acceptable value of R-squared and t statistic for β1. However,Granger and Newbold [1974] proved through simulation that even though xt andyt are independent, the regression of yt on xt outputs a significant t-statistic amajority of the time, that is a lot higher than the nominal significance level.Hence, they named this the spurious regression problem, where there is no sensein the relationship between y and x, despite an OLS regression indicating therelationship. [Woolridge, 2009]
In statistics, a unit root is a phenomenon within stochastic processes. Itcan cause statistical interference in time series models. Also, it is a method ofidentifying a case of spurious regression. A unit root value of 1 implies that thelinear stochastic process is the root of the process’ characteristic function. Ifa unit root exists, then the process is a non-stationary time series. There arevarious tests to find a unit root, and in this thesis the Dickey-Fuller test wasused. [Woolridge, 2009]
The Dickey-Fuller test examines two hypotheses. H0 is that the stochasticprocess has a unit root, while H1 states that the process is stationary. Considerthe autoregressive model:
∆yt = (θ − 1)yt−1 + εt = πyt−1 + εt (35)
25
where yt is the independent variable, t is the time, θ is a coefficient and ε is theerror term. A unit root is present if θ is equal to one, or in the latter stage ofthe expression if π is equal to zero. This is as π = θ - 1. When π is less thanzero, it is a stable autoregressive process, which implies that is asymptoticallyuncorrelated or weakly dependent. A value of π greater than zero is uncommon,as it means that the process is explosive. Thus, the method tests
H0: π = 0 against H1: π < 0
The Dickey-Fuller test then checks the t-test of H0, i.e.
τ =θ − 1
s.e.(θ)=
π
s.e.(π)(36)
It is worth noting that the distribution only holds if the errors εt are inde-pendent and identically distributed random variables. [Woolridge, 2009]
26
4 Method
This section will thoroughly describe the method used to study the problem andanswer the research questions of the thesis.
4.1 Data Collection
The data used to examine the relationship between the nominal exchange rateand commodity prices has been obtained from The Federal Reserve Bank of St.Louis’ database, FRED, the Bank for International Settlements, and ThomsonReuters Eikon. They consist of daily market closing price values. Spot priceswere used for the commodities. The commodity prices and the nominal exchangerate extend from January 2nd 2009 to December 30th 2016, excluding weekendsand on days when the market was closed, totaling a number of 2086 observations.Figure 1 below shows a plot of all of the data. Data for earlier periods of timewere not found for all the commodities.
2009 2010 2011 2012 2013 2014 2015 2016 2017
Date
0
0.5
1
1.5
2
2.5
3Exchange rate and Commodity indices
USDAUD
Gold
Crude oil
Natural Gas
Iron
Figure 1: Plots of the AUDUSD exchange rate and the exported commodities. Thecurves show the USD price per relevant unit of each data series (see appendix for units),scaled by the first value of the data series. That is, all series are divided by their valueat 2016-01-02, the start of the data series. Some of the major economic events thatoccured during the period of data can be found in table 22. Note that the exchange rateis usually quoted as AUDUSD, meaning the AUD price of 1 USD. Inverting this valuegives the USD price of 1 AUD and this is what is shown in the graph.
27
4.2 Literature Study
Prior to writing the theoretical sections Theoretical Background and Mathemat-ical Theory, a comprehensive examination of the literature was conducted. Adeeper understanding within the economical background was attained by usingkey words such as ”commodity currency”, ”real exchange rate”, ”purchasingpower parity”, ”Dutch disease”, ”econometrics” and ”time series regression”when searching for previous studies and relevant literature. Google Scholarand KTH library’s search function were used to find previous research withinthe topic. To ensure validity of our sources, only well-cited and peer-reviewedsources were selected. Also, primary sources were always preferred. Addi-tionally, Krugman’s and Well’s Economics [2013] was used as support for themacroeconomic theory.
Harald Lang’s Elements of Regression Analysis was used as base for the math-ematical theory, together with literature from the class in regression analysis(both KTH and NUS) and Introductory Econometrics - A Modern Approach byJeffrey Woolridge.
4.3 Choice of Country
Before choosing the country of study, some selection criterias were developed.The country must be a primary commodity producer, were primary means rawor minimally processed material, with commodity export constituting a largeshare of the total GDP. The country also needs to be an industrialized economyand an active participant in the global commodity markets. In addition, thecountry must have had a floating exchange rate regime, preferably for a longerperiod of time. Lastly, the currency of the country must be heavily tradedagainst the USD, as a highly liquid and stable foreign exchange market is cen-tral for a short-term trading strategy. A country that satisfies these criteria isa good candidate for a commodity based foreign exchange trading strategy, asthe effect of other non-economic variables on the export and exchange rate areminimized.
Australia is such a country, with primary commodities constituting more than60% of total exports [OEC, 2015], as it is one of the largest exporters among theindustrialized nations [CIA, 2017]. The four chosen commodities (gold, crudeoil, natural gas and iron) all constitute a large share of Australia’s total com-modity export. Despite being a large producer, Australia still holds only asmall share of the global commodity export. This also holds true for other com-modity exporting nations due to the large number of producers on the marketfor many of the world’s most heavily traded commodities. The world’s com-modity producers are all price takers, meaning that domestic events affectingcommodity production, generally, do not impact world markets. Some domesticevents might be driven by global macroeconomic events, but these affect otherproducers and consequently global markets. Furthermore, some producers form
28
organizations, of which the most famous is OPEC [OPEC, 2017], in order to co-ordinate commodity production to the benefit of the producers. However, com-modity producing countries generally do not hold the power to single-handedlyalter global prices, and this holds true for the Australian commodity export.Furthermore, Australia has had floating exchange rates ever since the collapseof the Bretton Woods system in the 1970s, with limited central bank interven-tion under the period of study [RBA, 2017].
The mathematical consequence of the factors mentioned in the previous sectionis that changes in the global commodity prices are exogeneous to the AUDUSDexchange rate. That is, changes in global commodity prices are not caused bythe Australian economy, for which the AUDUSD serves as proxy for. However,how the AUDUSD is affected by changes in global commodity prices is exactlythe problem under study in this thesis.
4.4 The Regression Model
The aim of the research project is to study if there is a consistent and traceablerelationship in daily movements of exchange rates and commodity prices. Asmentioned earlier, commodity prices are exogenous to changes in the AUDUSDand it is possible that changes in commodity prices affect the exchange rate,even on a daily basis. Fluctuations in commodity prices may produce, for ex-ample speculators to detect a rise in the commodity prices and take a positionin the exchange rate based on this. As the time aspect of the mechanism is notknown, the relationship at different lags in time was also studied, to allow for adelayed impact from the commodity on the exchange rate.
The first regression model is given in equation (37) and consists of the loga-rithm of returns on the AUDUSD, regressed on the daily changes in commodityprices,
log(yt/yt−1) = β0 +∑i
βi · (xi,t − xi,t−1) + εt (37)
where yt is the AUDUSD exchange rate at time t, xi,t is the price of commod-ity i at time t and εt is the error term. Studying the logarithm of the returnsis a ubiquitous approach in mathematical finance, partly due to the variance-stabilizing properties of the logarithm.
Using the logarithm also allows for modelling nonlinear relationships betweenthe dependent variable and the covariates. Furthermore, financial time seriesoften exhibit autoregressive behaviour, and unless the series are properly differ-enced, results from regressions might be invalid. Newbold and Granger [1974]illuminated in their influential paper the potential pitfalls of spurious correla-tion and regression using time series integrated of order 1 or higher. A few yearslater, Engle and Granger developed the concept of cointegration, which ”makesregressions involving I(1) variables potentially meaningful” [Woolridge, 2009,
29
p.646]. Briefly, cointegration implies that correlation between two time series isnot spurious, instead there is a relation (also known as Granger causality) be-tween the two. For example, two random walks can show high correlation with-out any real underlying relationship between the two. Newbold and Granger[1974] showed that standard test in regression does not apply when unit rootprocesses are involved. The thesis intends to study if the exchange rate and thecommodities are cointegrated, following the analysis by Cashin et al. [2003], byforming a weighted index of the commodities with weights based on their shareof the export, i.e. the index CI at time t is given by
CIt =1
CIt=1
∑i
wiPi,t (38)
where Pi is the price of commodity i at time t and wi is the weight, with∑i wi = 1.
Then, the Engle-Granger two-step approachwas used to study cointegrationbetween the two series, in which stationarity of the residuals of a regressionwith the level exchange rate and commodity series are investigated. If the twoseries are not cointegrated, a regression between them is spurious and gives nomeaningful information about a relationship between the two. It is still possibleto run a regression with the returns series, keeping in mind that this regressionexplains the returns in the exchange rate series based on the differences of thecommodity series. However, these results have nothing to do with a relationshipin levels [Woolridge, 2009].
The four commodities used are gold, crude oil, natural gas and iron ore. Themodel examines yearly periods over the data set, i.e. 2009-01-02 to 2009-12-30 and similarly all the way up to 2016-12-30, partitioning the data into eightperiods. It might be that the relationship between daily fluctuations in com-modity prices and exchange rates varies from year to year from an economicperspective. A regression over the whole data set would make such an analysisimpossible. Also, the exchange rate data consists of the nominal exchange rate,and so effects of inflation differentials on supply and demand are not accountedfor. This is, however, not a problem when studying the partitioned data as ef-fects of inflation are small over for each year. Furthermore, the relation betweenfluctuations is probably also affected by other global and domestic macroeco-nomic events and over an eight year period, many of such events may occur,as table 22 shows. From a mathematical perspective, partitioning might miti-gate potential heteroscedasticity in the data, as different subgroups in the datashould be more visible. Also, given the small number of covariates, the numberof data points is believed to be roughly sufficient with yearly partitions.
30
The regression model with lagged covariates, i.e. the change in price at ki,where ki is the lag for covariate i, is given in equation (39) below, with thesame notation as earlier.
log(yt/yt−1) = β0 +∑i
βi · (xi,t+ki − xi,t+ki−1) + εt (39)
4.5 Outline
A brief summary of the steps performed in the analysis is as follows. First, eachof the time series were studied separately for unit root behaviour. If evidencefor unit roots is found, then the form of regression equation (37) is warranted,as discussed above. Then, the Engle-Granger two-step approach was used toexamine the two series for a cointegrating relationship. Previous research in thefield has studied cointegration between commodities and exchange rates (see[Cashin et al. , 2003] and [Chen & Rogoff, 2002] and references therein). How-ever, all of these studies used monthly real effective exchange rates as the depen-dent variable. The data used in this thesis consists of daily nominal exchangerates. If there is evidence suggesting cointegration, then these results corrob-orate previous research but also suggests that the relation between exchangerates and commodities is discernible on a shorter time scale than previouslystudied.
After the cointegration analysis, the regression model in equation (37) wasstudied for each partition of the data. As the model in equation (37) givesno information regarding the predictability of exchange rate fluctuations basedon earlier movements in the commodities, equation (39) was studied at differentlags to investigate if there appears to be a consistent, but delayed, relationshipbetween the two. Appropriate lags were found by studying cross-correlationsbetween the logarithm of returns of the exchange rate and the differenced com-modity series. These results are also further supplemented by results fromstudying the similarity measure given in equation (11).
The potential benefits of using smoothed data in the regression model in equa-tion (37) was also studied. The idea is that patterns might be difficult to detecton a daily basis, but more pronounced when the daily variations are smoothed.For example, if the average return over the past three days of a commodity ispositive, it might produce a larger and consequently more discernible effect onthe exchange rate. The smoothing was performed using two different weightingmethods. One method used equally weighted moving averages, with weightsgiven by the inverse of the window length. The other used non-uniform weightswith larger weight given to more recent observations according to the equation
wi = i/
L∑j=1
j, i = 1,. . . ,L (40)
31
where L is the window length and wL is the weight for the most recent observa-tion. The same analysis of lag, as for the unsmoothed data, was also performedfor the smoothed data. All of these models were compared and analyzed.
Unlike for the models with lag, the regression in equation (37) can not be usedto make predictions about future returns for the exchange rate, at least notwithout a price model for each of the commodity series. Simple autoregressivemodels are fitted to each of the commodity series and predictions for each ofthese series are then used in the full regression equation to generate predictionsof the next day exchange rate return. The predictive performance and the trad-ing potential of the different commodity based models was then be comparedto a simple autoregressive model for the exchange rate.
32
5 Results
5.1 Preliminary analysis of the data and unit root analysis
Figure 1 shows a plot of the full data set over the entire time span. Figure 2 and3 below show the data for two of the yearly partitions, 2010 and 2014. Plots forthe other years can be found in the appendix. These two periods are presentedand studied in the following because they achieved the best and worst model fitrespectively. See appendix for similar analysis on the other years.
Jan 2010 Mar 2010 May 2010 Jul 2010 Sep 2010 Nov 2010 Jan 2011
Date
0.4
0.6
0.8
1
1.2
1.4
1.6Exchange rate and Commodity indices
USDAUD
Gold
Crude oil
Natural Gas
Iron
Figure 2: Plots of the data during 2010, the second partition of the data. Notethat all series are indices, created by dividing the series with their value for thefirst point in the partition, which in this case is the value at 2010-01-02. Iron oreprices hit all time high as disruptions in supply from India tightened the market.India is the third largest exporter of iron ore. Overall, the iron ore market sawa resurgence in production and higher demand from most countries after thestimuli packages from 2009 started to give effect [OECD, 2011]. Gold pricescontinued to rise amid economic uncertainty, currency market unpredictabilityand the possibility of the US government buying back bonds. [Smith, 2010]
There are no clear trends in any of the time series when studying the yearlypartitioned data, compared to figure 1 with the whole data set. The strikingfeature in figure 2 is how similar the movements of crude oil and AUDUSDappear to be. Also, gold and AUDUSD have similar movements. Figure 3 showssimilar results, although with a stronger similarity between gold and AUDUSD,while it is weaker between crude oil and AUDUSD. The price of natural gasappears to have been unstable for roughly the first two months of the year.
33
Jan 2014 Mar 2014 May 2014 Jul 2014 Sep 2014 Nov 2014 Jan 2015
Date
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Exchange rate and Commodity indices
USDAUD
Gold
Crude oil
Natural Gas
Iron
Figure 3: Same as in figure 2, but for 2014. Note that the series in this figureare scaled by their respective values at 2014-01-02. A cold 2013-2014 winterand record-high storage withdrawals led to high demand and a five year pricespike in February for natural gas. Prices remained high during the spring butdropped in the summer due to strong production and inventory rebuilds. Ironore prices slumped in 2014 as China’s economy slowed down and the world’s topminers ramped up production. Crude oil prices fell sharply in the last quarteras production exceeded demand, resulting in prices falling below the five-yearaverage. [Lannin, 2014] [Teller, 2015]
To study if the time series used in the regression are unit root processes, aninformal analysis of the autocorrelation (AC) of the level series and the differ-enced series are studied, together with the more formal Dickey-Fuller test. Ifthe time series has a unit root, then the AC should show a very slow decay asa function of the lag. Figure 9 in the appendix shows graphs of the AC of theoriginal time series in the left column and AC of the differenced time series inthe right column. The slow decay in all plots in the left column is expectedfor an autoregressive process. After differencing the series there is virtually noAC left in the series, which indicates that the series could be described well byautoregressive processes of order one. The blue lines are confidence bounds forthe AC of a completely random series, i.e. with no AC.
34
A Dickey-Fuller test was also conducted for each time series, where the nullhypothesis is that the process has a unit root against the alternative of theseries being stationary. Each test gave a very high p-value, with the smallestbeing 0.54 for natural gas, which should be interpreted as the data giving verylittle evidence against the null hypothesis. This is further indication that thetime series under study exhibit unit root behaviour.
5.2 Cointegration analysis
Following the approach used by Cashin et al. [2003], a weighted commodityindex was created, consisting of the USD price of the four commodities weightedby their share of the commodity. Following this, the Engle-Granger two-stepmethod was used to test for cointegration. xt represents the commodity indexand yt is the original exchange rate series, indexed using its first value. If xtand yt are non-stationary and cointegrated, a combination of them must bestationary. Letting β be the cointegration parameter, it is written as:
yt − βxt = ut (41)
where ut is a stationary process. As the cointegration parameter β and ut arenot known, they are estimated using the following regression:
yt = α+ γxt + et (42)
An estimate for the cointegration parameter β is now given by the estimate ofγ, γ, and an estimate for ut−1 is given by the residual et. Now, the estimatedseries can be tested for stationarity using the Dickey-Fuller test, in which asecond regression is run using the estimated series, i.e. ∆ut is regressed on utand the t-statistic for the coefficient on ut is studied using the critical values intable 1.
Significance level 1% 2.5% 5% 10%Critical value -3.90 -3.59 -3.34 -3.04
Table 1: Asymptotic critical values for cointegration test in the Engle-Grangertwo-step method. [Woolridge, 2009, p.647]
Values for the t-test, for each year, can be found in the table 2 below.
Year 2009 2010 2011 2012 2013 2014 2015 2016β 0.8285 0.6984 1.0390 1.4616 0.3269 1.3492 0.6600 1.2976t-stat -3.04 -2.46 -2.15 -2.12 -1.96 -3.02 -2.09 -1.92
Table 2: Table with estimated value for the cointegration parameter β and thecorresponding t-stat, for each year. The t-stat are compared to the critical valuesin table 1.
35
The values for the t-statistics are compared with the critical values in table1, to determine the level of significance. None of the t-stats are significanton a 10% level, which shows little evidence for rejecting the null hypothesisof no cointegration. Different lags of the residual series were also used in theDickey-Fuller test, to study if there is cointegration at any lags between theexchange rate and the commodity index. Lags up to 15 days were used butnone of these were significant at a 10% level, further indicating that the twoseries do not appear to be cointegrated. Note that equation (41) does not allowfor structural breaks, i.e. subpopulations with different properties in the series.The partition of data, however, is believed to mitigate the effect of such breaks,motivating the use of equation (41).
5.3 Regressions without lag
The results from the previous section indicate that there is no cointegrationbetween the level of the commodities and the exchange rate. This further war-rants the form of the regression model in equation (37), as discussed in earliersections. Equation (37) also allows us to study the specific effect of each of thefour commodities on the exchange rate. The results from the regressions for2010 and 2014 can be found in table 4 and 5 below. Results for the other yearscan be found in the appendix. Scatterplots for the data in these two regressionscan be found in the appendix (figure 4 and 5) and the variance inflation factorfor each covariate are given in table 3 below. The low VIF values indicate thatthe covariates have a low degree of correlation between each other, ensuring thatthe inflation of the OLS estimates is small.
2010 and 2014 are the years with the best and worst fit respectively and plots ofthe data for these years can be found in figures 2 and 3 above. Not surprisingly,crude oil series explains a lot of the variation in the exchange rate, indicatedby the magnitude of the coefficient and large t-stat. Gold also appears to beimportant in the model, while natural gas and iron could possibly be removedwithout reducing the fit of the model. The small t-statistic for iron is somewhatsurprising, as iron is one of Australia’s largest export, constituting roughly 20%of the total export in 2015 [OEC, 2015]. The sign for gold and crude oil is rea-sonable, as higher prices for the commodities should benefit the producer. Thepositive sign indicates that AUD becomes more expensive, in terms of USD,when the price of gold and crude oil does.
Gold Crude oil Natural gas Iron2010 1.0621 1.0789 1.0158 1.00892014 1.0213 1.0059 1.0102 1.0095
Table 3: Variance inflation factor for the two regression models, calculated ac-cording to equation (27).
The regression for 2014 shows similar results as for 2010 for all commodities
36
Coefficients Estimate SE tStat pValue
____________ __________ __________ ________ __________
Intercept 7.3236e-05 0.00041305 0.17731 0.85941
Gold 0.098894 0.037176 2.6602 0.008305
Croil 0.2738 0.02463 11.116 1.1409e-23
NG -0.014141 0.01617 -0.87453 0.38265
Iron 0.030313 0.027548 1.1004 0.27221
Number of observations: 260, Error degrees of freedom: 255
Root Mean Squared Error: 0.00658
R-squared: 0.382, Adjusted R-Squared 0.372
F-statistic vs. constant model: 39.4, p-value = 1.07e-25
Table 4: Results from the regression using equation (37) for the year 2010. Note thatthe differenced series are used for the covariates and the logarithm of the returns areused for the dependent variable. As the series are indices, all coefficients are unitless.
except crude oil, which now appears to be of no use in the model. This a strik-ing difference compared to the model for 2010, where crude oil had a very larget-statistic. The regression also shows a worse fit compared to 2010, with lowerR2 and adjusted R2 values. Comparing these results with regression results forthe other years, the conclusion is that natural gas and iron generally explainvery little of the variation in the exchange rate. The t-statistic for these com-modities all have large p-values for each year, with the exception of 2016 wherethe t-statistic for iron had a p-value of 0.035. Although rigorous analysis, forexample using F-tests and the AIC, is necessary before any final conclusions canbe drawn, the results indicate that only gold and crude oil prices affect the dailyreturns for the exchange rate, for the year under study. The intercept appearsto be insignificant in both regressions. Removing the intercept imposes strictassumptions of the dynamic of the relationships between the dependent variableand covariates. Specifically, it signifies that the mean of the dependent variableis zero when the covariates are zero, which might not be true. Therefore, it iskept in the model as given its small value in both regressions, it has a negligibleeffect on the dependent variable.
Further analysis and testing of this model is postponed until later sections andthe regressions with lagged variables are studied in the following.
37
Coefficients Estimate SE tStat pValue
____________ ___________ __________ ________ _________
Intercept -0.00022123 0.00030547 -0.72422 0.46959
Gold 0.11032 0.037114 2.9725 0.0032363
Croil 0.032482 0.033505 0.96947 0.33323
NG -0.0053388 0.0035708 -1.4951 0.13612
Iron 0.032003 0.028439 1.1253 0.26152
Number of observations: 260, Error degrees of freedom: 255
Root Mean Squared Error: 0.00474
R-squared: 0.0503, Adjusted R-Squared 0.0354
F-statistic vs. constant model: 3.38, p-value = 0.0103
Table 5: Results from the regression using equation (37) for the year 2014. Notethat since the covariates are indices, with different scales for each year, thecoefficients need to be re-scaled before comparison can be made between differentyears, as the OLS is not scaling invariant.
5.4 Regressions with lag
Plots of the sample cross-correlation for 2010 and 2014 can be found in figures 4and 5. The correlations at lag = 0 for each commodity is in correspondence withthe results from the regressions in the previous sections. The noticeable lags for2010 data, are at around -12 for gold, +15 for crude oil and around -3 and 20 foriron (in days). For the 2014 data, noteworthy lags are at +7 for gold, around -5for crude oil, +10 for natural gas and possibly +20 for iron. These values werealso compared to the ones obtained from the similarity measure in equation(11). A table of the values of equation (11) for each commodity at different lagscan be found in table 23 in the appendix. Regressions were run using differentlags for each commodity, at the best lags found in the analysis. That is, thelogarithm of the exchange rate was regressed on the commodity series, wheredifferent combinations of lags where included for each commodity. Note thatthe only restriction was that two adjacent lags, for a commodity, could not beused in the same regression as the two covariates would be perfectly correlated.
The same analysis was performed for each year, using the optimal lags found forthat year. The best model, over all years and combinations, is given in table 6.The t-stat for all coefficients are very small, not to mention the F-statistic versusa constant model and the negative adjusted R2. The other regressions are notpresented here as they all had very large F-statistics versus a constant model,with only an intercept, and values below 1% for R2 and even negative valuesfor the adjusted R2. These results suggest that model with lags included, evenwhen the lag is only 1, hold little information about the next day’s exchangerate. Different functional forms for the regression equation were also used, withquadratic and interaction terms for the covariates and relative returns, defined
38
as (yt−yt−1)yt−1
, for the dependent variable. None of these models offered a better
fit, compared to the model in 6, after controlling for irrelevant terms. Hence,further analysis was not necessary.
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
Sam
ple
Cro
ss C
orre
latio
n Gold
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
0.6
Sam
ple
Cro
ss C
orre
latio
n Crude Oil
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Natural Gas
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Iron
Figure 4: Plots of the cross-correlation between the logarithm of the exchangerate return and the four different commodities, where the correlation positiveand negative lags are calculated according to equation (32). Data is for 2010.
Coefficients Estimate SE tStat pValue
____________ __________ __________ ________ _______
Intercept 0.00038979 0.00053776 0.72484 0.46924
Gold, lag 1 -0.0028812 0.047925 -0.06012 0.95211
Gold, lag 3 -0.0099578 0.031697 -0.31415 0.75367
Croil, lag 2 0.018807 0.023317 0.80657 0.42069
Croil, lag 4 0.035385 0.0353 1.0024 0.31712
Croil, lag 7 -0.085277 0.047845 -1.7824 0.07592
Ngas, lag 2 0.025501 0.031754 0.80309 0.4227
Iron, lag 8 -0.0091222 0.02081 -0.43835 0.66151
Number of observations: 254, Error degrees of freedom: 246
Root Mean Squared Error: 0.0084
R-squared: 0.0199, Adjusted R-Squared -0.00799
F-statistic vs. constant model: 0.714, p-value = 0.661
Table 6: Table showing the regression output for the optimal model found withlags, for 2010. Note that all commodity series are differenced.
39
5.4.1 Smoothed data
To study if daily variations in data obscured potential long-term trends, wherelong-term in this sense is more than two days and shorter than a month,smoothed versions of the data were created. The smoothed data was obtainedusing moving averages, as described in the method, of different lengths up toa maximum of 15 days, corresponding to three business weeks. For each valueof the moving average window, the same analysis as performed above for themodels without lag was conducted for each year, according to equation (37).Different combinations of lags, found by studying plots of the sample autocor-relation and the similarity measure, were also experimented with in the regres-sions, according to equation (39). The smaller number of observations in theseregressions compared to the ones in the models without lags is due to the re-moved initial values for the series. The simple moving average weights eachobservation equally, with weights given by the inverse of the window length.Hence, the first points in the series, up to the size of the window length, wereremoved.
The emerging trend from the analysis was that the fit of the model generallyfollowed a U-shaped function of increasing window length, as table 8 shows.For the models without lag, the fit showed an initial large reduction for smalldegrees of smoothing with a slight improvement with increasing window length.This is somewhat surprising as longer periods of positive trends for the com-modity series is believed to produce periods of positive trends for the exchangerate, keeping all other factors fixed. None of the best models with smooth-ing and without lag offered improvements, compared to their non-smoothedcounterparts. The best model, in the sense that it had the highest value forthe F-statistic versus a constant model, R2, adjusted R2, over all years andsmoothing lengths are given in table 7.
The smoothing did not improve the models with lagged covariates, studied inthe previous section, either. Special care was necessary when using lags togetherwith smoothing, as lagged covariates of the same commodity become more cor-related with increasing window length. This multicollinearity can be toleratedas it is artificially introduced to the data, even though it inflates the varianceestimates of the OLS coefficients. However, none of the models with smoothingand lags showed a better model fit compared to the smoothed model withoutlag and were therefore not further analyzed.
40
Coefficients Estimate SE tStat pValue
____________ __________ __________ _______ ________
Intercept 0.00037897 0.00052307 0.72451 0.46943
Gold -0.49716 0.36928 -1.3463 0.17942
Croil 1.0667 0.21004 5.0785 7.4234e-07
Ngas 0.091905 0.16116 0.57029 0.56899
Iron -0.015212 0.1509 -0.10081 0.91979
Number of observations: 256, Error degrees of freedom: 251
Root Mean Squared Error: 0.00797
R-squared: 0.103, Adjusted R-Squared 0.0886
F-statistic vs. constant model: 7.19, p-value = 1.69e-05
Table 7: Table showing the regression output for the smoothed covariates, withno lag and a smoothing window of 5 days, for 2010. Note that all commodityseries are differenced.
Smooth 2 3 4 5 10 15R2 0.0118 0.00663 0.0156 0.0244 0.0277 0.0255adj. R2 -0.00376 -0.00907 -4.68e-06 0.00883 0.0118 0.00928F-stat 0.758 0.422 1 1.57 1.75 1.57p-value 0.553 0.792 0.408 0.184 0.141 0.183
Table 8: Table showing different regression statistics for the models withsmoothed data and no lags, for the year 2010. The F-statistic is versus a con-stant model. The values in the row named ”Smooth” indicates the length of thewindow used in the smoothing.
41
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Gold
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Crude Oil
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Natural Gas
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Iron
Figure 5: Same as in figure 4, but for 2014.
5.5 Analysis of models
The results in the earlier sections indicate that including lags in the regressionmodels does not add much explaining power, with the best model found givenin table 6. The low F-statistic and the negative adjusted R2 value indicate thatthese model are not preferable over a model with only an intercept. Similarly,analysis of smoothing in the previous section showed that using smoothed co-variates in the regression did not improve the model fit. Therefore, these modelsare not further analyzed and attention is instead focused on the models for 2010and 2014, without lag and smoothing. These models are given in table 4 and 5.It should be noted that the model fit measured by the R2 and the adjusted R2
does not imply good predictive properties for the model out of sample, which isthe important aspect in a model based trading strategy. Hence, the model for2014, could still generate good predictive performance. Here, a deeper analysisis made of the validity of the OLS assumptions and the properties of the regres-sion model.
Model selectionAs noted earlier in the result section, the coefficients for natural gas and iron donot appear to be significant in the model for 2010. An F-test for the restrictedmodel in table 9 against the full model has a p-value of 0.56424, indicating thatthe null hypothesis can not be rejected and that natural gas and iron are jointlyinsignificant in the model. The AIC for the full model is −1.8694 · 103 and themodel without natural gas and iron −1.8713·103, which further corroborates the
42
result from the F-test. Furthermore, the equal values for the adjusted R2, thedifference is less than 10−3, suggests that the two commodities can be removedfrom the model.
Coefficients Estimate SE tStat pValue
__________ __________ __________ _______ _________
Intercept 0.00014173 0.00041006 0.34563 0.7299
Gold 0.098564 0.037137 2.6541 0.0084482
Croil 0.27375 0.024412 11.214 5.089e-24
Number of observations: 260, Error degrees of freedom: 257
Root Mean Squared Error: 0.00658
R-squared: 0.377, Adjusted R-Squared 0.372
F-statistic vs. constant model: 77.9, p-value = 3.66e-27
Table 9: Regression for 2010, without natural gas and iron. Note that neither of thetwo became significant in the model, after removing natural gas and iron.
For 2014, natural gas and iron again appear to be of little use in the regressionmodel. The F-statistic for the restricted model without the two is 1.73822 andcorresponds to a p-value of 0.82208, indicating again that natural gas and ironare jointly insignificant in the model. The AIC gives the same result. Both ofthem are therefore dropped and regression results for the restricted model isgiven in table 10 below.
Coefficients Estimate SE tStat pValue
__________ __________ __________ _______ _________
Intercept -0.0002785 0.00030186 -0.92261 0.35708
Gold 0.10947 0.036905 2.9663 0.0032981
Croil 0.029939 0.033569 0.89185 0.37331
Number of observations: 260, Error degrees of freedom: 257
Root Mean Squared Error: 0.00476
R-squared: 0.0373, Adjusted R-Squared 0.0298
F-statistic vs. constant model: 4.98, p-value = 0.00753
Table 10: Regression for 2014, without natural gas and iron.
The difference between this restricted model for 2014 and the same model for2010 is that crude oil is non-significant, even at a 37% level, compared to theresult in table 9. To investigate if crude oil should be in the model, the F-statistic is calculated for the full model versus the restricted model with goldas the only covariate. The F-statistic is 1.42443, with a p-value of 0.76391,suggesting that the three covariates are jointly insignificant for 2014. The AICis also minimized for this model, taking the values −2.03959 ·103, −2.04006 ·103
and −2.04125 ·103 for the full, restricted and model with only gold, respectively.Residual analysis
43
Coefficients Estimate SE tStat pValue
__________ __________ __________ _______ _________
Intercept -0.00033516 0.00029498 -1.1362 0.25693
Gold 0.11154 0.036818 3.0294 0.0026989
Number of observations: 260, Error degrees of freedom: 258
Root Mean Squared Error: 0.00476
R-squared: 0.0343, Adjusted R-Squared 0.0306
F-statistic vs. constant model: 9.18, p-value = 0.0027
Table 11: Regression for 2014, without natural gas, iron and crude oil.
Plots of the residuals for the 2010 model in table 9 are shown in figure 6 inthe next page. The left plot shows that the residuals appear to follow a whitenoise process, with no particular trends or autoregressive behaviour. The sec-ond graph, the Quantile-Quantile plot, shows that the residuals could be closelyapproximated with a normal distribution, given the close similarity between thequantiles. A Durbin-Watson test was also used to test the residuals for auto-correlation, with a Durbin-Watson statistic of 1.9927 and a p-value of 0.6534.The null hypothesis for the test is that the residuals are serially uncorrelated,against the alternative of the residuals following an autoregressive process oforder 1, with the large p-value reported offering very little evidence against thenull hypothesis.
Plots of the residuals for the 2014 model can be found in figure 24 in the ap-pendix. The normality approximation appears to be slightly worse for thismodel, with more pronounced deviations in the QQ-plot compared to the onein figure 6. In particular, the residuals appear to follow a distribution withheavier tails compared to the normal distribution, which is common for returnsin financial times series. The Durbin-Watson statistic for this model is 2.0237with a p-value 0.9168, indicating that the residuals are not autocorrelated.
44
Jan 2010 Apr 2010 Jul 2010 Oct 2010 Jan 2011-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
-0.02 -0.01 0 0.01 0.02
Data
0.001
0.003
0.01
0.02
0.05
0.10
0.25
0.50
0.75
0.90
0.95
0.98
0.99
0.997
0.999
Pro
ba
bili
ty
Normal Probability Plot
Figure 6: The left plot shows the estimated residuals from the regression for2010, plotted against time. The right graph shows a Quantile-Quantile plot ofthe residuals. Both plots show a potential outlier, around May.
Heteroscedasticity analysis
By partitioning the data into yearly periods, most of the heteroscedasticity wasmitigated, which was verified by running the Breusch-Pagan test for regressionmodel for the whole data set and comparing it to the yearly sets, which hadmuch larger p-values compared to the whole data set. The null hypothesis forthe test is that the data is homoscedastic. Estimates of White’s heteroscedasticconsistent variance were also calculated and are shown in table 12, for the 2010model. The values differ from the original OLS variance estimates by a fewpercent at most and not enough to alter the conclusion from the t-tests, whichis in accordance with the result from the Breusch-Pagan test. The same holdstrue for the 2014 model, where the two standard errors estimated using White’smethod are 0.00031 and 0.03861, respectively.
Coefficients Estimate White’s SE tStat pValue
____________ __________ __________ ________ __________
Intercept 7.3236e-05 0.00042045 0.17418 0.85941
Gold 0.098894 0.038736 2.5530 0.008305
Croil 0.2738 0.02523 10.8521 1.0e-23
Number of observations: 260, Error degrees of freedom: 257
Root Mean Squared Error: 0.00658
R-squared: 0.382, Adjusted R-Squared 0.372
F-statistic vs. constant model: 39.4, p-value = 1.07e-25
Table 12: Results from the regression using equation (37) for the year 2010, with t-statand the corresponding p-value calculated using White’s estimator.
45
5.6 Trading results
As mentioned earlier in the method section, the regression model in equation 37can not be used to predict returns for the exchange rate, without predictions forthe commodity returns. The preliminary analysis of the data showed that thecommodity series could be modelled using an autoregressive process of order 1,denoted as AR(1). Results from the fitting of the commodity series in the modelin table 12, to AR(1) processes using OLS can be found in table 13 below. Asindicated in the earlier analysis, the φ-coefficients are all close to one, meaningthat the series exhibit unit root behaviour.
Parameter Value Standard Error t-statisticcg10 0.00529 0.00804 0.65820φg10 0.99614 0.00712 138.54000σ2g10 0.00013 9.12513·10−6 13.96860
cc10 0.01762 0.01591 1.10759φc10 0.98331 0.01593 61.71760σ2c10 0.00029 2.31508·10−5 12.68840
cg14 0.01720 0.01029 1.74604φg14 0.98278 0.00990 99.32970σ2g14 6.34177·10−5 5.00218·10−6 12.67800
Table 13: Table showing parameter estimates for AR(1) processes fitted to thecommodity series in the table 4 and 5. The notation ”g” stands for ”gold”, ”c”for crude oil, ”10” for 2010 and ”14” for 2014. The rows with the σ2:s give theestimated variance for the zero-mean noise term in the AR(1) model.
The QQ-plots above showed that the residuals from the OLS regressions areapproximately normally distributed. Assuming that this is the true distributionof the residuals, and assuming that zero-mean noise in the AR(1) processes alsofollow a gaussian distribution, the distribution for the next day exchange ratereturns can be derived. Specifically, if εt ∼ N(0, σ2
ε ), then
Xt+1 = c+ φXt + εt ∼ N(c+ φXt, σ2ε ) (43)
Subtracting with Xt on both sides now gives Xt+1−Xt ∼ N(c+Xt(φ−1), σ2ε ).
By noting that the sum of normally distributed variables also is normally dis-tributed with mean and variance given by the sum of the means and variances,the distribution for the logarithm of the exchange rate returns is given as follows
log
(yt+1
yt
)∼ N
(β0 +
∑i
βi(ci + xi,t(φi − 1)), σ2ε +
∑i
β2i σ
2εi
)(44)
where independence is assumed between the covariates in the calculation of thevariance. σ2
ε is the estimated variance for the residuals for the regression in table12 and σ2
ε are the estimated variance for each AR(1) series for the covariates,given in table 13 above. This equation gives the distribution for yt+1, which is
46
the indexed exchange rate at time t+ 1, after some simple algebra. Predictionsand confidence bounds for the next day exchange rate can now be calculatedusing the mean and standard deviation of equation (44). Results for in-sampleand out-of-sample prediction for the model in equation (12) can be found in fig-ure 7 below. As a comparison, an AR(1) process was also fitted to the exchangerate series. Prediction results for one-day ahead predictions for the two modelsare shown in Figure 7.
Dec 01, 2010 Dec 06, 2010 Dec 11, 2010 Dec 16, 2010 Dec 21, 2010 Dec 26, 2010 Dec 31, 2010 Jan 05, 2011 Jan 10, 2011 Jan 15, 2011 Jan 20, 2011 Jan 25, 2011 Jan 30, 2011
1.06
1.07
1.08
1.09
1.1
1.11
1.12
1.13
1.14
Prediction
Figure 7: Plots of the predictions results for the commodity model and the AR(1)model for the exchange rates. At each day, the plot shows the prediction gen-erated using data for the previous day for the commodity based model (red),predictions generated using data for the previous day for the AR(1) model forthe exchange rate (blue) and the true exchange rate for that day (black). Thedotted blue lines are the upper and lower 95% confidence bounds for the ex-change rate AR(1) process. Confidence bounds for the commodity model arenot visible in the figure, as they are much larger. Note that the blue curve isalmost not visible behind the black curve. The figure shows in-sample predictionfrom 2010-12-01 up to 2010-12-30, the last data point used in the estimationof the regression model, and out-of-sample prediction for one month, ending in2011-01-31.
The striking feature of the plot is how closely the simple AR(1) process forthe exchange rate series appears to follow the true price dynamics. The tablebelow shows the mean and variance of the relative errors for each predictionseries. As Figure 7 indicates, the autoregressive model for the exchange rateseries shows much better predictive performance compared to the commoditybased model. This is the case for both the 2010 model and the 2014 model.
47
Model Mean VarianceCommin,10 0.3269 0.5829Commout,10 0.5514 0.8037AR(1)FX,in,10 0.0207 0.5757AR(1)FX,out,10 -0.2169 0.7908
Commin,14 0.3540 0.4056Commout,14 0.3648 0.8315AR(1)FX,in,14 0.1540 0.4043AR(1)FX,out,14 0.1596 0.8169
Table 14: Table shows the mean and variance for the relative prediction error,given as percentages. Rows denoted with ”Comm” are for the commodity basedmodel from equation (44). Subscript ”in” refer to the in-sample prediction and”out” to the out-of-sample prediction.
Dec 01, 2014 Dec 06, 2014 Dec 11, 2014 Dec 16, 2014 Dec 21, 2014 Dec 26, 2014 Dec 31, 2014 Jan 05, 2015 Jan 10, 2015 Jan 15, 2015 Jan 20, 2015 Jan 25, 2015 Jan 30, 2015
0.86
0.87
0.88
0.89
0.9
0.91
0.92
0.93
0.94
0.95
0.96
Prediction
Figure 8: Plots of the predictions results for the commodity model and the AR(1)model for the exchange rates. The figure shows in-sample prediction from 2014-12-01 up to 2014-12-30, the last data point used in the estimation of the regres-sion model, and out-of-sample prediction for one month, ending in 2015-01-31.Note that performance for 2014 is comparable to the 2010 model, even thoughthe 2014 model had smaller values for the goodness-of-fit measures.
48
6 Discussion
The results from the cointegration analysis showed that there is very little ev-idence for cointegration, even for year 2010, which had the best model fit forall years studied. Lags of the residuals were also included in the Dickey-Fullertest to study a possible delayed cointegration, and again the results showedthat there was little evidence for cointegration. This is in contrast to previousresearch in Cashin et al. [2003] and the results in Chen and Rogoff [2002], forwhich cointegration was found between the monthly REERs and commodityprice indices for each of the commodity currencies studied. The period of studyin this thesis was also different from the one studied the two papers cited above.Both were written in the early 2000s and used data from the late 1970s up to theearly 2000s. The data studied in this thesis is from 2009-01-02 up to 2016-12-30and the global markets and macroeconomic conditions have definitely changed,with the easiest example being the 2008 financial crisis. This could explain thedifferent results obtained compared to previous research.
The commodity index used in the study of the cointegration was created us-ing the four commodities weighted according to each commodity’s share of thetotal export in 2015. This commodity index was used on all of the years, andthus not adjusted to reflect potential changes in the share of the total exportthat the commodities might have had. This could be regarded as a potentialsource of error in the cointegration. However, large changes in a country’s exportgenerally need a longer period of time to occur, as large-scale production facil-ities are usually run for decades. Also, the commodities studied are consumedin such a vast number of different ways that their total demand has probablynot affected by technological development, during the period study in this thesis.
As mentioned earlier, the implication of no cointegration between two-time se-ries is that a regression of one on the other is spurious and gives no meaningfulinformation about the level relationship between the two. However, it does notrule out the possibility of there being a relationship between the differencedseries. It might be that the level relationships between exchange rates and theircommodities only exist on the long-term, where trading is probably driven bymacroeconomic fundamentals such as PPP, inflation and interest rate differen-tials, global supply and demand, etc. It is possible that the mechanism thatdrives the relationship between the exchange rates and their respective exportcommodities needs some time to gain full effect, and therefore is not detectableon the shorter time scale studied in this thesis. For example, many major eco-nomic events that affect producers and investors occur at monthly or quarterlyintervals. Also, producers and consumers generally do not alter the timing oflarge-scale transactions based on daily price fluctuations.
Daily price fluctuations are probably mainly affected by speculators, in contrastto large corporations and governments, moving in and out of positions withshort duration. The fact that general high level of explaining power for all of
49
the models with the returns series and variables without lag seem to hold, mightbe an indication that speculators, at least partially, base their trading decisionson fluctuations in the respective commodity for the exchange rate. Furthermore,today’s electronic markets offer second-by-second trading, enabling speculatorsto rapidly respond to relevant new or price fluctuations in the commodities andexchange rates. It would be interesting to study the dynamics between exchangerates and commodities on a shorter time scale, to see if there is a strong rela-tionship between levels on a shorter duration.
Another indication that the daily fluctuations could be mainly driven by spec-ulators, are the varying estimates for the coefficients and the model fits. All ofthese regressions were run using the same regression model, equation (37), yetthe results for different years differ greatly, as shown in the comparisons for the2010 and 2014 data. Not surprisingly, global commodity markets were affectedby very different events, with a world market recovering from the recession andseeing the first effects of the stimulus package in 2010, and generally decliningcommodity prices in 2014, with natural gas being especially volatile. Most spec-ulators adapt their strategies to market conditions, which implies that tradingstrategies would look very different for different years. In other words, there isno trading strategy that suits all market conditions.
The most surprising result regarding the importance of the commodities in ex-plaining variations in the exchange rate is the small, and almost always insignif-icant, estimate of the coefficient for iron. Iron ore export is one of Australia’smost exported commodity, almost as large as the other commodities studiedcombined. One explanation for this could be the distribution of the world con-sumption of iron. China is the world’s largest importer of iron ore, responsiblefor over half of the worlds iron ore import. Hence, the demand for iron orefrom the Chinese market, and thus, the state of Chinese economic growth, is of-ten reflected in the price of iron ore. Consequently, Australia’s iron ore exportis likely highly correlated with the Chinese economy, although the AUDUSDmight not be affected by it.
The results in the section about lags show that the models with lagged covari-ates are inferior to the models without lag, even when compared to a constantmodel with only an intercept. The implications of this is that all explainingpower in the commodity series are concentrated into the daily fluctuations ofthe two, with lags holding no further information. Somewhat surprisingly, themodels with smoothed versions of the time series also showed no improvementcompared to the models without lags. The implication is similar as for the mod-els with non-smoothed data, with the addition that the relationships betweenthe exchange rate and commodities become less detectable with higher degreesof smoothing, further adding to the hypothesis that the daily fluctuations aremainly driven by speculators.
50
The poor fit for the model concerning year 2014 could possibly be explainedby the volatile spot price for natural gas and crude oil. Natural gas prices areprimarily determined as a function of supply and demand. As there are fewshort-term alternatives to natural gas, large price fluctuations can occur due toshort-term shifts in demand. Since natural gas is used as a fuel for heating andelectricity generation, weather changes have a major effect on demand, and thusthe price. For instance, cold winters can have a big impact on the prices, whilehot summers cause demand for cooling to increase, and therefore natural gasdemand by electric power plants. Other factors affecting the demand side areeconomic conditions and petroleum prices. This is due to petroleum’s perk asan economical substitute for large building owners, power generators, and man-ufacturers [USEIA, 2013]. The year of 2014 started off coming from a recordbreaking cold winter, resulting in high demands and storage withdrawals, whichwas reflected in the prices. However, the strong demand was followed by recordproduction and inventory refilling leading to a drop in price. Consequently, thisinfluenced our regression negatively.
In the trading analysis, two types of models were compared: a model usinginformation about commodities to predict exchange rates and a model, whichessentially is a random walk, for the exchange rate series. To make predictionsfor the commodity series, AR(1) processes were fitted to each series, for lack ofother short-term commodity models. The results show that the simple, and ina sense non-informative, AR(1) model outperforms the informative commoditymodel, with some margin. This in line with the most of the research in the field,beginning with Meese and Rogoff’s influential paper, where they showed thatexchange rate models failed to outperform the random walk in out-of-samplepredictions. This thesis shows that their conclusion also holds true for the dailydata studied here. Even though the regression model somewhat limits the pos-sible functional forms for the relation between the dependent variable and thecovariates, it still offers an approximation of the true model. As such, the in-ability of the model used in this thesis to outperform the random walk is morelikely a manifestation of the difficulty in modelling exchange rates, rather thana poor choice of regression model.
In an attempt to identify the Dutch disease in Australia, a first sign was thesignificant correlation between the four commodities and the Australian dol-lar. This itself does not prove the Dutch Disease, however, Australia has hadan abundance of resources during the last decades which inspired the initialthoughts of the phenomenon. When looking at figure 1, there is an increase ofiron, crude oil and gold prices during 2009-2014, while the currency also appre-ciated. According to the Dutch disease, the consequence should be a decliningmanufacturing sector. In 2014, the consequence was apparent, as Australia’s au-tomotive industry was dying. Major car manufacturers Ford, General Motorsand Toyota closed down their factories in Australia, which they had operatingfor over 40 years [Dowling, 2017]. Ever since the commodity boom in Australia
51
from year 2000 onwards, the manufacturing sector has been slowly diminish-ing. Investments in the sector are fading, whilst the sector stands for a smallerportion of the country’s GDP. In addition, the labour costs within the sectorhas doubled since year 2000, which is the highest increase in the world. Con-clusively, there are a lot of signs indicating that the Dutch disease has struckAustralia. [Langcake, 2016]
Summarizing the results, one main point is worth emphasizing. The instabilityof the coefficient estimates over time indicates that a trading strategy, focusedon the USDAUD and the Australian exports, needs to be highly adaptable tocurrent global macroeconomic events and factors affecting the consumers andproducers of commodities, as these appears to highly variable over time. Asthe results from the regressions show, it is not enough to train a model onone year’s data and used this model for trading during the following year. Itmight be possible to update the model parameters adaptively, as the suggestedmodel only describes the relation between exchange rates and their respectivecommodity currencies under current market conditions. However commoditymarkets are among the most volatile markets, making them potentially highlyprofitable but at the expense of a higher risk, and modelling of them shouldtake this into account.
To conclude the discussion and answer the original research question, the coin-tegration analysis showed that there is little evidence for a short-term relation-ships existing between the level of the nominal USDAUD exchange rate and thecommodity prices, but the data suggest that there could exist some relationshipbetween the returns. The results also show that information about the com-modity series offers no improvement in predictive performance over a simpleAR(1) model for the exchange rate, and the suggested model should thereforenot be used in a short-term trading strategy for the exchange rate.
52
7 Further Research
More research regarding the mechanism behind how daily prices affect the ex-change rates would be of interest. Current studies primarily focus on long-termeffects, rather than short-term. Indeed, it could be that short-term fluctuationsis mostly an effect of speculations but due to lack of research on the subject,conclusions are hard to draw.
Since this thesis only examined Australia, it would be of interest to study othercountries considered to have so-called ”commodity currencies”, especially thosethat do not have the same commodities as Australia as their main source ofexport. Looking at developing countries that have an export that is mainlyconsisting of commodities more than 80% would also be of interest. They werenot included in this thesis as these countries have issues with inflation, andthus their currencies would be more influenced by economic factors rather thancommodity prices. It would furthermore be of interest to compare to countriesthat are not considered to be commodity exporters. Data over more commodityprices could also have helped to improve the models offer a comparison.
Regarding the trading strategy, further research would be recommended tolook at shorter time spans, such as minute or second fluctuations. Previousresearch has found cointegration during monthly movements, however, it wouldbe groundbreaking if cointegration existed in shorter time spans.
53
8 References
[Aneuryn-Evans & Deaton, 1980] Aneuryn-Evans, Gwyn, & Deaton, Angus.1980. Testing Linear versus Logarithmic Regression Models. The Reviewof Economic Studies, Vol. 47, No. 1, Econometrics Issue, 275–291.
[Beine et al. , 2012] Beine, Michel, Bos, Charles S., & Coulombe, Serge. 2012.Does the Canadian Economy Suffer from Dutch Disease?
[Beningo & Lopez-Salido, 2004] Beningo, Pierpaolo, & Lopez-Salido, J. David.2004. Monetary Policy, Fiscal Policies and Labour Market, 31–127.
[Bjørnland & Hungnes, 2005] Bjørnland, Hilde C., & Hungnes, Havard. 2005.The Commodity Currency Puzzle.
[Caplinger, 2013] Caplinger, Dan. 2013. Price of Gold in 2013: Is This Year’s$475 Plunge Just the Beginning? Accessed: 2017-05-10.
[Cashin et al. , 2003] Cashin, Peter, Cespedes, Luis F., & Sahay, Ratna. 2003.Commodities and the real exchange rate.
[Catao, 2007] Catao, Luis A.V. 2007. Why Real Exchange Rates? Finance andDevelopment, IMF.
[Chen & Rogoff, 2002] Chen, Yu Chin, & Rogoff, Kenneth. 2002. CommodityCurrencies and Empirical Exchange Rate Puzzles. IMF Working Paper.
[Chen & Rogoff, 2012] Chen, Yu Chin, & Rogoff, Kenneth. 2012. Are the com-modity currencies an exception to the rule?
[CIA, 2017] CIA. 2017. URL = https://www.cia.gov/library/publications/the-world-factbook/rankorder/2078rank.html, Accessed: 2017-05-20.
[Corden & Neary, 1982] Corden, W.Max, & Neary, J.Peter. 1982. BoomingSector and De-Industrialisation in a Small Open Economy. Economic Journal.
[Dornbusch, 1976] Dornbusch, Rudi. 1976. Expectations and Exchange RateDynamics. The Journal of Political Economy.
[Dowling, 2017] Dowling, Joshua. 2017. Why Australian car manufacturing died— and what it means for our motoring future. Accessed: 2017-05-20.
[Druzic & Tica, 2006] Druzic, Ivo, & Tica, Josip. 2006. The Harrod-Balassa-Samuelson Effect: A Survey of Empirical Evidence. EFZG Working PapersSeries.
[Durbin & Watson, 1951] Durbin, James, & Watson, Geoffrey. 1951. Testingfor serial correlation in least squares regression, ii. Biometrika.
[Elliott, 2015] Elliott, Larry. 2015. Oil Price Falls to 11-year Low with GlobalGlut Expected to Deepen in 2016. Accessed: 2017-05-10.
54
[Els, 2015] Els, Frik. 2015. Iron Ore Price Hits Record Low. Accessed: 2017-05-10.
[Gelb & Associates, 1988] Gelb, & Associates. 1988. Oil Windfalls: Blessing orCurse? World Bank.
[Gnanadesikan & Wilk, 1968] Gnanadesikan, Ramanathan, & Wilk, Martin B.1968. Probability plotting methods for the analysis of data. Biometrika.
[Kennedy, 2008] Kennedy, Peter. 2008. A Guide to Econometrics. 6th edn.Wiley Blackewell.
[Keylor, 2001] Keylor, William R. 2001. The Twentieth-Century World: AnInternational History. 4th edn. New York: Oxford University Press.
[Kiev, 2014] Kiev, C.W. 2014. What Dutch disease is, and why it’s bad. TheEconomist.
[Kirby et al. , 2016] Kirby, Jason, Hutchins, Aaron, & Gillis, Charlie. 2016. Lifeat $20 a barrel: What the oil crash means for Canada. Accessed: 2017-04-13.
[Krugman & Wells, 2013] Krugman, Paul, & Wells, Robin. 2013. Economics.3rd edn. Worth Publishers.
[Lang, 2016] Lang, Harald. 2016. Elements of Regression Analysis.
[Langcake, 2016] Langcake, Sean. 2016. Conditions in the Manufacturing Sec-tor.
[Lannin, 2014] Lannin, Sue. 2014. Iron ore: Moody’s Says Impact of SlidingPrices Being Felt Across Economy. Accessed: 2017-05-02.
[Loayza et al. , 2007] Loayza, Norman V., Ranciere, Romain, Serve, Luis, &Ventura, Jaume. 2007. Macroeconomic Volatility and Welfare in DevelopingCountries: An Introduction. World Bank Economic Review 21.
[McKinnish, 2002] McKinnish, Terra. 2002. Interpreting lagged effects of theindependent variable: How does the local economy affect welfare caseloads?University of Colorado: Department of Economics. July.
[Murillo, 2016] Murillo, Carlos. 2016. Canada’s Oil Extraction Industry: Indus-trial Outlook Summer 2016.
[OEC, 2015] OEC. 2015. The Observatory of Economic Complexity. Accessed:2017-04-20.
[OECD, 2011] OECD. 2011. https://www.oecd.org/sti/ind/49214005.pdf, Ac-cessed: 2017-05-01.
[OPEC, 2017] OPEC. 2017. URL = http://www.opec.org/opecweb/en/index.htm,Accessed :2017− 05− 20.
55
[RBA, 2017] RBA. 2017. URL = http://www.rba.gov.au/mkt-operations/, Ac-cessed: 2017-05-20.
[Reinsdorf, 2009] Reinsdorf, Marshall. 2009. Terms of Trade Effects: Theory andMeasurement.
[Rogoff, 1996] Rogoff, Kenneth. 1996. The Purchasing Power Parity Puzzle. Jour-nal of Economic Literature, 647–668.
[Serapio, 2011] Serapio, Manolo. 2011. Iron Ore in Record Slide as China DemandSlows. Accessed: 2017-05-10.
[Smith, 2010] Smith, Aaron. 2010. Gold Prices Break Another Record. Accessed:2017-04-23.
[Spechler, 2012] Spechler, Lori. 2012. Gold Prices Already Peaked in 2011: Re-port.
[Taylor & Taylor, 2004] Taylor, Alan M., & Taylor, Mark P. 2004. The PurchasingPower Parity Debate. Journal of Economic Perspectives.
[Teller, 2015] Teller, Katie. 2015. Natural Gas Prices Drop Following Strong Pro-duction Growth. U.S. Energy Information Administration.
[Tencer, 2014] Tencer, Daniel. 2014. Canada Has Dutch Disease, Bank Of AmericaDeclares.
[Tsai & Upchurch, 2017] Tsai, Kristen, & Upchurch, Jason. 2017. Natural GasPrices in 2016 Were the Lowest in Nearly 20 years. U.S. Energy InformationAdministration.
[Uriel, 2013] Uriel, Ezequiel. 2013. Hypothesis testing in the multiple regressionmodel. University of Valencia: Department of Economics.
[USEIA, 2013] USEIA. 2013. 2012 Brief: Average Wholesale Natural Gas PricesFell 31% in 2012. U.S. Energy Information Administration. Accessed: 2017-05-10.
[van Wijnbergen, 2008] van Wijnbergen. 2008. The permanent income approachin practice. World Bank.
[Weisenthal, 2012] Weisenthal, Joe. 2012. Morgan Stanley Explains The Iron OrePrice Crash That Nobody Can Stop Talking About. Accessed: 2017-05-10.
[White, 1980] White, Halbert. 1980. A Heteroskedasticity-Consistent CovarianceMatrix and a Direct Test for Heteroskedasticity. Econometrica, Vol 48, 817–838.
[Woolridge, 2009] Woolridge, Jeffrey M. 2009. Introductory Econometrics, A Mod-ern Approach. 5th edn.
56
57
9 Appendices
9.1 Graphs
0 5 10 15 20-1
0
1Gold
0 5 10 15 20-1
0
1Gold
0 5 10 15 20-1
0
1Crude oil
0 5 10 15 20-1
0
1Crude oil
0 5 10 15 20-1
0
1
Sam
ple
Auto
corr
ela
tion
Natural gas
0 5 10 15 20-1
0
1
Sam
ple
Auto
corr
ela
tion
Natural gas
0 5 10 15 20-1
0
1Iron
0 5 10 15 20-1
0
1Iron
0 5 10 15 20
Lag
-1
0
1USDAUD
0 5 10 15 20
Lag
-1
0
1USDAUD
Figure 9: Plots of the sample autocorrelation for the original data in the leftcolumn and the differenced data in the right column. The blue lines are confi-dence bounds for the autocorrelation of a completely random series, i.e. with noautocorrelation.
58
Jan 2009 Mar 2009 May 2009 Jul 2009 Sep 2009 Nov 2009 Jan 2010
Date
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Exchange rate and Commodity indices
USDAUD
Gold
Crude oil
Natural Gas
Iron
Figure 10: Plot of the data during 2009. Note that all series are indices, createdby dividing the series with their value for the first point in the partition, whichin this case is the value at 2009-01-02.
Jan 2011 Mar 2011 May 2011 Jul 2011 Sep 2011 Nov 2011 Jan 2012
Date
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Exchange rate and Commodity indices
USDAUD
Gold
Crude oil
Natural Gas
Iron
Figure 11: Plot of the data during 2011. Uncertain economic conditions andfears of a global financial system collapse drove investors to gold, resulting inprices reaching record levels. Iron Ore saw its steepest slide ever after slowingdemand from the Chinese construction sector. China consumes over half of theworlds output in iron ore. [Spechler, 2012] [Serapio, 2011]
59
Jan 2012 Mar 2012 May 2012 Jul 2012 Sep 2012 Nov 2012 Jan 2013
Date
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3Exchange rate and Commodity indices
USDAUD
Gold
Crude oil
Natural Gas
Iron
Figure 12: Plots of the data during 2012. A mild 2011-12 winter, high naturalgas inventories, and increased supply contributed to lower average spot naturalgas prices during 2012. As production receded following lower prices, pricesstarted to recover from June through the rest of the year. Hot weather leadto greater demand for natural gas use for power generation, contributing tothe slight rise in prices during the summer months. However, prices remainedlower than seen in most of 2011. After prices reaching record high levels during2011, the price for Iron Ore fell during mid 2011. This was primarily due to aslowdown in growth in steel making in China, combined with Chinese steel millsoverproducing. [USEIA, 2013] [Weisenthal, 2012]
60
Jan 2013 Mar 2013 May 2013 Jul 2013 Sep 2013 Nov 2013 Jan 2014
Date
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Exchange rate and Commodity indices
USDAUD
Gold
Crude oil
Natural Gas
Iron
Figure 13: Plots of the data during 2013. The price of gold plunged by morethan 25% during 2013. Worries of a shift in the US Federal Reserves monetarypolicy and the Cyprus banking crisis. where investors feared a liquidation of theisland nation’s gold reserve contributed to the decline. [Caplinger, 2013]
Jan 2015 Mar 2015 May 2015 Jul 2015 Sep 2015 Nov 2015 Jan 2016
Date
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2Exchange rate and Commodity indices
USDAUD
Gold
Crude oil
Natural Gas
Iron
Figure 14: Plots of the data during 2015. Crude oil prices ended on the lowestnote since 2009, reflecting continued excess of crude oil supply over global de-mand. Concerns over an increased supply as a result of lifted sanctions on Iranled to a further decrease of the price. Declining demand for iron ore in China,and cheap new supply has put pressure on the iron ore prices since late 2013.[Elliott, 2015] [Els, 2015]
61
Jan 2016 Mar 2016 May 2016 Jul 2016 Sep 2016 Nov 2016 Jan 2017
Date
0.6
0.8
1
1.2
1.4
1.6
1.8
2Exchange rate and Commodity indices
USDAUD
Gold
Crude oil
Natural Gas
Iron
Figure 15: Plots of the data during 2016. Iron ore prices recovered during 2016as a result of steady demand from China and supply cutbacks from top producers.Natural gas spot prices reached its lowest level since 1999. Changing demand,large inventories, and temperatures warmer than usual through the year wasthe main factors driving the prices. Prices gradually increased during spring asdemand rose and production decreased before cold winter temperatures furthercontributed to the hike. [Tsai & Upchurch, 2017]
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
Sam
ple
Cro
ss C
orre
latio
n Gold
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
0.6
Sam
ple
Cro
ss C
orre
latio
n Crude Oil
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Natural Gas
-20 -10 0 10 20-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Iron
Figure 16: Cross-correlation for 2009
62
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
Sam
ple
Cro
ss C
orre
latio
n Gold
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
0.6
Sam
ple
Cro
ss C
orre
latio
n Crude Oil
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Natural Gas
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Iron
Figure 17: Cross-correlation for 2011
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
Sam
ple
Cro
ss C
orre
latio
n Gold
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
0.6
Sam
ple
Cro
ss C
orre
latio
n Crude Oil
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Natural Gas
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Iron
Figure 18: Cross-correlation for 2012
63
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
Sam
ple
Cro
ss C
orre
latio
n Gold
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Crude Oil
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Natural Gas
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Iron
Figure 19: Cross-correlation for 2013
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
Sam
ple
Cro
ss C
orre
latio
n Gold
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
Sam
ple
Cro
ss C
orre
latio
n Crude Oil
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Natural Gas
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Iron
Figure 20: Cross-correlation for 2015
64
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Gold
-20 -10 0 10 20
Lag
-0.2
0
0.2
0.4
Sam
ple
Cro
ss C
orre
latio
n Crude Oil
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Natural Gas
-20 -10 0 10 20
Lag
-0.2
-0.1
0
0.1
0.2
Sam
ple
Cro
ss C
orre
latio
n Iron
Figure 21: Cross-correlation for 2016
Correlation Matrix
-0.1 0 0.1
Iron
-0.1 0 0.1
Natural gas
-0.1 0 0.1
Crude oil
-0.05 0 0.05
Gold
-0.1
0
0.1
Iron
-0.1
0
0.1
Nat
ural
gas
-0.1
0
0.1
Cru
de o
il
-0.05
0
0.05
Gol
d
0.24 0.07 0.04
0.24 0.12 0.09
0.07 0.12 -0.01
0.04 0.09 -0.01
Figure 22: Correlation matrix for the 2010 data.
65
Correlation Matrix
-0.04
Iron
0 0.5
Natural gas
-0.05 0 0.05
Crude oil
-0.05 0 0.05
Gold
-0.05
0
0.05
Iron
-0.5
0
0.5
Nat
ural
gas
-0.05
0
0.05
Cru
de o
il
-0.05
0
0.05G
old
0.06 0.09 0.10
0.06 0.05 -0.00
0.09 0.05 0.01
0.10 -0.00 0.01
Figure 23: Correlation matrix for the 2014 data.
0 50 100 150 200 250 300-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
-0.01 -0.005 0 0.005 0.01 0.015
Data
0.001
0.003
0.01
0.02
0.05
0.10
0.25
0.50
0.75
0.90
0.95
0.98
0.99
0.997
0.999
Pro
ba
bility
Normal Probability Plot
Figure 24: he left plot shows the estimated residuals from the regression for2014, plotted against time. The right graph shows a Quantile-Quantile plot ofthe residuals.
66
9.2 Regression outputs
Coefficients Estimate SE tStat pValue
____________ __________ __________ _______ __________
Intercept 0.00029051 0.00063171 0.45988 0.646
Gold 0.08073 0.043813 1.8426 0.06655
Croil 0.14412 0.017097 8.4294 2.6237e-15
NG 0.004054 0.01634 0.2481 0.80425
Iron 0.040057 0.034761 1.1523 0.25026
Number of observations: 259, Error degrees of freedom: 254
Root Mean Squared Error: 0.01
R-squared: 0.263, Adjusted R-Squared 0.251
F-statistic vs. constant model: 22.6, p-value = 5.34e-16
Table 15: Model without lagged variables, y = log(returns), differenced covari-ates, 2009
Coefficients Estimate SE tStat pValue
___________ ___________ __________ ________ __________
Intercept -0.00011379 0.00046257 -0.24599 0.80589
Gold 0.023474 0.028369 0.82748 0.40874
Croil 0.23677 0.023525 10.065 2.8615e-20
NG 0.032636 0.023565 1.3849 0.1673
Iron -0.073591 0.050417 -1.4597 0.14562
Number of observations: 259, Error degrees of freedom: 254
Root Mean Squared Error: 0.0074
R-squared: 0.314, Adjusted R-Squared 0.303
F-statistic vs. constant model: 29.1, p-value = 6.61e-20
Table 16: This is what perfection looks like. Model without lagged variables, y= log(returns), differenced covariates, 2011
67
Coefficients Estimate SE tStat pValue
____________ ___________ __________ ___________ __________
Intercept -1.6375e-07 0.00029881 -0.00054802 0.99956
Gold 0.12757 0.031987 3.9882 8.7005e-05
Croil 0.16804 0.022255 7.5506 7.7118e-13
NG -0.019921 0.011241 -1.7722 0.077551
Iron 0.035998 0.026915 1.3375 0.18226
Number of observations: 260, Error degrees of freedom: 255
Root Mean Squared Error: 0.00481
R-squared: 0.266, Adjusted R-Squared 0.254
F-statistic vs. constant model: 23.1, p-value = 2.63e-16
Table 17: Model without lagged variables, y = log(returns), differenced covari-ates, 2012
Coefficients Estimate SE tStat pValue
____________ __________ __________ _______ _________
Intercept -0.0004377 0.00036817 -1.1889 0.2356
Gold 0.16503 0.035365 4.6665 4.953e-06
Croil 0.035108 0.036457 0.963 0.33646
NG 0.0046384 0.017098 0.27128 0.7864
Iron -0.03649 0.031147 -1.1715 0.24247
Number of observations: 260, Error degrees of freedom: 255
Root Mean Squared Error: 0.00589
R-squared: 0.0916, Adjusted R-Squared 0.0774
F-statistic vs. constant model: 6.43, p-value = 6.07e-05
Table 18: Model without lagged variables, y = log(returns), differenced covari-ates, 2013
9.3 Nominal Commodity Prices
Below is a list of the commodities used in this paper, accompanied by a briefdescription. The data has been selected according to their of the selected coun-tries total export, and their availability:
Crude Oil, West Texas Intermediate (WTI) - Cushing, Oklahoma, retrievedfrom FRED, Federal Reserve Bank of St. Louis, USD/Barrel
Iron Ore, China, Average Imported Iron Ore CIF Price, USD/Metric ton
Gold, retrieved from FRED, Federal Reserve Bank of St. Louis, Gold FixingPrice 10:30 A.M. (London time) in London Bullion Market, USD/Troy Ounce
68
Coefficients Estimate SE tStat pValue
____________ ___________ __________ ________ __________
Intercept -0.00018931 0.00047514 -0.39843 0.69065
Gold 0.17698 0.060906 2.9059 0.0039843
Croil 0.090326 0.020286 4.4527 1.2689e-05
NG 0.0080769 0.01654 0.48832 0.62575
Iron 0.026804 0.030914 0.86706 0.38672
Number of observations: 260, Error degrees of freedom: 255
Root Mean Squared Error: 0.0076
R-squared: 0.106, Adjusted R-Squared 0.0924
F-statistic vs. constant model: 7.59, p-value = 8.58e-06
Table 19: Model without lagged variables, y = log(returns), differenced covari-ates, 2015
Coefficients Estimate SE tStat pValue
____________ ___________ __________ _______ __________
Intercept -0.00024728 0.00041595 -0.5945 0.55271
Gold 0.065284 0.037286 1.7509 0.081161
Croil 0.076426 0.012932 5.9097 1.0934e-08
NG 0.0040218 0.010587 0.3799 0.70434
Iron 0.022544 0.010665 2.1139 0.035497
Number of observations: 260, Error degrees of freedom: 255
Root Mean Squared Error: 0.00666
R-squared: 0.148, Adjusted R-Squared 0.134
F-statistic vs. constant model: 11, p-value = 2.82e-08
Table 20: Model without lagged variables, y = log(returns), differenced covari-ates, 2016
69
Country Commodity1
Commodity2
Commodity3
Commodity4
Percentage1
Percentage2
Percentage3
Percentage4
% of Export
Australia Natural gas Gold Iron CrudePetroleum
7% 7% 20% 2.2% 36%
Table 21: Selected exported commodities of Australia and percentages of export
Event Timespan Commodities Involved Specific Currencies Involved
Commodities boom 2000-2014 Agriculture, oil, metals -
2000s energy crisis 2003-2008 Crude oil -
Subprime mortgage crisis 2007-2009 Gold USD
Greek government debt crisis 2009-2016 - Euro,
European debt crisis 2009-Present - Euro
Ukrainian crisis 2013-2014 - Russian ruble
Russian financial crisis 2014-Present Crude oil Russian ruble
Chinese stock market crash 2015-2016 Copper, cotton, soybeans Chinese Yuan
Table 22: Major Economic Events since 2000
70
Lag Gold Crude Oil Iron Natural Gas0 1 1 1 11 1.336233 1.862319 1.017516 1.0063942 1.349682 1.897501 0.985774 1.1068943 1.513653 1.822674 0.998362 1.1687264 1.434498 1.840121 1.037434 1.0819095 1.381118 1.876799 1.023219 1.1188706 1.496405 1.880863 1.059929 1.0693877 1.398668 1.947943 1.030811 1.1315378 1.445743 1.916924 1.053669 1.1730459 1.376593 1.744705 1.122516 1.11159310 1.254427 1.880878 1.004695 1.14045211 1.409021 1.853632 1.035053 1.21395712 1.519216 1.911945 1.060118 1.23644913 1.222323 1.884001 1.070541 1.19025614 1.414937 2.055312 1.045311 1.21147815 1.529393 2.254870 1.042609 1.27594716 1.450546 2.113394 1.084921 1.25906417 1.396264 1.911420 1.053835 1.16680918 1.366889 2.023599 1.026762 1.17707419 1.429018 2.016858 1.067844 1.36708220 1.310624 1.901829 1.100381 1.34692321 1.437761 2.006129 1.086618 1.28240022 1.294872 1.995560 1.081442 1.26648423 1.331450 2.090709 1.060193 1.23715924 1.312935 2.041580 1.107525 1.16657425 1.346667 1.977514 0.989382 1.29386326 1.236348 2.202997 1.068153 1.09534927 1.414031 2.014251 1.051031 1.09289128 1.479394 2.010969 1.052949 1.10424829 1.453619 1.967595 1.072991 1.18735130 1.238939 1.772300 1.052100 1.146121
Table 23: Values for the similarity measure at different lags, given in the firstcolumn, for 2010. The values in each column are index using the respectivevalue at lag 0 and show the relative increase or decrease in similarity for eachlag and covariate.
71
TRITA -MAT-K 2017:04
ISRN -KTH/MAT/K--17/04--SE
www.kth.se