high-frequency exchange-rate prediction with an artificial neural network

INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE AND MANAGEMENTIntell. Sys. Acc. Fin. Mgmt. (2012)Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/isaf.1329

HIGH-FREQUENCY EXCHANGE-RATE PREDICTION WITH ANARTIFICIAL NEURAL NETWORK

TAUFIQ CHOUDHRY, FRANK MCGROARTY,* KE PENG AND SHIYUN WANGSchool of Management, University of Southampton, Southampton, SO17 1BJ, UK

SUMMARYThis paper examines how market microstructure variables can be used to forecast foreign exchange (FX) rates atfrequencies of one to several minutes. We use a unique FX dataset of global inter-dealer electronic transactionsand applied the artificial neural network (ANN) as the predicting model. The immediately preceding bid and askprices are significant factors in these predictions, which is in keeping with market microstructure theory. Thesemicrostructure factors have not been tested in an ANN model before. High-frequency trading strategies based onthe ANN model are shown to be profitable even when transaction costs are included. Copyright © 2012 John Wiley& Sons, Ltd.

Keywords: artificial neural network; forecasting exchange rates; foreign exchange; high-frequency data

1. INTRODUCTION

It is widely accepted that foreign exchange (FX) rates are hard to predict. In a much-cited paper, Meeseand Rogoff (1983) showed that none of the FX rate models could beat a random walk in out-of-sampleforecasting. Indeed, Engel and West (2005) proposed an asset-price-based theory of exchange rateswhich predicts that the random walk is the actual pattern that we should expect FX rates to follow.However, a number of other researchers, including Mark (1995), MacDonald and Marsh (1997) andFroot and Ramadorai (2005), found that monetary-approach models have predictive power at time hor-izons of over 3 years. Furthermore, the small number of fundamental drivers in these macroeconomicmodels does not change very frequently. Most are quarterly variables, while some occur only once peryear. Flood and Rose (1995) observe that this is simply not sufficient variability in macroeconomicfundamentals to account for the high-frequency volatility observed in exchange rates. Consequently,in recent years, the focus of FX research has shifted to those potential driver variables which varysufficiently to be able to explain high-frequency FX variation. These market microstructure variablesinclude price, bid–ask spreads, trading volume and order flow. Evans and Lyons (2002) forged a clearlink between FX rates and these microstructure variables when they demonstrated a high correlationbetween daily price change and daily aggregated order flow. Flood (1994) and Bollerslev and Melvin(1994) developed models of how other market microstructure variables and market structure affectexchange-rate movements.Financial time-series data are usually noisy, especially when sampled at high frequencies, and the

underlying generating process is normally affected by a complicated interaction of factors. The majorityof extant FX microstructure models assume a linear structure. Our study explores a more powerfulnonlinear relationship between FX rates and market microstructure drivers that enables us to make

* Correspondence to: Frank McGroarty, School of Management, University of Southampton, Southampton, SO17 1BJ, UK.E-mail: [email protected]

Copyright © 2012 John Wiley & Sons, Ltd.

T. CHOUDHRY ET AL.

predictions over short horizons. The method we use is the artificial neural network (ANN). Thiscontains multiple layers of interconnected neurons and can accommodate various nonlinearities intime-series data and better capture the complex dynamic nature of the underlying process than linearmultivariate time-series models do. We are not the first to employ an ANN for forecasting exchangerates. Yu et al. (2007), Huang et al. (2007) and Chen and Leung (2004) applied ANNs in exchange-rateforecasting. We are not even the first to combine ANN exchange-rate forecasting with market micro-structure variables. Gradojevic (2007; Gradojevic and Yang, 2006) presented microstructure-basedANN models which use daily transaction price data. However, there are a number of nuances to ourapproach which make our contribution original.We use much shorter, intraday, time horizons, in contrast to the daily or longer sampling intervals

used by previous researchers. Our test horizons span from 1 min to 1 h. We were able to carry out thisstudy because we have access to a unique and rich high-frequency dataset of inter-dealer spot FXtrading data which includes bid and ask limit price data, as well as bid-side and ask-side tradingvolumes and market order prices for executed trades. At over 2 million observations, this is one ofthe largest datasets of exchange rates available. It enables us to examine the high-frequency interactionbetween FX microstructure variables and to see whether or not these are in line with our expectationsfrom market microstructure theory. An effective forecasting method which can produce a profitabletrading strategy would constitute evidence against the weak form of the efficient market hypothesis(EMH). Reliable FX forecasting models have additional uses beyond testing theory. Currency tradersat banks and specialist currency funds can exploit such models for profit.Our contribution is threefold. First, the application of the ANN using very high frequency interval

exchange rate data is unique in the field. To our knowledge, no other study does this kind of investiga-tion. Second, we compare the relative importance of groups of microstructure variables in modelpredictions. The result shows that bid and ask prices contain information separate from and in additionto the information contained in transaction prices, which is consistent the predictions of recent marketmicrostructure theory. Finally, we construct high-frequency trading strategies for three of the world’smost heavily traded exchange rates based on our ANN model, which proves to be profitable even afterthe transaction costs are taken into account.

2. DATA AND METHODOLOGY

Data used in this study are spot yen–dollar (JPY–USD), German mark–dollar (DEM–USD) anddollar–euro (USD–EUR) exchange rate observations, time-stamped to the nearest second,provided by Electronic Broking Services (EBS). The EBS data are unusually rich, containing spotFX limit order prices, traded prices, volume and order flow for two sample periods with fiveimportant exchange rates in each. The JPY–USD and USD–DEM data cover 1 August–4 September1998 and the USD–EUR data cover 1 August–3 September 1999. Each sample period contains 20 days’data. High-frequency FX data are very rare, particularly for inter-dealer transactions. The dataset used hereis one of the largest FX datasets ever made available for academic study, comprising a total of over 2million observations of limit orders and market orders for the three currency pairs that we study. TheEBS dataset contains twice as many limit orders as it does market orders, on average. This means that limitorders should arrive nearer the end of each 1 min sampling interval than market orders. Indeed, the timegap between the last limit order to arrive within an interval and the end of that interval should be halfthe size of the time gap for a market order, on average. Furthermore, limit order prices are more likelyto be informative than market order prices.

Copyright © 2012 John Wiley & Sons, Ltd. Intell. Sys. Acc. Fin. Mgmt., (2012)DOI: 10.1002/isaf

HIGH FREQUENCY EXCHANGE RATE PREDICTION WITH AN ANN

The ANN prediction equation is written as

rtþ1 ¼ fXKk¼1

akgXJj¼1

bkjXj

!" #þ mtþ1 (1)

where rt+ 1 is the return from t to t + 1, K is the number of neurons in the hidden layer, J is the number ofthe input variables (independent variables), ak and bkj are weights for the variables, and Xj is the jthinput variable.We define return rt+ 1 as the difference between log prices at times t and t+ 1, where those prices are

the prevailing mid-quote prices (i.e. (bid + ask)/2) at the time of the last realized transaction within thesample interval. This enables us to model returns easily while including or excluding transactions costs.Specifically, using the mid-quote prices alone delivers returns which exclude transactions. In order toinclude transactions costs, we add a half-spread to the mid-quote in the case of a buy trade and subtracta half-spread in the case of a sell trade. This procedure produces prices which are identical to the pricespaid for actual market orders at those times.The estimated equation is

_rtþ1 ¼ m rt; rt�1; . . . ; rt�l; hight; lowt; averaget; of t; vlt; bidt; asktð Þ (2)

where m is an unknown function identified by the neural networks, rt is the return during time t� 1 to t,hight and lowt are the highest and the lowest prices during the previous period, averaget is the averageprice during the previous period, oft and vlt are order flow and trading volume in the previous period,where order flow is the cumulated signed order flow during the previous period and trading volumeis the sum of buy and sell trading volume; bidt and askt are the nearest available bid and ask prices.We use the previous 1 min, 5 min and 60 min intervals to forecast the next period return.A multilayer feed-forward neural network requires that the raw data above be transformed by the

sigmoid function f( ) and g( ) to the normalized range of 0 to 1, which we implement as follows:

f xð Þ ¼ 1

1þ e�x(3)

The forecasting process involves three steps. Step 1 is network training. At time t, use the previous Pobservations as the training sample to estimate the network defined by equation (1). The independentvariables are series of the previous l lags of returns, the previous highest price, lowest price, averageprice, order flow, volume, and he last bid and ask prices. The dependent variable is the current returnseries rt� p+ 1, where p is from 1 to P. We choose P= 70, l= 3 and K= 3 to construct the networks.1

\Using the back-propagation algorithm, we obtained ak and bkj. Step 2, using equation (1) obtainthe return at time t + 1. Step 3, move forward at time t + 1, repeat step 1 and step 2 until the endof the dataset.We use four different combinations of predicting variables (PV): PV1 excludes bid–ask prices; PV2

does not include order flow; PV3 excludes trading volume; and PV4 includes all variables. Order flow,

1Our choice of parameters of P, l and K is based on trial and error. We also tried some other combinations and achieved very simi-lar results.


T. CHOUDHRY ET AL.

trading volume and bid–ask prices levels all affect currency return. Order flow conveys both privatefundamental information and semi-fundamental information. Trading volume, as a trading activitymeasure, is associated with volatility and information. Bid and ask prices in level provide informationon both the difference and the level. To understand the relative importance of these factors in FXprediction, we use the stated four combinations of predicting variables. Then a trading strategy isconstructed based on ANN prediction.Out-of-sample prediction power for any one of these four models implies rejection of Fama’s (1970)

weak-form EMH. In addition, an effective FX prediction model may be used in practice to profit fromcurrency trading. Market microstructure theory predicts that PV1 should work less well than the othermodels do. This is implied from the findings of Bloomfield et al. (2005) and Goettler et al. (2009), whoinformed that traders in an electronic order-driven market are more likely to exploit their informationadvantage by submitting bid and ask limit orders than by submitting market orders. There are manymore bid and ask limit orders in our data than there are market orders, which means the time gapbetween the arrival of a bid or ask limit order will be nearer the end of each sample interval, on average.Greater information content and greater recency suggest that bid and ask limit order prices shouldprove to be important factors for predicting exchange rates at high sampling frequencies.

3. EMPIRICAL RESULTS

Table 1 presents the in-sample and out-of-sample exchange rate return prediction accuracy using differ-ent combinations of predicting variables (PV1, PV2, PV3 and PV4). The returns are the average returnduring one period spanning 1 min, or 5 min, or 60 min. These results show that our ANN model has hit

Table I. The in-sample and out-of-sample FX rate return direction accuracy using different combination ofpredicting variables

PV1 FX rate return direction accuracy (%)JPY–USD DEM–USD USD–EUR

In sample Out of sample In sample Out of sample In sample Out of sample

1 min intervalPV1 90.6 55.5 77.9 53.1 79.2 51.8PV2 91.5 56.5 81.0 64.5 82.3 63.0PV3 90.5 55.6 82.5 62.5 83.1 61.5PV4 81.9 61.8 81.9 62.6 82.3 61.6



1The different combinations of predicting variables are as follows.PV1, without bid–ask prices: rt, rt�1, . . ., rt�3, hight, lowt, averaget, oft, vlt;PV2, without order flow: rt, rt�1,. . ., rt�3, hight, lowt, averaget, vlt, bidt, askt;PV3: without volume: rt, rt�1, . . ., rt�3, hight, lowt, averaget, oft, bidt, askt;PV4, includes all variables: rt, rt�1, . . ., rt�3, hight, lowt, averaget, oft, vlt, bidt, askt.



rates for out-of-sample forecasting that are statistically better for all exchange rates than pure luck orchance of 50%.For the JPY–USD exchange rate returns at 1 min intervals in Table 1, when the bid and ask prices are

excluded from the variables (PV1) to predict the next minute’s return, the out-of-sample directionalcorrectness for the prediction is 55.5%, which is higher than the average 50%, although the in-sampledirectional accuracy is high at 90.6%. However, when we add the current bid and ask prices, theprediction accuracy increases significantly. For example, in the out-of-sample period including thebid and ask prices but excluding the previous order flow from the variables (PV2), the directionalcorrectness increases to 56.5%. Similarly, without the trading volume (PV3), the directional correctnessis 55.6%. With all the prediction variables (PV4), the directional correctness is 61.8%. The results forDEM–USD and EUR–USD are similar to those of JPY–USD. Those with bid and ask prices in thepredicting variables (PV2, PV3, PV4) perform better that those without bid and ask prices (PV1). Thisis true for both in-sample and out-of-sample periods.The results of the predicting power at 5 min intervals in Table 1 are significantly improved compared

with those at 1 min prediction. This is especially true for the out-of-sample period. Using differentcombinations of predicting variables, the out-of-sample directional correctness is around or above70% for all three exchange rate returns, although the predicting power drops slightly when there areno bid and ask prices in the predicting variables. For both JPY–USD and DEM–USD the predictionsat 60 min (Table 1) are similar to those at 5 min rolling. The directional correctness for the predictionsis above 70% for both in-sample and out-of-sample for all the predicting variable combinations PV1,PV2, PV3 and PV4. The prediction directional correctness for EUR–USD is slightly lower than thatof JPY–USD and DEM–USD, though it is still above 60% for all the combinations of predictingvariables. In most cases once again, excluding the bid and ask prices in the predicting variables(PV1) provides the weakest result. No model specification is clearly dominant over the others forintraday FX forecasting across the three frequency intervals tested. However, the 5 min intervalanalysis produces the best out-of-sample results in most cases. Within the 5 min interval analysis, wefind that different model specifications work best for each exchange rate.In terms of out-of-sample performance, the weakest models are all within the 1 min forecast horizon

category. This is likely to be due, at least in part, to microstructure noise. Across all out-of-sampleresults, the PV1 model variant, which excludes bid and ask prices, performs worst in seven out of ninecases. Indeed, the overall bottom three model out-of-sample performances are all PV1 at the 1 minforecast horizon. The top-performing model out of sample, which has the best predictive accuracy infive out of the nine cases, was PV2, which includes bid and ask prices and volume. It is puzzling thatwhen we add order flow, both alongside volume (PV4) and on its own (PV3), out-of-sample predictiveaccuracy declines in most cases. This may suggest that the order flow variable introduces more noisethan information into the model at these high frequencies. What is evident from the preceding is thatno simple rule of thumb or linear model could approximate the ANN result. This is not surprising.As Johnson et al. (2006) concluded, simple linear forecast relationships are too easily observed andarbitraged away, but nonlinear combinations of variables and complex interactions between variablesare much harder to observe and, hence, much harder to arbitrage away. We believe that this is whatour results reveal. It should be noted that all of our model variants exhibit high predictive ability atall time horizons, both in sample and out of sample, which constitutes evidence against the weak formof EMH. That fact means that the core variables common to all our model variants (i.e. lagged returns,along with high, low and average trade prices from market orders) are important drivers of return atthese frequencies in our ANN model, and that bid and ask limit order prices contain additionalinformation which boosts forecast accuracy.


T. CHOUDHRY ET AL.

Figures 1 and 2 display the theoretical accumulated wealth increase using an ANN and buy and hold(based on uncovered interest rate parity2) investment strategies, with and without trading costs. Theaccumulated wealth is based on one unit of base currency invested; that is, one US dollar for theDEM–USD and JPY–USD pairs, and one euro for the USD–EUR pair. Using the ANN strategy, attime t, if the predicted return at t + 1 is positive or positive after considering the trading cost, the basecurrency is kept or the foreign currency is sold; and if the predicted return at t + 1 is negative ornegative after considering the trading cost, the foreign currency is kept or the base currency is sold.Figure 1 displays the wealth increase within 1 month based on the base currency value, at 1 min

predicting frequency. Assuming no trading cost, using the ANN strategy, an investor can obtain156%, 91% and 76% profit in the JPY–USD, DEM–USD and USD–EUR markets respectively. Whenthere is trading cost, using the ANN strategy, the profit is 25%, 25% and 6% respectively comparedwith only 9%, 2% and 0% using a simple buy-and-hold strategy.Figure 2 gives the accumulated wealth increase within 1 month using an ANN and buy-and-hold

strategy at 5 min predicting frequency. Without trading cost, the ANN strategy gives 74%, 37% and32% profit in the JPY–USD, DEM–USD and USD–EUR markets respectively. With trading cost, usingthe ANN strategy, the profit is 35%, 18% and 11% respectively, compared with only 8%, 2% and 1%using a buy-and-hold strategy.

4. CONCLUSION

We applied an ANN to predict high-frequency returns in the currency market. The data used in thisstudy are per-second spot FX observations provided by EBS. Our out-of-sample results show that ex-change rates are forecastable at short time horizons using current available information of returns, bidprices, ask prices, transaction prices and trading volume. The practitioners to whom this is relevantmust have an ability to use such short-term forecasts. The practitioners who fit that bill are currencytraders working for banks and specialist currency funds. There are no obvious implications or applica-tions for our model for market regulation or government policy objectives. The implications of ourwork for academic research are broader. First, our results are evidence against the weak form of theEMH. Second, we confirm predictions from market microstructure theory (Goettler et al., 2009) andexperimental analysis (Bloomfield et al., 2005), namely that bid and ask spreads contain informationbeyond that contained in transaction prices alone. Third, where previous machine-learning research intoexchange rate forecastability has tended to focus on comparatively low-frequency data (e.g. Chen andLeung, 2004; Gradojevic and Yang, 2006; Gradojevic, 2007; Huang et al., 2007), we show that veryhigh frequency, intraday exchange rate forecasting is a potentially fruitful avenue for machine-learningresearchers to pursue.

ACKNOWLEDGEMENTS

We thank the seminar participants at the 16th International Conference ‘Forecasting FinancialMarkets’, 2009, Luxembourg. Any remaining errors and omission are our responsibility alone.

2According to the uncovered interest rate parity relationship, the spot exchange rate should move over time at a rate determined bythe interest rate differential between the two countries. The currency with the higher interest rate should depreciate over time rela-tive to the lower interest rate country.


DEM-USD

ANN, tc=0 ANN, tc=s/2 Buy&hold

1.91

1.02

1.25

USD-EUR


1.76

1.00

1.06

0.5

1

1.5

2

2.5

0.5

1

1.5

2

2.5

980803 980806 980812 980818 980824 980828 980902

990802 990806 990812 990818 990824 990830 990903

b. One dollar investment in the DEM-USD market

c. One dollar investment in the USD-EUR market

a. One dollar investment in the JPY-USD market

Figure 1. The growth of cumulative wealth for one unit of base currency at 1 min predicting frequency: (a) $1investment in the JPY–USD market; (b) $1 investment in the DEM–USD market; (c) $1 investment in the

USD–EUR market.



JPY-USD

980803 980806 980812 980817 980821 980826 980901 980904


1.74

1.08

1.35

DEM-USD

980803 980806 980812 980817 980821 980826 980831 980904


1.37

1.02

1.18

USD-EUR

990802 990805 990811 990816 990820 990825 990831 990903


1.32

1.01

1.11

0.5

1

1.5

2

2.5

0.5

1

1.5

2

2.5

0.5

1

1.5

2

2.5

b. One dollar investment in the DEM-USD market

c. One dollar investment in the USD-EUR market

a. One dollar investment in the JPY-USD market

Figure 2. The growth of cumulative wealth for one unit of base currency investment at 5 min frequency: (a) $1investment in the JPY–USD market; (b) $1 investment in the DEM–USD market; (c) $1 investment in the

USD–EUR market.

T. CHOUDHRY ET AL.



REFERENCES

Bloomfield R, O’Hara M, Saar G. 2005. The ‘make or take’ decision in an electronic market: evidence on theevolution of liquidity. Journal of Financial Economics 75: 165–200.

Bollerslev T, Melvin M. 1994. Bid–ask spreads and volatility in the foreign exchange market: an empiricalanalysis. Journal of International Economics 36(3–4): 355–372.

Chen A, Leung M. 2004. Regression neural network for error correction in foreign exchange forecasting andtrading. Computers and Operations Research 31: 1049–1068.

Engel C, West KD. 2005. Exchange rates and fundamentals. Journal of Political Economy 113: 485–517.Evans M, Lyons R. 2002. Order flow and exchange rate dynamics. Journal of Political Economy 110(1): 170–180.Fama EF. 1970. Efficient capital markets: a review of theory and empirical work. Journal of Finance 25(2): 383–417.Flood M. 1994. Market structure and inefficiency in the foreign exchange market. Journal of International Money

and Finance 13(2): 131–158.Flood M, Rose A. 1995. Fixed exchange rates: a virtual quest for fundamentals. Journal of Monetary Economics

36: 3–37.Froot K, Ramadorai T. 2005. Currency returns, intrinsic value and institutional investor flows. Journal of Finance

60: 1535–1566.Goettler R, Parlour C, Rajan U. 2009. Informed traders and limit order markets. Journal of Financial Economics 93

(1): 67–87.Gradojevic N. 2007. Non-linear, hybrid exchange rate modeling and trading profitability in the foreign exchange

market. Journal of Economic Dynamics & Control 31: 557–574.Gradojevic N, Yang J. 2006. Non-linear, non-parametric, nonfundamental exchange rate forecasting, Journal of

Forecasting 25: 227–245.Huang W, Lai KK, Nakamori Y, Wang SY, Yu LA. 2007. Neural networks in finance and economics forecasting,

International Journal of Information Technology and Decision Making 6(1): 113–140.Johnson JEV, Jones O, Tang L. 2006. Exploring decision makers’ use of price information in a speculative market.

Management Science 52(6): 897–908.MacDonald R, Marsh I. 1997. On fundamentals and exchange rates: a Casselian perspective. Review of Economics

and Statistics 79: 655–664.Mark N. 1995. Exchange rates and fundamentals: evidence on long-horizon predictability. American Economic

Review 85: 210–218.Meese RA, Rogoff KS. 1983. Empirical exchange rate models of the seventies: do they fit out of sample? Journal

of International Economics 14: 3–24.Yu L, Wang S, Lai KK. 2007. Foreign Exchange Rate Forecasting with Artificial Neural Networks. Springer.


high-frequency exchange-rate prediction with an artificial neural network

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