Forecasting exchange rate volatility using high-frequency data: Is the euro different?

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<ul><li><p>.t</p><p>i</p><p>it,Abstract</p><p>We assess the performances of alternative procedures for forecasting the daily volatility of the euros bilateral exchange ratesusing 15 min data. We use realized volatility and traditional time series volatility models. Our results indicate that using high-frequency data and considering their long memory dimension enhances the performance of volatility forecasts significantly.We find that the intraday FIGARCH model and the ARFIMA model outperform other traditional models for all exchange rateseries.c 2011 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.</p><p>Keywords: Euro exchange rates; Volatility forecasting; High-frequency data; GARCH model; Long memory time series; Forecast evaluation</p><p>1. Introduction</p><p>Volatility forecasting of asset prices in general, andexchange rates in particular, has been the focus ofresearch in areas such as investment analysis, deriva-tive securities pricing and risk management. More-over, since the volatility of financial markets has a</p><p> Corresponding author. Tel.: +86 0 574 88180200; fax: +86 0574 88180125.</p><p>E-mail addresses: gchortar@econ.uoa.gr (G. Chortareas),ying.jiang@nottingham.edu.cn (Y. Jiang), jcnank@essex.ac.uk(J.C. Nankervis).</p><p>1 Tel.: +30 210 3689805; fax: +30 210 3689810.2 Tel.: +44 0 1206 873973; fax: +44 0 1206 873429.</p><p>direct influence on policymaking, volatility forecastscan play the role of a barometer for the vulnera-bility of financial markets and the economy (Poon&amp; Granger, 2003). Poon and Granger (2003) review93 papers in the volatility forecasting field and showthat different models for forecasting the exchange ratevolatility perform differently for different currencies.In this paper we evaluate the daily volatility fore-casting performances of alternative models for euroexchange rates using high-frequency data.</p><p>Until quite recently, the literature typically focusedon daily returns for forecasting the daily volatility,and used the daily squared returns as a measure ofthe true volatility. However, daily squared returns</p><p>0169-2070/$ - see front matter c 2011 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.doi:10.1016/j.ijforecast.2010.07.003Available online at www</p><p>International Journal of Forecas</p><p>Forecasting exchange rate volatilthe euro d</p><p>Georgios Chortareasa,1, Ying J</p><p>a Department of Economics, Universb Nottingham University Business School China, University of No</p><p>c Essex Business School, University of Essexsciencedirect.com</p><p>ing 27 (2011) 10891107www.elsevier.com/locate/ijforecast</p><p>ty using high-frequency data: Isifferent?</p><p>iangb,, John. C. Nankervisc,2</p><p>ty of Athens, Athens, 10559, Greecetingham Ningbo, 199 Taikang East Road, Ningbo 315100, ChinaWivenhoe Park, Colchester, CO4 3SQ, UK</p></li><li><p>u1090 G. Chortareas et al. / International Jo</p><p>are not an accurate measure of the true volatility,since they are calculated from closing prices andtherefore cannot capture price fluctuations during theday (see Andersen &amp; Bollerslev, 1998). In responseto these limitations, Andersen and Bollerslev (1998)propose the realized volatility (constructed fromintraday returns) as a measure of the true volatility,and this measure has since become very popular.High-frequency data carry more information on dailytransactions, and are useful not only in measuringvolatility, but also in direct model estimation andforecast evaluation. Many recent methodologicaladvances focus on high-frequency data,3 while anumber of studies build on this literature to evaluatethe performance of alternative models for volatilityforecasting.4</p><p>While there exist a number of studies on foreignexchange volatility forecasting,5 as is discussed inSection 2, to the best of our knowledge, limitedwork has been done on forecasting the volatility ofeuro exchange rates. Since its introduction in 1999,the euro has become a major international currency,quickly establishing itself as the second most widelyused international currency after the US dollar.6</p><p>Nevertheless, the literature on exchange rate volatilityforecasting focuses on USD exchange rates alone.</p><p>Our study addresses this gap in the literature byproviding a characterization of the euros exchangerate volatility at both the daily and intraday frequen-cies, and considers questions such as: Are the samemodels appropriate for the euro exchange rate as forthe USD exchange rate? Do high-frequency euro ex-change rates have properties similar to those of otherhigh-frequency data? Can a long memory factor im-prove the performance of exchange rate volatility fore-casting?</p><p>3 Examples of this type of analysis include the use of longmemory ARFIMA (Autoregressive Fractional Integration MovingAverage) models for forecasting the realized volatility (e.g., Pong,Shackleton, Taylor, &amp; Xu, 2004), extending the daily model toinclude intraday information (e.g., Koopman, Jungbacker, &amp; Hol,2005) and the direct modelling of intraday returns using standardvolatility models (e.g., Marlik, 2005).</p><p>4 For example, see Andersen, Bollerslev, Diebold, and Labys(2003, ABDL hereafter), Hol and Koopman (2002), Martens (2001)and Martens and Zein (2004).</p><p>5 Examples include Andersen and Bollerslev (1998), Andersen,Bollerslev, Diebold, and Labys (1999, 2000, 2003), Martens (2001),Vilasuso (2002) and West and Cho (1995).</p><p>6 European Central Bank (1999).rnal of Forecasting 27 (2011) 10891107</p><p>To answer these questions we compare the out-of-sample daily volatility forecast performances oftraditional time series volatility models with that ofa realized volatility model at high frequencies. Thetraditional time series volatility models consideredinclude the GARCH model, the stochastic volatility(SV) model, the stochastic volatility with exogenousvariables (SVX) model, and finally, the fractionallyintegrated GARCH (FIGARCH) model. The realizedvolatility model is an ARFIMA model.7,8 Wecompare the performances of the two types of longmemory models (FIGARCH and ARFIMA) usinghigh-frequency data. We also compare the propertiesof the intraday GARCH and FIGARCH models withthose of ARFIMA models which use the daily realizedvolatility. Finally, we compare the intraday GARCHmodel with the intraday FIGARCH model to provideevidence on whether modelling the long memoryproperty in a high-frequency volatility process canimprove the daily forecast performance.</p><p>For the intraday GARCH and FIGARCH modelswe use deseasonalized 15 min data on returns for a pe-riod covering almost four years. We thus obtain a verylarge number of observations relative to other studiesthat apply standard volatility models to intraday re-turns (e.g., Beltratti &amp; Morana, 1999; Marlik, 2005;Martens, 2001; Rahman &amp; Ang, 2002). Marlik (2005),for example, uses 30 min data covering a period of fourmonths.</p><p>We employ a battery of tests to evaluate the out-of-sample forecast performances of the models con-sidered. In addition to the regression test and theaccuracy test, we also use the superior predictiveability test (Hansen, 2005) and an equal accuracytest, namely the adjusted Diebold-Mariano (1995)test. The results of these tests show that the intradayFIGARCH model always outperforms other tradi-tional models, and produces results that are notsignificantly different to those from the realizedvolatility (ARFIMA) model. This is not atypical of the</p><p>7 The ARFIMA model is fitted to the daily realized volatility. TheGARCH and FIGARCH models are both fitted to deseasonalized15 min returns. The GARCH, SV and SVX models are also fitted todaily returns.</p><p>8 This paper focuses on the ARFIMA model alone. Other newlydeveloped realized volatility models include the HeterogeneousAutoregressive (HAR) model (Corsi, 2009) and the Mixed DataSampling (MIDAS) model (Ghysels, Sinko, &amp; Valkanov, 2007).</p></li><li><p>lG. Chortareas et al. / International Journa</p><p>outcomes of previous research (see Hol &amp; Koopman,2002; Martens &amp; Zein, 2004; Pong et al., 2004, etc.).</p><p>Our findings suggest that the use of high-frequencydata enhances the performance of daily volatility fore-casting. Moreover, the forecasting accuracy is im-proved further when the long memory property istaken into account explicitly (i.e., comparing the in-traday FIGARCH with GARCH models). We alsofind that the performance levels of the daily GARCHmodel and the SV models are different across the cur-rencies considered.</p><p>The remainder of the paper is arranged as follows.Section 2 reviews some of the main findings and cur-rent arguments in the volatility forecasting literature.Section 3 focuses on the data and methodology usedin this paper. Section 4 discusses forecast evaluationmethods. Section 5 evaluates the estimation results andcompares the out-of-sample forecast performances ofthe models. Finally, Section 6 concludes.</p><p>2. Literature review</p><p>The literature on volatility forecasting applied tohigh-frequency data includes, but is not limited to,studies of the realized volatility, model comparisonsusing high-frequency versus daily data, assessments ofthe standard volatility model at high frequencies, andthe data properties of specific assets/series.</p><p>Since the true volatility is unobservable, dailysquared returns are popularly used in the literatureas a measure of volatility. Andersen and Bollerslev(1998) suggest that the realized volatility is a more ac-curate proxy of the true volatility. Using 5 min dataas a new volatility measure, they demonstrate a dra-matic improvement in the volatility forecasting per-formance of a daily GARCH model. A number offurther studies have since focussed on realized vola-tility forecasting and its properties. Andersen, Boller-slev, Diebold, and Labys (ABDL hereafter) (1999)recommend the ARFIMA model for forecasting therealized volatility, and further show that the realizedvolatility is a consistent estimator of the integratedvolatility (ABDL, 2001). Applying the ARFIMAmodel to exchange rates, ABDL (2001) show thatthe realized volatility can improve forecasting if itis modelled by a parametric model directly, ratherthan simply being used in the evaluation of othermodels forecasting behaviours. The findings of theof Forecasting 27 (2011) 10891107 1091</p><p>above studies constitute the theoretical basis for usingthe realized volatility in exchange rate volatility fore-casting directly. Furthermore, ABDL (2003) proposea long memory Gaussian vector autoregressive pro-cess (VAR) for modelling and forecasting the realizedvolatility, and produce strong evidence that the VAR-RV model outperforms the other candidate models.</p><p>A second strand in the literature considers the ad-vantages of using high-frequency data and comparesvolatility forecasts using intraday data with those us-ing daily data, as well as those from the option-implied volatility model. Martens (2001) comparesdaily exchange rate volatility forecasts, constructedfrom multiple volatility forecasts of intraday intervals,with forecasts from a daily model and a daily modelextended by an intraday information term. He findsthat the higher the intraday frequency used, the betterthe out-of-sample daily volatility forecasts. The dailymodel, which includes the realized volatility as an ex-planatory variable, displays a similar performance tothose of models using only intraday exchange ratereturns. Martens and Zein (2004) produce evidenceshowing that high-frequency data can improve boththe measurement accuracy and the forecasting per-formance. In addition, they show that long memorymodels improve the forecasting performance. Hol andKoopman (2002) compare the predictive powers ofrealized volatility models and daily time-varyingvolatility models using the S&amp;P100 stock index. Theresults of the out-of-sample evaluation indicate that anARFIMA model fitted to the realized volatility givesthe most accurate forecasts. Pong et al. (2004) com-pare exchange rate volatility forecasts obtained froman option implied volatility model, a short memorymodel (ARMA), a long memory model (ARFIMA)and a daily GARCH model. They find that the mostaccurate volatility forecasts are generated using high-frequency returns rather than a long memory specifi-cation.</p><p>Naturally, one question that arises is whether thestandard models are still valid when using high-frequency returns. There is plenty of evidence testify-ing to the performance of the realized volatility. Never-theless, there is still scope for a further examination ofwhether traditional time series models can capture theproperties of high-frequency data and provide a goodfit for the intraday returns series. No consensus onthis issue has yet been reached. For example, Rahman</p></li><li><p>u1092 G. Chortareas et al. / International Jo</p><p>and Ang (2002) show that the intraday volatility canbe described best by a standard GARCH(1, 1) model,while Jones (2003), based on simulation results, sug-gests that standard time series models cannot capturethe intraday exchange rate returns generating processsuccessfully at frequencies higher than 24 h.</p><p>Finally, another set of studies considers the proper-ties of high-frequency data for specific markets. Theliterature discussed above focuses on high-frequencyexchange rate returns in developed financial mar-kets. Some of their stylized properties include firstorder negative autocorrelation, non-normal distribu-tions, an increasing fat tail with an increasing fre-quency, and periodicity (Dacorogna, Gencay, Muller,Olsen, &amp; Pictec, 2001). Other authors who haveconsidered developing/emerging markets have foundthat high-frequency returns series display featureswhich are consistent with the above stylized properties(e.g., Barbosa, 2002; Kayahan &amp; Stengos, 2002).</p><p>However, limited evidence exists on forecasting theeuro exchange rate volatility and on how the alterna-tive models perform this task. Heaney and Pattenden(2005) evaluate the change in unconditional variancesfor the euro/GBP and euro/USD exchange rates during2002 and 2003. Clements, Galvao, and Kim (2008) ex-amine quantile forecasts of the daily exchange rate re-turns of five currencies versus the USD, including theeuro. Bauwens and Sucarrat (2010) evaluate modelsof weekly NOK/euro exchange rate volatility forecaststhat are generated by applying a general-to-specificeconometric methodology. Marlik (2005) models thevolatility of the USD against the euro and GBP usingGARCH, FIGARCH, and SV models. This paper con-tributes to this body of literature by focusing on theeuros daily volatility forecasting at high frequenciesand comparing the performances of competing mod-elling frameworks.</p><p>3. Data and estimation methodology</p><p>3.1. Data, properties and the stylized facts</p><p>The original data sets we use are 5 min interval spotforeign exchange rates of the euro against the Swissfranc (CHF), the UK pound (GBP), the Japanese yen(JPY) and the US dollar (USD), provided by Olsen andAssociates. These are the major currencies in termsof trading volume, accounting for over 85% of allrnal of Forecasting 27 (2011) 10891107</p><p>foreign exchange transactions. Since the CHF, GBPand JPY are all direct trading currencies, we avoidusing cros...</p></li></ul>

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