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We assess the performances of alternative procedures for forecasting the daily volatility of the euro’s bilateral exchange rates using 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 rate series.

Volatility forecasting of asset prices in general, and exchange rates in particular, has been the focus of research in areas such as investment analysis, derivative securities pricing and risk management. Moreover, since the volatility of financial markets has a direct influence on policymaking, volatility forecasts can play the role of a ‘barometer for the vulnerability of financial markets and the economy’ (Poon & Granger, 2003). Poon and Granger (2003) review 93 papers in the volatility forecasting field and show that different models for forecasting the exchange rate volatility perform differently for different currencies. In this paper we evaluate the daily volatility forecasting performances of alternative models for euro exchange rates using high-frequency data. Until quite recently, the literature typically focused on daily returns for forecasting the daily volatility, and used the daily squared returns as a measure of the ‘true volatility’. However, daily squared returns are not an accurate measure of the true volatility, since they are calculated from closing prices and therefore cannot capture price fluctuations during the day (see Andersen & Bollerslev, 1998). In response to these limitations, Andersen and Bollerslev (1998) propose the realized volatility (constructed from intraday returns) as a measure of the true volatility, and this measure has since become very popular. High-frequency data carry more information on daily transactions, and are useful not only in measuring volatility, but also in direct model estimation and forecast evaluation. Many recent methodological advances focus on high-frequency data,3 while a number of studies build on this literature to evaluate the performance of alternative models for volatility forecasting.4 While there exist a number of studies on foreign exchange volatility forecasting,5 as is discussed in Section 2, to the best of our knowledge, limited work has been done on forecasting the volatility of euro exchange rates. Since its introduction in 1999, the euro has become a major international currency, quickly establishing itself as the second most widely used international currency after the US dollar.6 Nevertheless, the literature on exchange rate volatility forecasting focuses on USD exchange rates alone. Our study addresses this gap in the literature by providing a characterization of the euro’s exchange rate volatility at both the daily and intraday frequencies, and considers questions such as: Are the same models appropriate for the euro exchange rate as for the USD exchange rate? Do high-frequency euro exchange rates have properties similar to those of other high-frequency data? Can a long memory factor improve the performance of exchange rate volatility forecasting? To answer these questions we compare the out-of-sample daily volatility forecast performances of traditional time series volatility models with that of a realized volatility model at high frequencies. The traditional time series volatility models considered include the GARCH model, the stochastic volatility (SV) model, the stochastic volatility with exogenous variables (SVX) model, and finally, the fractionally integrated GARCH (FIGARCH) model. The realized volatility model is an ARFIMA model.7,8 We compare the performances of the two types of long memory models (FIGARCH and ARFIMA) using high-frequency data. We also compare the properties of the intraday GARCH and FIGARCH models with those of ARFIMA models which use the daily realized volatility. Finally, we compare the intraday GARCH model with the intraday FIGARCH model to provide evidence on whether modelling the long memory property in a high-frequency volatility process can improve the daily forecast performance. For the intraday GARCH and FIGARCH models we use deseasonalized 15 min data on returns for a period covering almost four years. We thus obtain a very large number of observations relative to other studies that apply standard volatility models to intraday returns (e.g., Beltratti and Morana, 1999, Marlik, 2005, Martens, 2001 and Rahman and Ang, 2002). Marlik (2005), for example, uses 30 min data covering a period of four months. We employ a battery of tests to evaluate the out-of-sample forecast performances of the models considered. In addition to the regression test and the accuracy test, we also use the superior predictive ability test (Hansen, 2005) and an equal accuracy test, namely the adjusted Diebold-Mariano (1995) test. The results of these tests show that the intraday FIGARCH model always outperforms other traditional models, and produces results that are not significantly different to those from the realized volatility (ARFIMA) model. This is not atypical of the outcomes of previous research (see Hol and Koopman, 2002, Martens and Zein, 2004 and Pong et al., 2004, etc.). Our findings suggest that the use of high-frequency data enhances the performance of daily volatility forecasting. Moreover, the forecasting accuracy is improved further when the long memory property is taken into account explicitly (i.e., comparing the intraday FIGARCH with GARCH models). We also find that the performance levels of the daily GARCH model and the SV models are different across the currencies considered. The remainder of the paper is arranged as follows. Section 2 reviews some of the main findings and current arguments in the volatility forecasting literature. Section 3 focuses on the data and methodology used in this paper. Section 4 discusses forecast evaluation methods. Section 5 evaluates the estimation results and compares the out-of-sample forecast performances of the models. Finally, Section 6 concludes.

This paper considers daily volatility forecasts of various euro exchange rates using high-frequency data (15 min intervals), and examines the relative performances of alternative volatility forecasting models. We provide evidence to suggest that the traditional volatility model can be useful for volatility forecasting in high-frequency applications, provided that it captures the features of the intraday volatility successfully. We find that using a long memory specification in high-frequency data can improve the forecasting power and accuracy significantly, a result that corroborates the findings of ABDL (2001), Corsi (2009) and Martens and Zein (2004). This finding, however, is contrary to the existing literature, which suggests that the improvement in the forecasting performance comes only from the high frequency of the data (see Pong et al., 2004). Our results show that the intraday FIGARCH model produces forecasts which are as good as those from the ARFIMA model, and that they are jointly superior to all of the other models considered in most of the out-of-sample evaluation tests. The intraday GARCH model, which does not take the long memory property of volatility into account, produces unsatisfactory forecasts. The good performance of the ARFIMA model in this study is consistent with the literature on the dollar exchange rates, which suggests that the ARFIMA model is the best model for high-frequency applications (see Hol and Koopman, 2002 and Pong et al., 2004). The intraday FIGARCH model’s outstanding performance, however, is a somewhat surprising finding, given that the FIGARCH model has seldom been regarded as the preferred model in high-frequency applications. This finding challenges the view that the traditional volatility model cannot fit the data when focusing on higher frequencies. After deseasonalizing the raw returns of the euro exchange rates and modelling the long memory property, it emerges that the FIGARCH model can produce the same satisfactory forecast results as were obtained from the newly developed models. Thus, the traditional volatility model could also be an alternative for volatility forecasting in a high-frequency framework and should be considered along with the newer models. Analyzing the properties of the euro bilateral exchange rates, we find that they are consistent with the stylized properties of other financial series (stock market indices and other exchange rates) at high frequencies in many respects. This suggests that these properties are not specific to certain kinds of high-frequency data, but most probably reflect some general features that all such data share.