A Comparison of Seasonal Adjustment Methods When Forecasting Intraday Volatility

Abstract

In this article we compare volatility forecasts over a thirty-minute horizon for the spot exchange rates of the Deutsche mark and the Japanese yen against the U.S. dollar. Explicitly modeling the intraday seasonal pattern improves the out-of-sample forecasting performance. We find that a seasonal estimated from the log of squared returns improves with the use of simple squared returns, and that the flexible Fourier form (FFF) is an efficient way of determining the seasonal. The two-step approach that first estimates the seasonal using the FFF and then the parameters of the generalized autoregressive conditional heteroskedasticity (GARCH) model for the deseasonalized returns performs only marginally worse than the computationally expensive periodic GARCH model that includes the FFF. Southern Finance Association and the Southwestern Finance Association.

Robust estimation of intraweek periodicity in volatility and jump detection

“…The RMSE of the ShortH, WSD, OLS and TML periodicity estimators is little affected by the inclusion of jumps in the price process. The robustness of the OLS estimator is surprising at first sight, but it corroborates Martens et al (2002)'s intuition that the log-transformation shrinks the outliers and makes the estimators based on a regression of the log absolute returns more robust to jumps. Note, however, that the TML estimator has a significantly lower RMSE than the OLS estimator in all simulations considered here.…”

“…In the simulation study of Section 2.3 we find that in particular the ML estimator has a large bias in the presence of jumps. Martens et al (2002)) mention that the effect of jumps on the OLS estimator is attenuated because the regression is based on the log of the standardized returns, but solely a log-transformation is not sufficient to attain robustness to jumps.…”

Bayesian non-parametric signal extraction for Gaussian time series

“…Some remarkable works on the subject are those by Andersen (2001), Martens et al (2002), Deo et al (2006) and Wongswan (2006).…”

Asymptotic inference of unstable periodic ARCH processes

“…Proposed by Bollerslev and Ghysels (1996), this class of models has paid particular attention in the recent statistical and econometric time series literature because it has proved suitable for modeling time series characterized by a conditional variance with periodic dynamic structure (e.g. Paap 2000, 2004;Ghysels and Osborn 2001;Taylor 2004Taylor , 2006Martens et al 2002;Aknouche and Bibi 2009). Most of the proposed estimating methods for these models are based on the quasi maximum likelihood (QML) method which provides asymptotically Gaussian estimates which are efficient in the case of conditional normality (Francq and Zakoïan 2004;Aknouche and Bibi 2009).…”