Do We Need Stochastic Volatility and GARCH? Comparing Squared End-of-Day Returns on FTSE

Abstract

The paper examines the relative performance of Stochastic Volatility (SV) and GARCH(1,1) models fitted to ten years of daily data for FTSE. As a benchmark, we use the realized volatility (RV) of FTSE sampled at 5-minute intervals, taken from the Oxford Man Realised Library. Both models demonstrate comparable performance and are correlated to a similar extent with the RV estimates, when measured by OLS. However, a crude variant of Corsi's (2009) HAR model, applied to squared demeaned daily returns on FTSE, appears to predict the daily RV of FTSE better than either of the two models. Quantile regressions suggest that all three methods capture tail behaviour similarly and adequately. This leads to the question of whether we need either of the two standard volatility models, if the simple expedient of using lagged squared demeaned daily returns provides a better RV predictor, at least in the context of the sample.