Asymmetric Conditional Volatility Models: Empirical Estimation and Comparison of Forecasting Accuracy

This paper compares several statistical models for daily stock return volatility in terms of sample fit and out-of-sample forecast ability. The focus is on U.S. and Romanian daily stock return data corresponding to the 2002-2010 time interval. We investigate the presence of leverage effects in empirical time series and estimate different asymmetric GARCH-family models (EGACH, PGARCH and TGARCH) specifying successively a Normal, Student's t and GED error distribution. We find that GARCH family models with normal errors are not capable to capture fully the leptokurtosis in empirical time series, while GED and Student’s t errors provide a better description for the conditional volatility. In addition, we outline some stylized facts about volatility that are not captured by conventional ARCH or GARCH models, but are considered by the asymmetric models and document their presence in empirical time series. Finally, we report that volatility estimates given by the EGARCH model exhibit generally lower forecast errors and are therefore more accurate than the estimates given by the other asymmetric GARCH models.