Asymmetries in Conditional Mean and Variance: Modelling Stock Returns by asMA-asQGARCH

Abstract

The asymmetric moving average model (asMA) is extended to allow for asymmetric quadratic conditional heteroskedasticity (asQGARCH). The asymmetric parametrization of the conditional variance encompasses the quadratic GARCH model of Sentana (1995). We introduce a framework for testing asymmetries in the conditional mean and the conditional variance, separately or jointly. Some of the new model's moment properties are also derived. Empirical results are given for the daily returns of the composite index of the New York Stock Exchange. There is strong evidence of asymmetry in both the conditional mean and conditional variance functions. In a genuine out-of-sample forecasting experiment the performance of the best fitted asMA-asQGARCH model is compared to pure asMA and no-change forecasts. This is done both in terms of conditional mean forecasting as well as in terms of risk forecasting.