Asymmetries in conditional mean and variance: Modelling stock returns by asMA-asQGARCH

The asymmetric moving average model (asMA) is extended to allow for asymmetric quadratic
conditional heteroskedasticity (asQGARCH). The asymmetric parametrization of the condi-
tional 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. Em-
pirical 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 condi-
tional variance functions. In a genuine out-of-sample forecasting experiment the performance
of the best ¯tted asMA-asQGARCH model is compared to pure asMA and no-change fore-
casts. This is done both in terms of conditional mean forecasting as well as in terms of risk
forecasting.