Stock return prediction under GARCH — An empirical assessment

The GARCH model and its numerous variants have been applied widely both in the financial literature and in practice. For purposes of quasi maximum likelihood estimation, innovations to GARCH processes are typically assumed to be identically and independently distributed, with mean zero and unit variance (strong GARCH). Under less restrictive assumptions (the absence of unconditional correlation, weak GARCH), higher order dependency patterns might be exploited for the ex ante forecasting of GARCH innovations, and hence, stock returns. In this paper, rolling windows of empirical stock returns are used to test the independence of consecutive GARCH innovations. Rolling p-values from independence testing reflect the time variation of serial dependence, and provide useful information for signaling one-step-ahead directions of stock price changes. Ex ante forecasting gains are documented for nonparametric innovation predictions, especially if the sign of the innovation predictors is combined with independence diagnostics (p-values) and/or the sign of linear return forecasts.