Are the directions of stock price changes predictable? A generalized cross-spectral approach

Using a generalized cross-spectral approach, we propose a model-free omnibus statistical procedure to check whether the direction of changes in an economic variable is predictable using the history of its past changes. A class of separate inference procedures are also given to gauge possible sources of directional predictability. They can reveal information about whether the direction of future changes is predictable using the direction, level, volatility, skewness, and kurtosis of past changes. An important feature of the proposed procedures is that they check many lags simultaneously, which is particularly suitable for detecting the alternatives whose directional dependence is small at each lag but it carries over a long distributional lag. At the same time, the tests naturally discount higher order lags, which is consistent with the conventional wisdom that financial markets are more influenced by the recent past events than by the remote past events. We apply the proposed procedures to four daily U.S. stock price indices. We find overwhelming evidence that the directions of excess stock returns are predictable using past excess stock returns, and the evidence is stronger for the directional predictability of large excess stock returns. In particular, the direction and level of past excess stock returns can be used to predict the direction of future excess stock returns with any threshold, and the volatility, skewness and kurtosis of past excess stock returns can be used to predict the direction of future excess stock returns with nonzero thresholds (i.e., large returns). The well-known strong volatility clustering together with weak serial dependence in mean cannot completely explain all documented directional predictability for stock returns. To exploit the economic significance of the documented directional predictability for stock returns, we consider a class of autologit models for directional forecasts and find that they have significant out-of-sample directional predictive power. Some trading strategies based on these models and their combinations can earn significant out-of-sample extra risk-adjusted returns over the buy-and-hold trading strategy