A quantilogram approach to evaluating directional predictability

In this note we propose a simple method of measuring directional predictability and testing for the hypothesis that a given time series has no directional predictability. The test is based on the correlogram of quantile hits. We provide the distribution theory needed to conduct inference, propose some model free upper bound critical values, and apply our methods to stock index return data. The empirical results suggest some directional predictability in returns, especially in mid-range quantiles like 5%-10%.