This paper proposes the cross-quantilogram to measure the quantile dependence between two time series. We apply it to test the hypothesis that one time series has no directional predictability to another time series. We establish the asymptotic distribution of the cross quantilogram and the...

We propose several multivariate variance ratio statistics. We derive the asymptotic distribution of the statistics and scalar functions thereof under the null hypothesis that returns are unpredictable after a constant mean adjustment (i.e., under the Efficient Market Hypothesis). We do not...

We propose an alternative Ratio Statistic for measuring predictability of stock prices. Our statistic is based on actual returns rather than logarithmic returns and is therefore better suited to capturing price predictability. It captures not only linear dependence in the same way as the...