One of the approaches to compare forecasts is to test whether the loss from a benchmark prediction is smaller than the others. The test can be embedded into the general problem of testing functional inequalities using a one-sided Kolmogorov-Smirnov functional. This paper shows that such a test...

This paper considers the cross-quantilogram, which measures the quantile dependence between 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...

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...

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,...