  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 corresponding
test statistic. The limiting distributions depend on nuisance parameters. To
construct consistent confidence intervals we employ the stationary bootstrap
procedure; we show the consistency of this bootstrap. Also, we consider the
self-normalized approach, which is shown to be asymptotically pivotal under the
null hypothesis of no predictability. We provide simulation studies and two
empirical applications. First, we use the cross-quantilogram to detect
predictability from stock variance to excess stock return. Compared to existing
tools used in the literature of stock return predictability, our method
provides a more complete relationship between a predictor and stock return.
Second, we investigate the systemic risk of individual financial institutions,
such as JP Morgan Chase, Goldman Sachs and AIG. This article has supplementary
materials online.
