The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series

TL;DR

The paper introduces the cross-quantilogram, a new statistical tool for measuring quantile dependence and directional predictability between time series, with applications in finance and systemic risk analysis.

Contribution

It develops the asymptotic theory for the cross-quantilogram and proposes bootstrap and self-normalized methods for inference, advancing quantile dependence testing.

Findings

Detects predictability from stock variance to excess returns

Provides a more complete relationship between predictors and stock returns

Analyzes systemic risk of major financial institutions

Abstract

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.