Testing for cross-quantilogram change

TL;DR

This paper introduces a bootstrap-based test to compare cross-quantilograms across two time periods, helping to detect changes in directional dependence between two time series while accounting for covariates.

Contribution

The paper proposes a novel bootstrap test for assessing the stability of cross-quantilograms over different time periods, extending Han's estimators for this purpose.

Findings

The test effectively detects changes in cross-quantilograms between periods.

Bootstrap approach provides accurate p-values for the test.

Method accounts for covariate effects in time series dependence.

Abstract

For two time series $\{ (Y_t, Z_t^Y) \}_{t}$ and $\{(X_t, Z_t^X)\}_{t}$, the directional dependence of $\{ X_t \}_{t}$ on $\{ Y_t \}_{t}$ while removing the impact of $Z_t^X$ on $X_t$ and the impact of $Z_t^Y$ on $ Y_t$ can be measured by cross-quantilograms. When the two time series are obeserved over two periods of time, it can be of interest to learn whether the cross-quantilograms remain the same for the two periods of time. We propose a test for this purpose, and the cross-quantilograms are estimated using the estimators proposed by Han (2016). The $p$-value of the proposed test is obtained based on a bootstrap approach.