Testing for cross-quantilogram change

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.

13 pages