A generalized portmanteau test of independence between two stationary time series

TL;DR

This paper introduces generalized portmanteau tests in the frequency domain to assess independence between two stationary time series, accommodating various memory properties and demonstrating good statistical properties.

Contribution

It extends existing portmanteau tests to handle short, long, and anti-persistent memory in stationary time series, with asymptotic normality under mild conditions.

Findings

Tests have reasonable size and power.

Applicable to series with diverse memory properties.

Asymptotic normal distribution established.

Abstract

We propose generalized portmanteau-type test statistics in the frequency domain to test independence between two stationary time series. The test statistics are formed analogous to the one in Chen and Deo (2004, Econometric Theory 20, 382-416), who extended the applicability of portmanteau goodness-of-fit test to the long memory case. Under the null hypothesis of independence, the asymptotic standard normal distributions of the proposed statistics are derived under fairly mild conditions. In particular, each time series is allowed to possess short memory, long memory or anti-persistence. A simulation study shows that the tests have reasonable size and power properties.