A Projective Approach to Conditional Independence Test for Dependent Processes

Yeqing Zhou, Yaowu Zhang and Liping Zhu

Journal of Business & Economic Statistics, 2022, vol. 40, issue 1, 398-407

Abstract: Conditional independence is a fundamental concept in many scientific fields. In this article, we propose a projective approach to measuring and testing departure from conditional independence for dependent processes. Through projecting high-dimensional dependent processes on to low-dimensional subspaces, our proposed projective approach is insensitive to the dimensions of the processes. We show that, under the common β-mixing conditions, our proposed projective test statistic is n-consistent if these processes are conditionally independent and root-n-consistent otherwise. We suggest a bootstrap procedure to approximate the asymptotic null distribution of the test statistic. The consistency of this bootstrap procedure is also rigorously established. The finite-sample performance of our proposed projective test is demonstrated through simulations against various alternatives and an economic application to test for Granger causality.

Date: 2022
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DOI: 10.1080/07350015.2020.1826952

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