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A Projective Approach to Conditional Independence Test for Dependent Processes

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  • Yeqing Zhou
  • Yaowu Zhang
  • Liping Zhu

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.

Suggested Citation

  • Yeqing Zhou & Yaowu Zhang & Liping Zhu, 2022. "A Projective Approach to Conditional Independence Test for Dependent Processes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 398-407, January.
    • Handle: RePEc:taf:jnlbes:v:40:y:2022:i:1:p:398-407
    DOI: 10.1080/07350015.2020.1826952
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    Cited by:

    1. Zhang, Yaowu & Zhou, Yeqing & Zhu, Liping, 2024. "A post-screening diagnostic study for ultrahigh dimensional data," Journal of Econometrics, Elsevier, vol. 239(2).

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