Testing for (in)finite moments

Trapani, Lorenzo

Abstract

This paper proposes a test to verify whether the th moment of a random variable is finite. We use the fact that, under general assumptions, sample moments either converge to a finite number or diverge to infinity according as the corresponding population moment is finite or not. Building on this, we propose a test for the null that the th moment does not exist. Since, by construction, our test statistic diverges under the null and converges under the alternative, we propose a randomised testing procedure to discern between the two cases. We study the application of the test to raw data, and to regression residuals. Monte Carlo evidence shows that the test has the correct size and good power; the results are further illustrated through an application to financial data.

Citation

Trapani, L. (2016). Testing for (in)finite moments. Journal of Econometrics, 191(1), https://doi.org/10.1016/j.jeconom.2015.08.006

• Journal Article Type: Article
• Acceptance Date: Aug 31, 2015
• Online Publication Date: Oct 30, 2015
• Publication Date: Mar 1, 2016
• Deposit Date: Oct 3, 2017
• Publicly Available Date: Oct 3, 2017
• Journal: Journal of Econometrics
• Print ISSN: 0304-4076
• Electronic ISSN: 0304-4076
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 191
• Issue: 1
• DOI: https://doi.org/10.1016/j.jeconom.2015.08.006
• Keywords: Finite moments; Randomised tests; Chover-type Law of the Iterated Logarithm; Strong Law of Large Numbers
• Public URL: https://nottingham-repository.worktribe.com/output/978166
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0304407615002596