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Testing for (in)finite moments

Trapani, Lorenzo

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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.

Journal Article Type Article
Publication Date Mar 1, 2016
Journal Journal of Econometrics
Print ISSN 0304-4076
Electronic ISSN 0304-4076
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 191
Issue 1
APA6 Citation Trapani, L. (2016). Testing for (in)finite moments. Journal of Econometrics, 191(1), https://doi.org/10.1016/j.jeconom.2015.08.006
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
Publisher URL http://www.sciencedirect.com/science/article/pii/S0304407615002596
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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