Test for the Existence of Finite Moments Via Bootstrap

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Abstract

This paper develops a bootstrap hypothesis test for the existence of finite moments of a random variable, which is nonparametric and applicable to both independent and dependent data. The test is based on a property in bootstrap asymptotic theory, in which the m out of n bootstrap sample mean is asymptotically normal when the variance of the observations is finite. Consistency of the test is established. Monte Carlo simulations are conducted to illustrate the finite sample performance and compare it with alternative methods available in the literature. Applications to financial data are performed for illustration.

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Key words

Central limit theorem,heavy tail,Hill estimator,Kolmogorov-Smirnov test,m out of n bootstrap

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