A simple nonparametric test for the existence of finite moments

Fedotenkov, Igor (2015): A simple nonparametric test for the existence of finite moments.

Abstract

This paper proposes a simple, fast and direct nonparametric test to verify if a sample is drawn from a distribution with a finite first moment. The method can also be applied to test for the existence of finite moments of another order by taking the sample to the corresponding power. The test is based on the difference in the asymptotic behaviour of the arithmetic mean between cases when the underlying probability function either has or does not have a finite first moment. Test consistency is proved; then, test performance is illustrated with Monte-Carlo simulations and a practical application for the S&P500 index.

• Item Type: MPRA Paper
• Language: English
• Keywords: Heavy tails, tail index, finite moment, test, consistency
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General

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