A Nonparametric Sequential Test with Power 1 for the Mean of Lévy-stable Laws with Infinite Variance

Abdelhakim Necir ()
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Abdelhakim Necir: Laboratory of Applied Mathematics

Methodology and Computing in Applied Probability, 2006, vol. 8, issue 3, 321-343

Abstract: Abstract A nonparametric sequential test with power one for the mean of Lévy-stable laws with infinite variance is given. Our considerations are based on a law of the iterated logarithm for Peng’s estimator [Peng, Stat. Probab. Lett., 52:255–264, 2001] of the mean of heavy-tailed distributions. Our main motivation comes from applications to financial data, and in particular to sequential control of daily asset returns.

Keywords: Heavy tails; Hill’s estimator; Lévy-stable law; Law of the iterated logarithm; Sequential test; Asset returns; Primary 62G32; Secondary 62G05; 62G20 (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s11009-006-9749-9

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