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Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique

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  • McCulloch, J Huston

Abstract

A generalized Pareto or simple Pareto tail-index estimate above 2.0 has frequently been cited as evidence against infinite-variance stable distributions. It is demonstrated that this inference is invalid; tail index estimates greater than 2.0 are to be expected for stable distributions with alpha as low as 1.65. The nonregular distribution of the likelihood ratio statistic for a null of normality and an alternative of symmetric stability is tabulated by Monte Carlo methods and appropriately adjusted for sampling error in repeated tests. Real stock returns yield a stable alpha of 1.845 and reject iid normality at the 0.996 level.

Suggested Citation

  • McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
  • Handle: RePEc:bes:jnlbes:v:15:y:1997:i:1:p:74-81
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