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

J. Huston McCulloch

Journal of Business & Economic Statistics, 1997, vol. 15, issue 1, 74-81

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.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:bes:jnlbes:v:15:y:1997:i:1:p:74-81

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