A note on the relationship between GARCH and symmetric stable processes

Patrick A. Groenendijk*, André Lucas, Casper G. de Vries

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


This note provides some explanations and extensions for the interesting results in Ghose and Kroner (1995). Specifically, we address the following points: (1) It is shown that the stable distribution and the stationary ARCH distributions are partially nested with respect to their tail shapes; (2) A novel interpretation of the McCulloch estimator is developed from the vantage point of extreme value theory; (3) This interpretation not only explains the apparent bias in some of the reported estimates, but it also helps in remedying the problem. Taken together, all three points reinforce the main conclusion of Ghose and Kroner.

Original languageEnglish
Pages (from-to)253-264
Number of pages12
JournalJournal of Empirical Finance
Issue number3
Publication statusPublished - 1995


  • Stable distributions
  • Tail index estimators


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