Tail Probabilities for Regression Estimators

Thomas Mikosch () and Casper G. de Vries ()
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Thomas Mikosch: University of Copenhagen

No 06-085/2, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: Estimators of regression coefficients are known to be asymptotically normally distributed, provided certain regularity conditions are satisfied. In small samples and if the noise is not normally distributed, this can be a poor guide to the quality of the estimators. The paper addresses this problem for small and medium sized samples and heavy tailed noise. In particular, we assume that the noise is regularly varying, i.e., the tails of the noise distribution exhibit power law behavior. Then the distributions of the regression estimators are heavy tailed themselves. This is relevant for regressions involving financial data which are typically heavy tailed. In medium sized samples and with some dependency in the noise structure, the regression coefficient estimators can deviate considerably from their true values. The relevance of the theory is demonstrated for the highly variable cross country estimates of the expectations coefficient in yield curve regressions.

Keywords: heavy tails; regression estimators; expectations hypothesis (search for similar items in EconPapers)
JEL-codes: C13 C16 C20 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2006-10-06
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Persistent link: http://EconPapers.repec.org/RePEc:dgr:uvatin:20060085

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