T. Mikosch
http://repub.eur.nl/ppl/11153/
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RePub, Erasmus University RepositoryHeavy tails of OLS
http://repub.eur.nl/pub/37658/
Tue, 18 Sep 2012 00:00:01 GMT<div>T. Mikosch</div><div>C.G. de Vries</div>
Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving financial data. We derive explicit finite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium sized samples reveal considerable deviations of the coefficient estimates from their true values, in line with our theoretical formulas. The formulas provide a benchmark for judging the observed highly variable cross country estimates of the expectations coefficient in yield curve regressions. Tail Probabilities for Registration Estimators
http://repub.eur.nl/pub/8072/
Fri, 06 Oct 2006 00:00:01 GMT<div>T. Mikosch</div><div>C.G. de Vries</div>
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 relavant 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.