Heavy tails of OLS

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 probabilitie...

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Bibliographic Details
Published in:Journal of econometrics 2013-02, Vol.172 (2), p.205-221
Main Authors: Mikosch, Thomas, de Vries, Casper G.
Format: Article
Language:English
Subjects:
Benchmarks
Data analysis
Econometrics
Estimating techniques
Estimation
Heavy tails
OLS estimator distribution
Probability
Probability distribution
Regression analysis
Simulation
Small sample inference
Studies
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Summary: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.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2012.08.015