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TAIL DEPENDENCE OF OLS

Published online by Cambridge University Press:  02 July 2021

Jochem Oorschot  and
Chen Zhou
Jochem Oorschot*
Affiliation:
Erasmus University Rotterdam Tinbergen Institute
Chen Zhou
Affiliation:
Erasmus University Rotterdam De Nederlandsche Bank Tinbergen Institute
*
Address correspondence to Jochem Oorschot, Department of Econometrics, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands; e-mail: [email protected].
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Abstract

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This paper shows that if the errors in a multiple regression model are heavy-tailed, the ordinary least squares (OLS) estimators for the regression coefficients are tail-dependent. The tail dependence arises, because the OLS estimators are stochastic linear combinations of heavy-tailed random variables. Moreover, tail dependence also exists between the fitted sum of squares (FSS) and the residual sum of squares (RSS), because they are stochastic quadratic combinations of heavy-tailed random variables.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 2 , April 2022 , pp. 273 - 300
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

Views expressed do not reflect the official position of De Nederlandsche Bank. We are grateful to two referees for their insightful comments.

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