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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.

References

REFERENCES

Basrak, B., Davis, R. A., & Mikosch, T. (2002) Regular variation of GARCH processes. Stochastic Processes and Their Applications 99(1), 95–115.CrossRefGoogle Scholar
Bingham, N. H., Goldie, C. M., & Teugels, J. L. (1989) Regular Variation, Vol. 27. Cambridge University Press.Google Scholar
Blattberg, R. & Sargent, T. (1971) Regression with non-Gaussian stable disturbances: Some sampling results. Econometrica 39(3), 501–510.CrossRefGoogle Scholar
Breiman, L. (1965) On some limit theorems similar to the arc-sin law. Theory of Probability and Its Applications 10(2), 323–331.CrossRefGoogle Scholar
Breusch, T., Robertson, J., & Welsh, A. (1997) The emperor’s new clothes: A critique of the multivariate t regression model. Statistica Neerlandica 51(3), 269–286.CrossRefGoogle Scholar
Embrechts, P. & Goldie, C. M. (1980) On closure and factorization properties of subexponential and related distributions. Journal of the Australian Mathematical Society 29(2), 243–256.CrossRefGoogle Scholar
Feller, W. (1971) Introduction to Probability Theory and Its Applications, Vol. II. Wiley.Google Scholar
Han, C., Cho, J. S., & Phillips, P. C. (2011) Infinite density at the median and the typical shape of stock return distributions. Journal of Business & Economic Statistics 29(2), 282–294.CrossRefGoogle Scholar
He, X., Jurečková, J., Koenker, R., & Portnoy, S. (1990) Tail behavior of regression estimators and their breakdown points. Econometrica 58(5), 1195–1214.CrossRefGoogle Scholar
Hotelling, H. (1953) New light on the correlation coefficient and its transforms. Journal of the Royal Statistical Society. Series B (Methodological) 15(2), 193–232.CrossRefGoogle Scholar
Jansen, D. W. & de Vrie, C. G. (1991) On the frequency of large stock returns: Putting booms and busts into perspective. The Review of Economics and Statistics 73(1), 18–24.CrossRefGoogle Scholar
Mikosch, T. & de Vries, C. G. (2013) Heavy tails of OLS. Journal of Econometrics 172(2), 205–221.CrossRefGoogle Scholar
Potter, H. (1942) The mean values of certain Dirichlet series, II. Proceedings of the London Mathematical Society 2(1), 1–19.CrossRefGoogle Scholar
Qin, H. & Wan, A. T. (2004) On the properties of the t-and F-ratios in linear regressions with nonnormal errors. Econometric Theory 20(4), 690–700.CrossRefGoogle Scholar
Resnick, S. I. (2007) Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. Springer Science & Business Media.Google Scholar
van Oordt, M. (2013) On extreme events in banking and finance. PhD thesis, Tinbergen Institute.Google Scholar