Tail Index Estimation: Quantile Driven Threshold Selection

74 Pages Posted: 18 Jan 2016

See all articles by Jon Danielsson

Jon Danielsson

London School of Economics - Systemic Risk Centre

Lerby Murat Ergun

Bank of Canada; London School of Economics & Political Science (LSE)

Laurens de Haan

Erasmus University Rotterdam (EUR) - Department of Econometrics

Casper G. de Vries

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE); Tinbergen Institute; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: January 2016

Abstract

The selection of upper order statistics in tail estimation is notoriously difficult. Most methods are based on asymptotic arguments, like minimizing the asymptotic mse, that do not perform well in finite samples. Here we advance a data driven method that minimizes the maximum distance between the fitted Pareto type tail and the observed quantile. To analyse the finite sample properties of the metric we organize a horse race between the other methods. In most cases the finite sample based methods perform best. To demonstrate the economic relevance of choosing the proper methodology we use daily equity return data from the CRSP database and find economic relevant variation between the tail index estimates.

Keywords: Hill estimator, Heavy tails, Optimal extreme sample fraction

JEL Classification: G32

Suggested Citation

Danielsson, Jon and Ergun, Lerby Murat and de Haan, Laurens and De Vries, Casper, Tail Index Estimation: Quantile Driven Threshold Selection (January 2016). Available at SSRN: https://ssrn.com/abstract=2717478 or http://dx.doi.org/10.2139/ssrn.2717478

Jon Danielsson

London School of Economics - Systemic Risk Centre ( email )

Houghton Street
London WC2A 2AE
United Kingdom
+44.207.955.6056 (Phone)

HOME PAGE: http://www.riskreasearch.org

Lerby Murat Ergun (Contact Author)

Bank of Canada ( email )

234 Wellington Street
Ontario, Ottawa K1A 0G9
Canada

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

Laurens De Haan

Erasmus University Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Casper De Vries

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands
+31 10 408 8956 (Phone)
+31 10 408 9147 (Fax)

Tinbergen Institute

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands
+31 10 408 8956 (Phone)
+31 10 408 9147 (Fax)

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

HOME PAGE: http://www.CESifo.de

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