Statistics of Heteroscedastic Extremes

J.H.J. Einmahl, L.F.M. de Haan, C. Zhou

Research output: Working paperDiscussion paperOther research output

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Abstract

Abstract: We extend classical extreme value theory to non-identically distributed observations. When the distribution tails are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated nonparametrically along with the (common) extreme value index. Joint asymptotic normality of both estimators is shown; they are asymptotically independent. We develop tests for the proportionality function and for the validity of the model. We show through simulations the good performance of tests for tail homoscedasticity. The results are applied to stock market returns. A main tool is the weak convergence of a weighted sequential tail empirical process.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages25
Volume2014-015
Publication statusPublished - 2014

Publication series

NameCentER Discussion Paper
Volume2014-015

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Statistics
Proportionality
Stock market returns
Simulation
Extreme values
Extreme value theory
Estimator
Empirical process
Weak convergence
Asymptotic normality
Extreme value statistics

Cite this

Einmahl, J. H. J., de Haan, L. F. M., & Zhou, C. (2014). Statistics of Heteroscedastic Extremes. (CentER Discussion Paper; Vol. 2014-015). Tilburg: Econometrics.
Einmahl, J.H.J. ; de Haan, L.F.M. ; Zhou, C. / Statistics of Heteroscedastic Extremes. Tilburg : Econometrics, 2014. (CentER Discussion Paper).
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Einmahl, JHJ, de Haan, LFM & Zhou, C 2014 'Statistics of Heteroscedastic Extremes' CentER Discussion Paper, vol. 2014-015, Econometrics, Tilburg.

Statistics of Heteroscedastic Extremes. / Einmahl, J.H.J.; de Haan, L.F.M.; Zhou, C.

Tilburg : Econometrics, 2014. (CentER Discussion Paper; Vol. 2014-015).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Statistics of Heteroscedastic Extremes

AU - Einmahl, J.H.J.

AU - de Haan, L.F.M.

AU - Zhou, C.

N1 - Pagination: 25

PY - 2014

Y1 - 2014

N2 - Abstract: We extend classical extreme value theory to non-identically distributed observations. When the distribution tails are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated nonparametrically along with the (common) extreme value index. Joint asymptotic normality of both estimators is shown; they are asymptotically independent. We develop tests for the proportionality function and for the validity of the model. We show through simulations the good performance of tests for tail homoscedasticity. The results are applied to stock market returns. A main tool is the weak convergence of a weighted sequential tail empirical process.

AB - Abstract: We extend classical extreme value theory to non-identically distributed observations. When the distribution tails are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated nonparametrically along with the (common) extreme value index. Joint asymptotic normality of both estimators is shown; they are asymptotically independent. We develop tests for the proportionality function and for the validity of the model. We show through simulations the good performance of tests for tail homoscedasticity. The results are applied to stock market returns. A main tool is the weak convergence of a weighted sequential tail empirical process.

M3 - Discussion paper

VL - 2014-015

T3 - CentER Discussion Paper

BT - Statistics of Heteroscedastic Extremes

PB - Econometrics

CY - Tilburg

ER -

Einmahl JHJ, de Haan LFM, Zhou C. Statistics of Heteroscedastic Extremes. Tilburg: Econometrics. 2014. (CentER Discussion Paper).