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Journal of Financial Econometrics 2005 3(2):227-255; doi:10.1093/jjfinec/nbi012
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.

Nonparametric Inference of Value-at-Risk for Dependent Financial Returns

Song Xi Chen
     Iowa State University

Cheng Yong Tang
     Iowa State University

Address correspondence to Song Xi Chen, Department of Statistics, Iowa State University, Ames, IA 50011-1210, or e-mail: songchen{at}iastate.edu.

The article considers nonparametric estimation of value-at-risk (VaR) and associated standard error estimation for dependent financial returns. Theoretical properties of the kernel VaR estimator are investigated in the context of dependence. The presence of dependence affects the variance of the VaR estimates and has to be taken into consideration in order to obtain adequate assessment of their variation. An estimation procedure of the standard errors is proposed based on kernel estimation of the spectral density of a derived series. The performance of the VaR estimators and the proposed standard error estimation procedure are evaluated by theoretical investigation, simulation of commonly used models for financial returns, and empirical studies on real financial return series.

KEYWORDS: {alpha}-mixing, kernel estimation, sample quantile, spectral density estimation, standard error estimation

Received March 26, 2004; revised January 5, 2005; accepted January 12, 2005


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