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Journal of Financial Econometrics Advance Access originally published online on December 13, 2007
Journal of Financial Econometrics 2008 6(2):253-270; doi:10.1093/jjfinec/nbm022
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© The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Kernel Conditional Quantile Estimation for Stationary Processes with Application to Conditional Value-at-Risk

Wei Biao Wu
     University of Chicago

Keming Yu
     Brunel University

Gautam Mitra
     Brunel University

Address correspondence to Wei Bao Wu, Department of Statistics, University of Chicago, 5734 University Avenue, Chicago, IL 60637 USA, or e-mail: wbwu{at}galton.uchicago.edu.


  Abstract

The paper considers kernel estimation of conditional quantiles for both short-range and long-range-dependent processes. Under mild regularity conditions, we obtain Bahadur representations and central limit theorems for kernel quantile estimates of those processes. Our theory is applicable to many price processes of assets in finance. In particular, we present an asymptotic theory for kernel estimates of the value-at-risk (VaR) of the market value of an asset conditional on the historical information or a state process. The results are assessed based on a small simulation and are applied to AT&T monthly returns.

KEYWORDS: asymptotic expansion, Bahadur representation, causal process, central limit theorem, kernel estimation, long-range dependence, quantile estimation, short-range dependence, value-at-risk

The authors would like to thank the Editors and referees for their valuable suggestions and comments that greatly improved the presentation.

Received July 12, 2006; revised April 16, 2007; accepted September 24, 2007


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