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ESTIMATION OF AND INFERENCE ABOUT THE EXPECTED SHORTFALL FOR TIME SERIES WITH INFINITE VARIANCE

Published online by Cambridge University Press:  16 January 2013

Oliver Linton  and
Zhijie Xiao
Oliver Linton
Affiliation:
University of Cambridge
Zhijie Xiao*
Affiliation:
Boston College
*
*Address correspondence to Zhijie Xiao, Department of Economics, Boston College, Chestnut Hill, MA 02467, USA; e-mail: xiaoz@bc.edu.
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Abstract

We study estimation and inference of the expected shortfall for time series with infinite variance. Both the smoothed and nonsmoothed estimators are investigated. The rate of convergence is determined by the tail thickness parameter, and the limiting distribution is in the stable class with parameters depending on the tail thickness parameter of the time series and on the dependence structure, which makes inference complicated. A subsampling procedure is proposed to carry out statistical inference. We also analyze a nonparametric estimator of the conditional expected shortfall. A Monte Carlo experiment is conducted to evaluate the finite sample performance of the proposed inference procedure, and an empirical application to emerging market exchange rates (from October 1997 to October 2008) is conducted to highlight the proposed study.

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 4 , August 2013 , pp. 771 - 807
Copyright
Copyright © Cambridge University Press 2013 

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