Estimation of Distortion Risk Measures

Hideatsu Tsukahara

Journal of Financial Econometrics, 2013, vol. 12, issue 1, 213-235

Abstract: For the class of distortion risk measures, a natural estimator has the form of L-statistics. In this article, we investigate the large sample properties of general L-statistics based on weakly dependent data and apply them to our estimator. Under certain regularity conditions, which are somewhat weaker than the ones found in the literature, we prove that the estimator is strongly consistent and asymptotically normal. Furthermore, we give a consistent estimator for its asymptotic variance using spectral density estimators of a related stationary sequence. The behavior of the estimator is examined using simulation in two examples: inverse-gamma autoregressive stochastic volatility model and GARCH(1,1). Copyright The Author, 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com, Oxford University Press.

Date: 2013
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