Efficient estimation of conditional risk measures in a semiparametric GARCH model

Oliver Linton, Dajing Shang and Yang Yan
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Dajing Shang: Institute for Fiscal Studies
Yang Yan: Institute for Fiscal Studies

No CWP25/12, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: This paper proposes efficient estimators of risk measures in a semiparametric GARCH model defined through moment constraints. Moment constraints are often used to identify and estimate the mean and variance parameters and are however discarded when estimating error quantiles. In order to prevent this efficiency loss in quantile estimation we propose a quantile estimator based on inverting an empirical likelihood weighted distribution estimator. It is found that the new quantile estimator is uniformly more efficient than the simple empirical quantile and a quantile estimator based on normalized residuals. At the same time, the efficiency gain in error quantile estimation hinges on the efficiency of estimators of the variance parameters. We show that the same conclusion applies to the estimation of conditional Expected Shortfall. Our comparison also leads to interesting implications of residual bootstrap for dynamic models. We find that these proposed estimators for conditional Value-at-Risk and expected shortfall are asymptotically mixed normal. This asymptotic theory can be used to construct confidence bands for these estimators by taking account of parameter uncertainty. Simulation evidence as well as empirical results are provided.

Keywords: Empirical Likelihood; Empirical process; GARCH; Quantile; Value-at-Risk; Expected Shortfall. (search for similar items in EconPapers)
JEL-codes: C14 C22 G22 (search for similar items in EconPapers)
Date: 2012-09-21
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-rmg and nep-upt
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Working Paper: Efficient estimation of conditional risk measures in a semiparametric GARCH model (2012)
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