Arbeitspapier
Efficient estimation of conditional risk measures in a semiparametric GARCH model
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.
- Language
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Englisch
- Bibliographic citation
-
Series: cemmap working paper ; No. CWP25/12
- Classification
-
Wirtschaft
Semiparametric and Nonparametric Methods: General
Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
Insurance; Insurance Companies; Actuarial Studies
- Subject
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Empirical Likelihood
Empirical process
GARCH
Quantile
Value-at-Risk
Expected Shortfall
- Event
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Geistige Schöpfung
- (who)
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Yan, Yang
Shang, Dajing
Linton, Oliver
- Event
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Veröffentlichung
- (who)
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Centre for Microdata Methods and Practice (cemmap)
- (where)
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London
- (when)
-
2012
- DOI
-
doi:10.1920/wp.cem.2012.2512
- Handle
- Last update
-
10.03.2025, 11:44 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Yan, Yang
- Shang, Dajing
- Linton, Oliver
- Centre for Microdata Methods and Practice (cemmap)
Time of origin
- 2012
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