Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified

Mohamed El Ghourabi, Christian Francq and Fedya Telmoudi

Journal of Time Series Analysis, 2016, vol. 37, issue 1, 46-76

Abstract: type="main" xml:id="jtsa12136-abs-0001"> A two-step approach for conditional value at risk estimation is considered. First, a generalized quasi-maximum likelihood estimator is employed to estimate the volatility parameter, then the empirical quantile of the residuals serves to estimate the theoretical quantile of the innovations. When the instrumental density h of the generalized quasi-maximum likelihood estimator is not the Gaussian density, both the estimations of the volatility and of the quantile are generally asymptotically biased. However, the two errors counterbalance and lead to a consistent estimator of the value at risk. We obtain the asymptotic behavior of this estimator and show how to choose optimally h.

Date: 2016
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Citations: View citations in EconPapers (4)

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Working Paper: Consistent estimation of the Value-at-Risk when the error distribution of the volatility model is misspecified (2013)
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