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

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  • Mohamed El Ghourabi
  • Christian Francq
  • Fedya Telmoudi

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.

Suggested Citation

  • Mohamed El Ghourabi & Christian Francq & Fedya Telmoudi, 2016. "Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 46-76, January.
    • Handle: RePEc:bla:jtsera:v:37:y:2016:i:1:p:46-76
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    4. Abdelhakim Aknouche & Eid Al-Eid & Nacer Demouche, 2018. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 485-511, October.

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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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