Optimal predictions of powers of conditionally heteroskedastic processes

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• Francq, Christian
• Zakoian, Jean-Michel
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Abstract

In conditionally heteroskedastic models, the optimal prediction of powers, or logarithms, of the absolute process has a simple expression in terms of the volatility process and an expectation involving the independent process. A standard procedure for estimating this prediction is to estimate the volatility by gaussian quasi-maximum likelihood (QML) in a first step, and to use empirical means based on rescaled innovations to estimate the expectation in a second step. This paper proposes an alternative one-step procedure, based on an appropriate non-gaussian QML estimation of the model, and establishes the asymptotic properties of the two approaches. Their performances are compared for finite-order GARCH models and for the infinite ARCH. For the standard GARCH(p, q) and the Asymmetric Power GARCH(p,q), it is shown that the ARE of the estimators only depends on the prediction problem and some moments of the independent process. An application to indexes of major stock exchanges is proposed.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22155.

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Handle: RePEc:pra:mprapa:22155

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Related research

Keywords: APARCH; Infinite ARCH; Conditional Heteroskedasticity; Efficiency of estimators; GARCH; Prediction; Quasi Maximum Likelihood Estimation;

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Find related papers by JEL classification:
• C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
• C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
• C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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References

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Citations

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Cited by:
1. El Ghourabi, Mohamed & Francq, Christian & Telmoudi, Fedya, 2013. "Consistent estimation of the Value-at-Risk when the error distribution of the volatility model is misspecified," MPRA Paper 51150, University Library of Munich, Germany.
2. Chen, Min & Zhu, Ke, 2013. "Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations," MPRA Paper 50487, University Library of Munich, Germany.
3. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
4. Francq, Christian & Zakoian, Jean-Michel, 2012. "Risk-parameter estimation in volatility models," MPRA Paper 41713, University Library of Munich, Germany.

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