Francq, Christian and Zakoian, JeanMichel (2010): Optimal predictions of powers of conditionally heteroskedastic processes.

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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 quasimaximum 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 onestep procedure, based on an appropriate nongaussian QML estimation of the model, and establishes the asymptotic properties of the two approaches. Their performances are compared for finiteorder 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.
Item Type:  MPRA Paper 

Original Title:  Optimal predictions of powers of conditionally heteroskedastic processes 
Language:  English 
Keywords:  APARCH; Infinite ARCH; Conditional Heteroskedasticity; Efficiency of estimators; GARCH; Prediction; Quasi Maximum Likelihood Estimation 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  22155 
Depositing User:  Christian Francq 
Date Deposited:  19 Apr 2010 17:57 
Last Modified:  30 Sep 2019 17:34 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/22155 