Optimal predictions of powers of conditionally heteroskedastic processes
AbstractIn 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 InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 22155.
Date of creation: 17 Apr 2010
Date of revision:
APARCH; Infinite ARCH; Conditional Heteroskedasticity; Efficiency of estimators; GARCH; Prediction; Quasi Maximum Likelihood Estimation;
Other versions of this item:
- Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, 03.
- Christan Francq & Jean-Michel Zakoian, 2012. "Optimal Predictions of Powers of Conditionally Heteroskedastic Processes," Working Papers 2012-17, Centre de Recherche en Economie et Statistique.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-04-24 (All new papers)
- NEP-ECM-2010-04-24 (Econometrics)
- NEP-ETS-2010-04-24 (Econometric Time Series)
- NEP-FOR-2010-04-24 (Forecasting)
- NEP-ORE-2010-04-24 (Operations Research)
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