Francq, Christian and Zakoian, Jean-Michel
(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 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.

Item Type: | MPRA Paper |
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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 - Time-Series 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.uni-muenchen.de/id/eprint/22155 |