Optimal predictions of powers of conditionally heteroskedastic processes

Christian Francq and Jean-Michel Zakoian

MPRA Paper from University Library of Munich, Germany

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.

Keywords: APARCH; Infinite ARCH; Conditional Heteroskedasticity; Efficiency of estimators; GARCH; Prediction; Quasi Maximum Likelihood Estimation (search for similar items in EconPapers)
JEL-codes: C01 C13 C22 (search for similar items in EconPapers)
Date: 2010-04-17
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-for and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/22155/1/MPRA_paper_22155.pdf original version (application/pdf)

Related works:
Journal Article: Optimal predictions of powers of conditionally heteroscedastic processes (2013)
Working Paper: Optimal Predictions of Powers of Conditionally Heteroskedastic Processes (2012)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:22155

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().