Economics at your fingertips  

Testing the existence of moments for GARCH processes

Christian Francq () and Jean-Michel Zakoian ()

MPRA Paper from University Library of Munich, Germany

Abstract: It is generally admitted that many financial time series have heavy tailed marginal distributions. When time series models are fitted on such data, the non-existence of appropriate moments may invalidate standard statistical tools used for inference. Moreover, the existence of moments can be crucial for risk management, for instance when risk is measured through the expected shortfall. This paper considers testing the existence of moments in the framework of GARCH processes. While the second-order stationarity condition does not depend on the distribution of the innovation, higher-order moment conditions involve moments of the independent innovation process. We propose tests for the existence of high moments of the returns process which are based on the joint asymptotic distribution of the Quasi-Maximum Likelihood (QML) estimator of the volatility parameters and empirical moments of the residuals. A bootstrap procedure is proposed to improve the finite-sample performance of our test. To achieve efficiency gains we consider non Gaussian QML estimators founded on reparametrizations of the GARCH model, and we discuss optimality issues. Monte-Carlo experiments and an empirical study illustrate the asymptotic results.

Keywords: Conditional heteroskedasticity; Efficiency comparisons; Non-Gaussian QMLE; Residual Bootstrap; Stationarity tests (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 (search for similar items in EconPapers)
Date: 2019-12-02
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) original version (application/pdf)

Related works:
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:

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 ().

Page updated 2020-10-29
Handle: RePEc:pra:mprapa:98892