Open Access
Translator Disclaimer
August 2013 Inference in nonstationary asymmetric GARCH models
Christian Francq, Jean-Michel Zakoïan
Ann. Statist. 41(4): 1970-1998 (August 2013). DOI: 10.1214/13-AOS1132

Abstract

This paper considers the statistical inference of the class of asymmetric power-transformed $\operatorname{GARCH}(1,1)$ models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameter, including the power but without the intercept, when strict stationarity does not hold. Two important issues can be tested in this framework: asymmetry and stationarity. The tests exploit the existence of a universal estimator of the asymptotic covariance matrix of the QMLE. By establishing the local asymptotic normality (LAN) property in this nonstationary framework, we can also study optimality issues.

Citation

Download Citation

Christian Francq. Jean-Michel Zakoïan. "Inference in nonstationary asymmetric GARCH models." Ann. Statist. 41 (4) 1970 - 1998, August 2013. https://doi.org/10.1214/13-AOS1132

Information

Published: August 2013
First available in Project Euclid: 23 October 2013

zbMATH: 1277.62210
MathSciNet: MR3127855
Digital Object Identifier: 10.1214/13-AOS1132

Subjects:
Primary: 62M10
Secondary: 62F05, 62F12

Rights: Copyright © 2013 Institute of Mathematical Statistics

JOURNAL ARTICLE
29 PAGES


SHARE
Vol.41 • No. 4 • August 2013
Back to Top