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


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.


Download Citation

Christian Francq. Jean-Michel Zakoïan. "Inference in nonstationary asymmetric GARCH models." Ann. Statist. 41 (4) 1970 - 1998, August 2013.


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

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

Primary: 62M10
Secondary: 62F05 , 62F12

Keywords: GARCH models , inconsistency of estimators , local power of tests , nonstationarity , quasi maximum likelihood estimation

Rights: Copyright © 2013 Institute of Mathematical Statistics


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