Inference in nonstationary asymmetric GARCH models

The Annals of Statistics · 2013 · Volume 41 · Issue 4

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.

Keywords

62F05, 62F12, 62M10, GARCH models, inconsistency of estimators, local power of tests, nonstationarity, quasi maximum likelihood estimation

Enable JavaScript for citation tools and additional paper interactions.