Inference in nonstationary asymmetric GARCH models

TL;DR

This paper investigates statistical inference for asymmetric GARCH(1,1) models under nonstationarity and explosiveness, establishing asymptotic properties of estimators and testing procedures for asymmetry and stationarity.

Contribution

It develops asymptotic normality results for the QMLE in nonstationary asymmetric GARCH models and introduces tests for asymmetry and stationarity in explosive regimes.

Findings

Asymptotic normality of QMLE without stationarity

Universal estimator for asymptotic covariance matrix

LAN property established in nonstationary context

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.