INFERENCE IN NONSTATIONARY ASYMMETRIC GARCH MODELS

• 成果类型: Article
• 署名作者: Francq, Christian; Zakoian, Jean-Michel
• 署名单位: Institut Polytechnique de Paris; ENSAE Paris; Universite de Lille
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1132
• 发表日期: 2013
• 页码: 1970-1998
• 关键词: autoregressive conditional heteroscedasticity; time-series; nonparametric-estimation; ASYMPTOTIC INFERENCE; strict stationarity; Adaptive estimation; ARCH; tests

摘要

This paper considers the statistical inference of the class of asymmetric power-transformed 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.