Inference in nonstationary asymmetric GARCH models.(English)Zbl 1277.62210

Summary: 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 parameters, 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.

MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F12 Asymptotic properties of parametric estimators 62F05 Asymptotic properties of parametric tests
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