LOCAL ASYMPTOTIC NORMALITY OF GENERAL CONDITIONALLY HETEROSKEDASTIC AND SCORE-DRIVEN TIME-SERIES MODELS

The paper establishes the local asymptotic normality property for general conditionally heteroskedastic time series models of multiplicative form, $\epsilon _t=\sigma _t(\boldsymbol {\theta }_0)\eta _t$ , where volatility $\sigma }_0)$ is a parametric function $\{\epsilon _{s}, s< t\}$ and $(\eta _t)$ sequence i.i.d. random variables with common density $f_{\boldsymbol }_0}$ . In contrast earlier results, finite dimensional parameter $\boldsymbol }_0$ enters in both specifications. To deal nondifferentiable functions, we introduce conditional notion familiar quadratic mean differentiability condition which takes into account variation errors density. Our results are illustrated on two particular models: APARCH asymmetric Student- t distribution, Beta- -GARCH model, extended to handle mean.