LOCAL ASYMPTOTIC NORMALITY OF GENERAL CONDITIONALLY HETEROSKEDASTIC AND SCORE-DRIVEN TIME-SERIES MODELS
证明了乘法形式的一般条件异方差时间序列模型的局部渐近正态性，其中参数同时影响波动率和误差密度，并引入条件二次均值可微性概念处理不可微函数。
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 the volatility $\sigma _t(\boldsymbol {\theta }_0)$ is a parametric function of $\{\epsilon _{s}, s< t\}$ , and $(\eta _t)$ is a sequence of i.i.d. random variables with common density $f_{\boldsymbol {\theta }_0}$ . In contrast with earlier results, the finite dimensional parameter $\boldsymbol {\theta }_0$ enters in both the volatility and the density specifications. To deal with nondifferentiable functions, we introduce a conditional notion of the familiar quadratic mean differentiability condition which takes into account parameter variation in both the volatility and the errors density. Our results are illustrated on two particular models: the APARCH with asymmetric Student- t distribution, and the Beta- t -GARCH model, and are extended to handle a conditional mean.