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

研究问题: 研究在参数同时进入条件波动率和创新密度、模型函数还可能不可微时，如何建立一般条件异方差时间序列模型的局部渐近正态性。
方法与思路: 作者提出条件二次均值可微概念，同时处理波动率与误差密度的参数变化，并以两类波动率模型说明结果及扩展至条件均值。
材料陈述的贡献: 摘要称，局部渐近正态性结果涵盖参数同时影响波动率和密度的情形，并用于非对称 Student-t APARCH 与 Beta-t-GARCH 模型。
阅读关注点: 应核对条件二次均值可微的定义、不可微模型的处理方式，以及局部渐近正态性所需的矩、初始值和时间依赖条件。
阅读边界: 仅据所给 Crossref 摘要，无法判断完整正则条件或具体估计量的效率；局部渐近正态性本身不直接保证所有推断程序有效。

GPT-6.1 Sol · 高 · 2026-10-03

原文摘要

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.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.

摘要来源：Crossref

笔记与分组

分类依据与纠错

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

代码、数据与补充材料

一般条件异方差与得分驱动时间序列模型的局部渐近正态性

原文摘要

同方向的基础文献

同方向的基础文献