Statistical inference for nonparametric GARCH models

被引：6

作者：

Meister, Alexander ^{[1
]}

Kreiss, Jens-Peter ^{[2
]}

机构：

[1] Univ Rostock, Inst Math, D-18051 Rostock, Germany

[2] TU Braunschweig, Inst Math Stochast, D-38092 Braunschweig, Germany

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2016年 / 126卷 / 10期

关键词：

Autoregression; Financial time series; Inference for stochastic processes; Minimax rates; Nonparametric regression; MAXIMUM-LIKELIHOOD ESTIMATION; ITERATED RANDOM FUNCTIONS; CONDITIONAL HETEROSCEDASTICITY; ARCH(INFINITY) MODELS; TIME-SERIES; HETEROSKEDASTICITY; EFFICIENCY; ESTIMATOR;

D O I：

10.1016/j.spa.2016.03.010

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider extensions of the famous GARCH(1, 1) model where the recursive equation for the volatilities is not specified by a parametric link but by a smooth autoregression function. Our goal is to estimate this function under nonparametric constraints when the volatilities are observed with multiplicative innovation errors. We construct an estimation procedure whose risk attains nearly the usual convergence rates for bivariate nonparametric regression estimation. Furthermore, those rates are shown to be nearly optimal in the minimax sense. Numerical simulations are provided for a parametric submodel. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：3009 / 3040

页数：32

共 31 条

[1] Tree-structured generalized autoregressive conditional heteroscedastic models [J].