GARCH processes:: structure and estimation

被引：281

作者：

Berkes, I

Horváth, L

Kokoszka, P

机构：

[1] Hungarian Acad Sci, A Renyi Inst Math, H-1364 Budapest, Hungary

[2] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[3] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

来源：

BERNOULLI | 2003年 / 9卷 / 02期

关键词：

asymptotic normality; consistency; GARCH(p; q); sequence; martingales; quasi-maximum likelihood;

D O I：

10.3150/bj/1068128975

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 study the structure of a GARCH(p, q) sequence. We show that the conditional variance can be written as an infinite sum of the squares of the previous observations and that the representation is unique. We prove the consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of the GARCH(p, q) sequence under mild conditions.

引用

页码：201 / 227

页数：27

共 13 条

[1]

BASRAK B, 2001, SAMPLE MULTIVARIATE

[2]

Billingsley P, 1968, CONVERGE PROBAB MEAS

[3] GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY [J].