Stationarity and geometric ergodicity of BEKK multivariate GARCH models

被引：56

作者：

Boussama, Farid ^{[2
]}

Fuchs, Florian ^{[3
,4
]}

Stelzer, Robert ^{[1
]}

机构：

[1] Univ Ulm, Inst Math Finance, D-89081 Ulm, Germany

[2] Univ Montpellier 1, Dept Math & Informat, F-34000 Montpellier, France

[3] Tech Univ Munich, TUM Inst Adv Study, D-85748 Garching, Germany

[4] Tech Univ Munich, Zentrum Math, D-85748 Garching, Germany

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2011年 / 121卷 / 10期

关键词：

beta-mixing; Foster Lyapunov drift condition; Geometric ergodicity; Harris recurrence; Multivariate GARCH; Stationarity; Stochastic volatility; CENTRAL-LIMIT-THEOREM; AUTOREGRESSIVE PROCESSES; MARKOV-CHAINS; TIME-SERIES;

D O I：

10.1016/j.spa.2011.06.001

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：

Conditions for the existence of strictly stationary multivariate GARCH processes in the so-called BEKK parametrisation, which is the most general form of multivariate GARCH processes typically used in applications, and for their geometric ergodicity are obtained. The conditions are that the driving noise is absolutely continuous with respect to the Lebesgue measure and zero is in the interior of its support and that a certain matrix built from the GARCH coefficients has spectral radius smaller than one. To establish the results, semi-polynomial Markov chains are defined and analysed using algebraic geometry. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：2331 / 2360

页数：30

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