多元BEKK模型的平稳性和几何遍历性
Stationarity and Geometric Ergodicity of BEKK Multivariate GARCH Models
摘要：
在所谓的BEKK参数化，这是最一般的形式，多元Gestival过程的应用中通常使用的严格平稳的多元Gestival过程的存在条件，并为他们的几何遍历性。条件是驾驶噪声相对于勒贝格测度是绝对连续的，并且零在其支撑的内部，并且从Gestern系数构建的某个矩阵具有谱半径小于1。为了建立半多项式马尔可夫链的结果定义和分析使用代数几何。
英文摘要：
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.
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