周期多元BEKK-GARCH模型的几何遍历性与β-混合

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-06-24 DOI:10.1007/s10255-025-0012-y

Farid Boussama, Hafida Guerbyenne, Khedidja Serier Abdallah

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引用次数: 0

摘要

本文介绍了一类新的周期多元GARCH模型的周期BEKK规范。将半多项式马尔可夫链与代数几何结合，得到了半多项式马尔可夫链的不可约性等性质。通过锥上的正线性算子理论，我们对过程的严格周期平稳性和几何遍历性施加了弱条件：假设零属于驱动噪声密度的支持，它相对于勒贝格测度是绝对连续的，并且由模型的周期系数建立的矩阵的谱半径小于1。

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Geometric Ergodicity and β-mixing of the Periodic Multivariate BEKK-GARCH Model

This paper introduces the new class of periodic multivariate GARCH models in their periodic BEKK specification. Semi-polynomial Markov chains combined with algebraic geometry are used to obtain some properties like irreducibility. We impose weak conditions to obtain the strict periodic stationarity and the geometric ergodicity of the process, via the theory of positive linear operators on a cone: it is supposed that zero belongs to the support of the driving noise density which is absolutely continuous with respect to the Lebesgue measure and the spectral radius of a matrix built from the periodic coefficients of the model is smaller than one.

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来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.