混合自回归条件异方差模型的谱分析

Spectral Analysis of a Mixture Autoregressive Conditional Heteroscedastic Model

线性时间序列模型谱密度的计算可以直接由定义获得,而非线性时间序列模型谱密度的计算目前还没有一般的理论.2001年Wong Chun-shan等将混合自回归(MAR)模型推广到混合自回归条件异方差(MAR-ARCH)模型,并且讨论了该模型的参数估计及模型选择问题,本文导出了MAR-ARCH模型自协方差函数的递推关系式及计算谱密度的算法,从而解决了这类模型的谱分析问题.

Spectual density computation of linear time series models can be directly achieved by definition,whereas no general theory about computing of the spectual density of non-linear time series models has been formulated.In 2001, Chun Shan et al,generalized the mixture autoregressive（MAR）model to a mixture autoregressive conditional heteroscedastic（MAR-ARCH）model and discussed parameter estimation and problems of selecting a model.In this paper,the recursive formula of auto-covariance function and the＂algorithm＂of computing spectral density of MAR-ARCH model are worked out,thus solving the problem associated with spectual analysis of this kind of models.