非线性时间序列建模的混合GARCH方法

Mixture Generalized Autoregressive Conditional Heteroscedastic for Nonlinear Time Series Modeling

在文献[1]的基础上,首次提出混合广义自回归条件异方差(MixtureGeneralizedAutoregressiveConditionalHeteroscedasticModel简记MGARCH)模型;给出并证明了MGARCH模型的一阶平稳性的充分必要条件及二阶平稳性的充分条件;给出该模型参数估计的EM算法;利用BIC定阶准则对MGARCH模型的各成份进行定阶;计算结果表明该模型对金融非线性时间序列中存在的变异率现象具有较强的描述能力,有广阔的应用前景。

A new mixture generalized autoregressive conditional heteroscedastic（MGARCH） model, which consists of a mixture of k autoregressive components with generalized autoregressive conditional heteroscedasticy, is proposed for modeling nonlinear time series. The stationary conditions of the model are derived. The estimation of the parameters can be easily done through EM algorithm and the order of the model is also easily selected by BIC criterion. The shape-changing feature of conditional distributions makes the new model capable of modeling time series with multimodal conditional distributions and with heteroscedasticity. The model is applied to two real data sets and compared with other competing models, the MGARCH model appears to capture features of the data better than other competing models.