左偏长尾状态空间SV-MG模型的参数估计

Parameters Estimates and Empirical Study of Left-skewness and Long-tailed SV-MG Model Based on Its State Space

针对SV模型转换为线性状态空间形式之后带来的非高斯对数卡方误差,文章以高斯混合分布近似具有左偏长尾性质的对数卡方分布,得到状态空间SV-MG(SV with Mixture-of-Guass)模型。结合MCMC方法和EM算法估计SV模型参数和高斯混合参数,并利用近似滤波(AMF)算法实现SV-MG模型的样本外预测。据此对沪深股市进行了实证研究。

First, a Mixture-of-Gauss distribution approximate logarithmic chi-square distribution with left-skewness and long-tailed in this paper, for the SV model transform into a linear state-space form after bringing the non-Gaussian logarithmic chi-square error. And we get the state-space SV-MG （SV with Mixture-of-Gauss） model. Then, the paper combined with MCMC method and EM algorithm to estimate SV model parameters and Gaussian mixture distribution parameters. And we using the ap- proximate filter （AMF） algorithm to realize the out-of-sample forecasting of SV-MG models. We conduct an empirical study on shanghai and shenzheng stock Maekets.