SV和GARCH模型拟合优度比较的似然比检验

Comparative research of goodness of fit between SV and GARCH models by likelihood ratio test

讨论了在金融时间序列中广泛应用的两类波动性模型,即ARCH模型和SV模型的比较问题.从似然比原理出发,提出了一种基于随机模拟的似然比检验方法,阐明了利用该方法进行模型间比较的基本步骤,并利用基于随机模拟方法的似然比检验,分别比较了SV与GARCH(1,1)、SV与t GARCH对上海股市数据拟合优度,结果表明:SV模型对于上海股市时间序列数据的拟合好于GARCH(1,1)模型,而SV模型上海股市时间序列数据的拟合与t GARCH(1,1)模型效果相当.

In this paper, the comparative problem between ARCH models and SV models which are widely applied in analyzing financial time series is studied. According to likelihood ratio theory, this paper brings forward a new likelihood ratio test based on stochastic simulation and illustrates the main process of this method. With this method we compare the goodness of fit between SV and GARCH models and between SV and t_GARCH models for Shanghai stock market. The conclusion is that the goodness of fit of SV model is better than that of GARCH(1,1), and equals to that of t_GARCH(1,1) model.