上证综指Markov预测模型合理性卡方检验方法

Rationality verification of Markov model for composite index of Shanghai stock exchange by Chi-square test

在建立上证综合指数Markov预测模型过程中,连续型指数需转换为较少状态的离散时间序列。只有选择恰当离散化方法,才能保证所得离散时间序列满足马尔科夫性。借助同分布卡方检验方法,可检验给定两个出发状态的转移概率分布之间是否存在差异。若同一转移概率矩阵不同行的分布差异较大,表明两个出发状态确有差异,即这两行对应的状态划分合理。而不同历史时期转移概率矩阵同一行的比较,可作为检验马尔科夫链非齐次性的一种方法。

In process of establishing Markov model to predict the Shanghai Composite Index, the con- tinuous index must be converted to a discrete time series with few status. When the discrete method is suitably selected, it can guarantee that the obtained discrete time series satisfies the Markovian property. With the help of Chi-square test method, the difference between probability distribution for given two setting status can be tested by comparing corresponding rows of transition probability matrix. If there is more difference between two rows in same transition probability matrix, then one status can be distinguished from another, that is, two sta- tus corresponding to those rows are reasonable setting. Furthermore, by comparing same row of different transi- tion probability matrix, a method is given to test the non-homogeneous of the Markov chain.