高阶马尔可夫链的降阶模型及其应用

本文通过对传统高阶马尔可夫链模型的状态空间进行阶数重构,导出一个在重构状态空间上的降阶马尔可夫模型。理论分析证明,降阶马尔可夫链模型不但可以描述传统高阶马尔可夫链模型的全部性态,更能表达较传统模型细微的随机结构。然后,应用降阶模型对我国股票指数的动态变化进行实证分析,讨论了阶数的选取和高阶马尔可夫性检验,分析了股票市场内在波动结构。最后,对股指序列作出短期与长期的预测分析。

Order Reduction for Higher Order Markov Chain Model and Its Application

An order reduction model for the higher order Markov chain based on reconstruction state space is proposed in this paper.Through theoretical analysis,it shows that the new Markov model can describe not only the behavior of the traditional higher order Markov chain model,but also more subtle random structure.After that,the newly reduction model is apphed to empirical analysis of the stock index to inherent volatility of the stock market structure.The higher order Markov property is proved and the order selection is further discussed.Finally the short and long forecasts are respectively implemented based on China stock market data.