基于证据理论的马尔可夫模型及其应用

发布时间：2018-03-25 20:22

本文选题：马尔可夫模型　切入点：隐马尔可夫模型　出处：《江西师范大学》2017年硕士论文

【摘要】：马尔可夫链是随机过程理论的组成部分,具有重要的地位并获得了广泛的应用[7-13],经典的马尔可夫链模型在状态转移矩阵确定的过程上具有机械性,方法单一。证据理论在表示和解决不确定性信息这一问题上比概率论更有效,这一理论被众多学者认可、改进,在各个领域被广泛的应用。邓鑫洋[6]首次大胆尝试引进证据理论对马尔可夫模型状态转移矩阵进行了改进。本文基于这一理念,提出了一种改进状态间的转移矩阵的方法,通过引入D-S理论对原始数据所处的状态进行处理得到与之对应的信度函数值,并给出了连续状态信度函数值确定的一般方法;再通过基于后退偏差平方和加权的方法对信度函数值进行权重分配形成转移矩阵,使得该转移矩阵考虑状态间影响的累积效应。最后通过实例分析,对比不同模型下状态间的回代误差,得到了较好的预测结果。隐马尔可夫模型是以马尔可夫模型为前提并加以扩充的一种统计分析模型,是一个包含一定状态数的马尔可夫链过程以及显示随机观测函数集的双重随机过程。本文针对HMM的三个经典问题,分别给出了详细的解决方法并进行了具体的实例演算。同时,结合证据理论以及pignistic概率转换思想,对矩阵进行行、列分配,提出了改进隐马尔可夫模型中转移矩阵的新方法;接着采用2005年-2016年股市上证综指走势为例,先利用信度加权的马尔科夫模型及层次分析法,证明了股市的走势是一个周期过程。最后利用隐马尔科夫模型中的解码问题对股市市场连续9天的股市走势进行预测,达到了预期效果。
[Abstract]:Markov chain is an important part of stochastic process theory and has been widely used [7-13]. The classical Markov chain model is mechanical in the process of determining the state transition matrix. The method is simple. Evidence theory is more effective than probability theory in expressing and solving the problem of uncertain information, which has been recognized and improved by many scholars. Deng Xinyang has made the first bold attempt to introduce evidence theory to improve the state transition matrix of Markov model. Based on this concept, a method of improving the transition matrix between states is proposed in this paper. By introducing D-S theory to deal with the state of the original data, the corresponding reliability function value is obtained, and the general method of determining the continuous state reliability function value is given. Then the weight distribution of the reliability function value based on the sum of square weight of backward deviation is used to form the transfer matrix, which makes the transfer matrix consider the cumulative effect of the influence between states. A better prediction result is obtained by comparing the regression error between different models. The hidden Markov model is a statistical analysis model which is based on the Markov model and is expanded. It is a Markov chain process with a certain number of states and a double stochastic process that shows the set of random observation functions. In this paper, we give a detailed solution to the three classical problems of HMM and carry out a concrete example calculus. Combined with evidence theory and pignistic probability transformation thought, this paper proposes a new method to improve the transfer matrix in hidden Markov model, and then uses the trend of Shanghai Stock Exchange Composite Index from 2005 to 2016 as an example. This paper first proves that the trend of stock market is a periodic process by using the reliability weighted Markov model and the analytic hierarchy process. Finally, using the decoding problem in the hidden Markov model, the paper forecasts the stock market trend for 9 consecutive days. The expected effect has been achieved.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C815

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