隐马尔科夫模型的改进及其在金融预测中的应用

发布时间：2018-01-09 23:10

本文关键词：隐马尔科夫模型的改进及其在金融预测中的应用　出处：《工程数学学报》2017年05期 　论文类型：期刊论文

【摘要】：隐马尔科夫模型(Hidden Markov Model)在诸多领域都有广泛应用.本文从不同角度对现有的HMM进行改进并应用于金融预测.首先,我们采取固定K-means方法的初始点,使得K-means的聚类结果更加稳定,由此为Baum-Welch算法确定更好的初始迭代值.其次,为更进一步提升预测效果,与已有方法不同,我们将由BaumWelch算法所得到的模型参数值作为Vertibi算法的输入来确定隐状态的最优取值序列,由此重新划分观测向量,进而得到各个隐状态对应的观测向量的集合;基于Vertibi算法的输出结果,我们重新计算不同类观测向量的均值与方差,将新的均值向量和协方差矩阵作为Baum-Welch算法初始迭代值,最终确定HMM最优的模型参数.最后,代替现有方法仅在历史区间中简单寻求相似走势的做法,我们不仅导出了预测值发生的多步条件概率的精细表达式,而且通过极大化该条件概率的值来得到更佳的预测值.基于中国证券市场具体数据的实证结果表明了本文所提出改进HMM的优越性.
[Abstract]:Hidden Markov Model (Hidden Markov Model) is widely used in many fields. This paper improves the existing HMM from different angles and applies it to financial forecasting. We adopt the fixed K-means method of the initial point, so that K-means clustering results more stable, thus for the Baum-Welch algorithm to determine a better initial iterative value. Secondly. In order to further improve the prediction effect, it is different from the existing methods. We use the model parameter value obtained by BaumWelch algorithm as the input of Vertibi algorithm to determine the optimal value sequence of hidden state, and then repartition the observation vector. Then the set of observation vectors corresponding to each hidden state is obtained. Based on the output of Vertibi algorithm, we recalculate the mean and variance of different kinds of observation vectors, and take the new mean vector and covariance matrix as the initial iteration value of Baum-Welch algorithm. Finally, instead of simply looking for similar trend in the historical interval, we not only derive the fine expression of the probability of multi-step condition for the occurrence of the predicted value, but also determine the optimal model parameters of HMM. The empirical results based on the specific data of the Chinese stock market show the superiority of the improved HMM proposed in this paper.
【作者单位】：西安交通大学数学与统计学院;
【基金】：国家自然科学基金(71371152;11571270)~~
【分类号】：F832.51;O211.62
【正文快照】： 1引引言1966年,Baum和Petrie[1]提出了隐马尔科夫模型(Hidden Markov Model,HM-M).该模型应用广泛,目前已经成为语音识别、图像处理、故障检测、脑疾诊断等领域内的重要工具.例如,Baum等人[2]将HMM应用于语音识别问题,并且取得了长足的发展.Su等人[3]将HMM应用于手写汉字识别,

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