Stock Price Time Series Prediction Based On Hidden Markov Model And Computational Intelligence

Stock price time series is the comprehensive external manifestation of the stock market. Stock price time series attracts attention of the people constantly, and it accesses to the people's lives. The necessity of research on stock price time series prediction has become a general consensus for practical and academic circles.However, because stock price time series is complexity, diversity and variability, there are many factors affect the changes of stock price time series, some factors can be measured, and some factors are difficult to quantify, it is difficult scientific computing and evaluation, and thus it is difficult to study. Currently, the extensive use of Hidden Markov Model (HMM) and the continues development of computational intelligence (CI) technology, open a new way for stock price time series prediction research ,and provide a new theoretical and technical support. In this paper, based on HMM and several CI method: artificial neural network (ANN), fuzzy logic (FL), and evolutionary algorithm (EA), to systematic research on stock price time series prediction, and establish a hybrid forecasting model, to enrich and improve stock price time series prediction research. The structure of this paper is progressive, and the proposed prediction model is improved gradually.Firstly, based on HMM we introduce an unsupervised clustering method. The clustering method uses HMM to identify the similar data patterns in the dataset. For a given dataset, HMM is used to determine the number of clusters, and calculate the log-likelihood value of each data pattern, then based on the log-likelihood values we cluster the data patterns into different clusters. To evaluate the recognized and clustering capabilities of this clustering method, we compare this clustering method with the other three clustering methods.Secondly, based on the proposed unsupervised clustering method, we design a basic forecasting model for stock price time series. From the past dataset, the basic forecasting model finds out the data patterns which match the current stock price behaviors. Then we interpolate the appropriate neighbouring price values into the dataset, and predict the stock price of the next time unit. To evaluate the performance of the basic forecasting model, we predict six stocks price from Shanghai Stock Exchange, and compare with the other prediction methods. Then use ANN and genetic algorithm (GA) to improve the basic forecasting model. ANN is used to convert the input observation sequence of HMM, and GA is used to optimize the initial parameters of HMM. The improved prediction model has solved the problem of the limitations of the basic forecasting model, and improved the accuracy of the prediction. In order to prove the improved prediction model is better, we use the same six stocks price time series as the empirical study objectives, and use the mean absolute percentage error (MAPE) as the criteria, to do empirical forecasting study and compare with the other prediction methods.Thirdly, fuzzy logic theory is introduced into the improved prediction model to deal with the non-stationary of the stock price time series. We construct a data-driven hybrid HMM-Fuzzy forecasting model, which can improve the prediction accuracy with the minimum fuzzy rules. A key advantage of this hybrid model is that it is not necessary to analyze the training dataset before using the model, but it is necessary for the other existing data-driven models. In addition, the hybrid model is not limited by the defined parameters. We do the empirical research by using the hybrid model to forecast two time series datum. One is Mackey-Glass time series data, which is non-linear and strong non-stationary, and another is six stocks price time series data, which is non-linear and weak non-stationary. The HMM-Fuzzy model predicts well for both of these two datasets. However, when the prediction object is non-linear and strong non-stationary time series data, the number of fuzzy rules is very large, it leads the model to become complex.Finally, evolutionary algorithm (EA) is introduced into the model to reduce the number of fuzzy rules, when forecasting the non-linear and strong non-stationary time series data. We propose a hybrid HMM-Fuzzy-EA prediction model. The hybrid model minimizes the number of fuzzy rules by choosing the appropriate mean square error (MSE). If the choice of MSE is not appropriate, it may lead to generate a large number of fuzzy rules, and over-fitting problem. To overcome the problem, we use a multi-objective EA to find a range of compromise solutions between the optimal number of fuzzy rules and the prediction accuracy. According to the empirical study, the appropriate choice of MSE is not only can increase the prediction accuracy but also can reduce the number of fuzzy rules.The research on stock price time series prediction based on Hidden Markov Model and computational intelligence, is conducive to develop cross-disciplinary and multi-channel prediction modeling methods, enriches the theoretical and empirical research results of hybrid forecasting model, and provides better scientific guidance and effective help for stock price time series study.