Prediction Of Stock Price Index With Second-order Continuous Hidden Markov Model

Stock price index is a statistic generated by stock exchange that calculates the local representative stock,which describes changes in the local stock market as a composite price indicator.However,prediction of stock price index movement is regarded as a challenging task of financial time series prediction.As a result,more and more scholars are scrambling into prediction of the stock price index,making it a research hot.So the development of efficient forecasting model is very meaningful.As the stock price index is of the property of hidden Markov chain,a new prediction method of stock price index based on hidden Markov model is proposed in this paper.The first-order continuous hidden Markov model is generalized to the second-order continuous hidden Markov model through the deduction of Baum-Welch algorithm.The stock price index is successfully predicted with the change trend and change rate which are predicted with the proposed method.The main content in this paper is as follows:Firstly the S&P 500 index data which is one of the important measures of economic market of the United States is collected and the closing price after adjustment from 1 July,2014 to 6 November,2014,91 days is taken as the research object.The scatterplot of the closing price can be drawn with Matlab and the change rule which can be clearly found is full with complex nonlinearity and randomness.Then combined with K-Means clustering algorithm and the dichotomy,a new prediction model of stock price index with two states is proposed by studying the property of the hidden Markov model and using evaluating,decoding and learning problems in the hidden Markov model.And the new prediction method for the stock price index is verified to have a certain validity and feasibility.Finally extending the discrete hidden Markov model to continuous hidden Markov model and extending the first-order continuous hidden Markov model to second-order continuous hidden Markov model with the actual situation.A prediction of stock price index is made with the new proposed method based on the continuous hidden Markov model.The experiment proved that the proposed prediction method based on second-order continuous hidden Markov model for the stock price index doesn't only have faster convergence speed,but also have a higher degree of accuracy than that based on the first-order continuous hidden Markov model.