Prediction Of Financial Local Trends With Gaussion Hidden Markov Model

The application and development of Data mining is becoming more and more popular in many areas.With the increasing of data,using machine learning algorithm to analysis data would bring us immeasurable value.Especially in the finance,analysing data with algorithm would help investors make better decisions.In this study,we use Hidden Markov Model to forecast the stock price.First we make a comprehensive introduce about the model.Including the definition and the parameters: observation sequence,state sequence,state transition probability matrix,observation probability matrix,and initial state distribution.Given the model HMM,there are three fundamental problems: evaluation problem,decoding problem,and learning problem.We give a detailed analysis for these three problems which relate to Forward-Backward,Viterbi,and BaumWelch algorithm.In real world,it would be advantageous to be able to use HMMs with continuous observation densities.Thus we consider the Gaussian mixture HMM,giving the estimation formulas for the coefficients of the GHMM.Considering the maturity of foreign stock market,we choose the stock price of IBM as the experiment subject.Using the close price and volume as observation data,split data into train data and test data.Then modeling train data with HMM,finding the optimal state sequence,and getting state sequence probability matrix for forecast price.Finally we use the Mean Absolute Deviation to evaluate the precision of prediction.