The Research Of Hidden Markov Model And Its Application In Financial Time Series

Financial time series have typical characteristics of outliers, trends and meanreversion. The validity of the unknown parameter estimates of the financial timeseries forecasting model will be affected by these characteristics. And the model’sprediction-error becomes larger. This paper presents the regime switching mixturepredict model based on the Hidden Markov Model(HMM) to predict a financialtime series. The method reduces the prediction error.First, create a HMM by using data of a financial time series. Assuming themodel has two hidden states: normal state and abnormal state. Calculate theprobabilities of data points in two hidden states with Viterbi algorithm. Determinethe point in an abnormal state when it’s abnormal-state-probability lager than giventhreshold value. Else is normal state point. Divide financial time series data intotwo categories according to the state of the data points. The two categories is classof the normal state and the class of abnormal state. Calculate the two statesprobability at time T+1: T1(i)by using the two states probability at time T:T(i)and State transition probability. And decide the hidden state of point at timeT+1according to the given threshold value.Then predict the value of the financial time series by three kinds of regimeswitching mixture predict model. When the number of data isn’t large, the model isLSSVM-LSSVM model: Establish the Least Squares Support Vector MachineModel (LSSVM) by the normal state data in the training sample set to predict thevalue of time T+1when the hidden state is the normal state. Establish the LSSVMby all data in the training sample set to predict the value of time T+1when thehidden state is the abnormal state. When the number of data is large, the model isKERNEL-KERNEL model: Establish the non-parametric kernel regression modelby the normal state data in the training sample set to predict the value of time T+1when the hidden state is the normal state. Establish the non-parametric kernelregression model by all data in the training sample set to predict the value of timeT+1when the hidden state is the abnormal state. As the improvement of KERNEL--KERNEL model, the KERNEL-LSSVM model is: Establish the non-parametrickernel regression model by the normal state data in the training sample set to predict the value of time T+1when the hidden state is the normal state. Establishthe LSSVM model by the abnormal state data in the training sample set to predictthe value of time T+1when the hidden state is the abnormal state.Some empirical analysis of the Shanghai Composite Index and the NasdaqComposite Index will confirm that the method of regime switching mixture predictmodel in this paper can predict the financial time series effectively and be betterthan the ordinary non-parametric kernel regression model and the ordinary LSSVMmodel. The data of the empirical analysis is2932closing prices of ShanghaiComposite Index until March11,2012and5000closing prices of NasdaqComposite Index until March11,2012.