Gaussian kernel based HMM for time series data analysis

An algorithm for incorporating a Gaussian kernel function in to a novel version Hidden Markov Model(HMM) has been proposed for forecasting the stock market levels by classifying current financial data using historical data. K-means algorithm has been invoked for forming arbitrary clusters of the data which in turn have been subjected to minimum distance algorithm for the extraction of features corresponding to expected return and risk. A HMM has been trained with the classified historical data with these attributes. This trained HMM has been used to predict return and risk for NSE index data. Various stages of the proposed model have been explained to list out all the observation and state vectors. Detailed comparative study using statistical distribution of Benchmark data, namely Standard and Poor 500 index and DJIA index, clearly indicate the superiority of this version of HMM tool over the other statistical tools.