Asian Journal of Probability and Statistics

The HMM is generally applied to forecast the hidden system of observation data. In this paper, we deal with the development of HMM for a proper understanding of finance variables in the stock market. Formulation of relationships between and within both the changing share values of Housing Development Finance Corporation Bank Limited (HDFC Bank Ltd) as visible/observed states influenced by the indicators of S&P Bombay Stock Exchange Sensitive Index (Sensex) as invisible/influencing states. Stochastic modeling with hidden Markov models is carried out for exploring various parameters of the model. Mathematical derivations for all the required statistical measures are obtained using the method of moments for the proposed probability distribution. Deducing mathematical formulation of initial probability vector, transition and observed probability matrices were carried out with the empirical data sets. Probability distribution for visible states of various lengths is obtained. It is observed from the empirically analysis that there is the maximum likelihood of rising the share prices of HDFC bank in consecutive two days. Furthermore, an attempt is made to estimate the long-run steady-state behavior of both the SENSEX and HDFC Bank share prices. The share value of HDFC bank will be on rising state from the 19^th day onwards and it may be recommended for good investment choice for the long run. The findings of these studies will be valid for effective decision-making in portfolio management.