Stochastic Modeling for the Analysis and Forecasting of Stock Market Trend using Hidden Markov Model
Gulbadin Farooq Dar *
Ramanujan School of Mathematical Science, Department of Statistics, Pondicherry University, Puducherry - 605014, India.
Tirupathi Rao Padi
Ramanujan School of Mathematical Science, Department of Statistics, Pondicherry University, Puducherry - 605014, India.
Sarode Rekha
Ramanujan School of Mathematical Science, Department of Statistics, Pondicherry University, Puducherry - 605014, India.
Qaiser Farooq Dar
Division of International Trade, Institute of Digital Economy, Incheon National University, Incheon - 22012, South Korea.
*Author to whom correspondence should be addressed.
Abstract
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 19th 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.
Keywords: Markov chain, hidden Markov models, parameters of HMM, stock market, portfolio management