Markov Chain applied to Returns on Stock Price

Abstract

Markov chain models are commonly used in stock market analysis, manpower planning, and in many other
areas because of its efficiency in predicting long run behaviour. This study proposes a simple predicting tool to forecast the future behaviour of stock prices. The study analyses the stock price model using Akaikes Information Criterion (AIC) and Bayes Information Criterion (BIC). The analysis shows that the AIC supports a second order model whereas the BIC supports a first order model. The maximum likelihood function was found to be of the second order. Apparently, the stock price model is time dependent and time homogeneous and thus, best forecasted using a second order model. As described by the GARCH model, the presence of time varying conditional volatility of stock prices, and a lasting effect of today’s shock on forecast were found. These results agree with the Markov model based on the AIC. The returns were explored for both short and long run behaviours and it was found that if there is a transition between the states of the return in a current week, the expected return would be higher than the overall average return and this would be realized within the next one week, but if the return is in a stable state then the expected return may move above the overall average return after two weeks.The result also shows that in the long run, the stock price is more stable, and the stock return has a higher probability of remaining in an upward state than in a downward state. This paper uniquely contributes to the literature by demonstrating that NSE series can be modelled as a three-state movement - the upward state, the stable state, and the downward state. This method could help investors save time and make optimal decisions.