A Markov Chain Model for the Analysis, Prediction and Comparison of Stock Exchange Markets

Stock Exchange Markets are part of the general indicators of the state of an economy and are usually characterized by randomness and volatility. Several methods have been developed for the analysis of such markets to explain and perhaps, predict their long run behavior. These methods are either deterministic or stochastic in approach. This study was intended to analyze the price movements in three selected stock Markets and establish a long-term pattern for their stability and volatility. Data for the study were collected from stock reports for 102 consecutive trading days for the stock markets. The strength and direction of volatility was utilized to define five states of the system, and transition probabilities between states were computed intuitively from available data. The data were then transformed into a 5-state Markov Chain process and analyzed as a transition probability scheme. The stochastic features of Markov Chains were then utilized to compute limiting distributions for the system. Results of analysis established the comparative stability and volatility indices of each of the markets, and this was subsequently used to predict expected outcomes in the short run. The choice of the three exchange markets for this study was informed primarily by the strategic regional importance and size of their capitalizations. Time Series graphical analysis were also employed for further illustration.