Markov Chain Models for Stock Prices Forecasts and Analysis

Under the condition of complexity and volatility of financial markets, stock price prediction remains a challenging research topic. Markov chain models, with their “memoryless” nature, provide a probabilistic framework for analyzing stock price dynamics. This article reviews various Markov chain applications in stock forecasting, including discrete-time and continuous-time models, the Maximum A Posteriori Hidden Markov model approach, hybrid approaches combined with neural networks or Bayesian inference, and Markov chain-based predictive models. Case studies demonstrate that Markov chains can effectively capture short-term fluctuations, identify long-term steady-state behaviour, and provide interpretable conclusions with minimal data requirements. However, this approach also has limitations: most models rely solely on historical prices, assume constant transition probabilities, and often ignore macroeconomic factors or sudden market shocks. Future research could explore higher-order Markov chains, incorporate multiple inputs such as trading volume and stock correlations, and integrate real-time data to improve forecast accuracy and robustness. Overall, although Markov chains struggle to predict exact prices, they still hold significant application value in probabilistic forecasting, portfolio optimization, and risk management, particularly when combined with big data and computational technologies.