Simulation, Estimation, and Prediction of Autoregressive Markov Switching Models

MATLAB is a widely used programming language and computing environment designed for algorithm development, data visualization, data analysis, and numerical computation. The autoregressive Markov switching model represents a statistical framework where time series data undergoes regime changes governed by an unobserved Markov chain, with each regime characterized by distinct autoregressive parameters. Through MATLAB implementation, users can simulate these models using functions like hmmgenerate for state sequence generation and custom AR parameter estimation routines, enabling deeper understanding of model dynamics and performance characteristics. The simulation process involves generating state-dependent autoregressive processes and estimating model parameters through maximum likelihood methods using the hmmestimate function. Furthermore, model simulations facilitate forecasting and parameter estimation through Bayesian filtering techniques and the forward-backward algorithm, implemented via MATLAB's Statistical and Machine Learning Toolbox functions. This approach helps researchers analyze relationships between data patterns and model structures, and demonstrates practical applications for time series analysis and predictive modeling.