A Markov Switching Autoregressive Model with Time-Varying Parameters

Abstract

This study showcased the Markov switching autoregressive model with time-varying parameters (MSAR-TVP) for modeling nonlinear time series with structural changes. This model enhances the MSAR framework by allowing dynamic parameter adjustments over time. Parameter estimation uses maximum likelihood estimation (MLE) enhanced by the Kim filter, which integrates the Kalman filter, Hamilton filter, and Kim collapsing, further refined by the Nelder–Mead optimization technique. The model was evaluated using U.S. real gross national product (GNP) data in both in-sample and out-of-sample contexts, as well as an extended dataset to demonstrate its forecasting effectiveness. The results show that the MSAR-TVP model improves forecasting accuracy, outperforming the traditional MSAR model for real GNP. It consistently excels in forecasting error metrics, achieving lower mean absolute percentage error (MAPE) and mean absolute error (MAE) values, indicating superior predictive precision. The model demonstrated robustness and accuracy in predicting future economic trends, confirming its utility in various forecasting applications. These findings have significant implications for sustainable economic growth, highlighting the importance of advanced forecasting models for informed economic policy and strategic planning.