On robust estimation of hidden semi-Markov regime-switching models

Regime-switching models provide an efficient framework for capturing the dynamic behavior of data observed over time and are widely used in economic or financial time series analysis. In this paper, we propose a novel and robust hidden semi-Markovian regime-switching (rHSMS) method. This method uses a general $$\rho $$ ρ -based distribution to correct for data problems that contain atypical values, such as outliers, heavy-tailed or mixture distributions. Notably, the rHSMS method enhances not only the scalability of the distribution assumptions for all regimes, but also the scalability to accommodate arbitrary sojourn types. Furthermore, we develop a likelihood-based estimation procedure coupled with the use of the EM algorithm to facilitate practical implementation. To demonstrate the robust performance of the proposed rHSMS method, we conduct extensive simulations under different sojourns and scenarios involving atypical values. Finally, we validate the effectiveness of the rHSMS method using monthly returns of the S &P500 Index and the Hang Seng Index. These empirical applications demonstrate the utility of the rHSMS approach in capturing and understanding the complexity of financial market dynamics.