A constrained robust Markov regime-switching model for long-term risk evaluation

Markov Regime-Switching (MRS) models are widely used for modeling equity return time series. Yet standard MRS models may inadequately capture the mean reversion behavior of long-term equity returns and exhibit unstable parameter estimation due to their reliance on normality assumptions within each regime. These limitations in model adequacy can compromise the accuracy of risk exposure measurements for invested assets. To address these issues, we propose a constrained robust MRS (CRMRS) model, which integrates an order restriction and sparse constraints on regime means and transition probabilities to better capture mean reversion while employing a general ρ-based least favorable distribution to improve distributional flexibility across regimes. We assess the method's performance through finite-sample simulations under various scenarios in the presence or absence of atypical values. Furthermore, we empirically validate the improvements in model adequacy and risk exposure measurement using monthly returns from the S&P/TSX Composite Index, the benchmark for Canadian equity performance, where S&P and TSX stand for Standard & Poor's and the Toronto Stock Exchange, respectively. Our findings demonstrate that the proposed CRMRS-Huber produces stable parameter estimates and superior approximations of higher-order moments, such as skewness and kurtosis, and provides balanced intermediate risk evaluation across all cases.