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

Area of Science:

• Quantitative Finance
• Econometrics
• Time Series Analysis

Background:

• Standard Markov Regime-Switching (MRS) models struggle with mean reversion in long-term equity returns.
• Normality assumptions in MRS models lead to unstable parameter estimation and compromise risk assessment.
• Existing models inadequately capture distributional properties of equity returns.

Purpose of the Study:

• To propose a Constrained Robust Markov Regime-Switching (CRMRS) model for enhanced equity return time series analysis.
• To improve the modeling of mean reversion and distributional flexibility in financial time series.
• To enhance the accuracy of risk exposure measurements for invested assets.

Main Methods:

• Developed a CRMRS model incorporating order restriction and sparse constraints on regime means and transition probabilities.
• Employed a general ρ-based least favorable distribution for improved distributional flexibility.
• Conducted finite-sample simulations and empirical validation using S&P/TSX Composite Index monthly returns.

Main Results:

• The CRMRS-Huber model demonstrated stable parameter estimates across various scenarios.
• Achieved superior approximations of higher-order moments like skewness and kurtosis.
• Provided balanced intermediate risk evaluation, outperforming standard MRS models.

Conclusions:

• The proposed CRMRS model enhances model adequacy for equity return time series.
• CRMRS improves risk exposure measurement accuracy compared to traditional MRS models.
• This approach offers a more robust framework for financial time series analysis and risk management.