Aims: The aim of this study is to develop and evaluate a robust mathematical framework for stock market regime classification using the Median Absolute Deviation (MAD), and to compare its performance with conventional standard deviation-based and quantile-based classification methods under non-Gaussian financial conditions. Study Design: Quantitative analytical study based on statistical modelling and empirical evaluation. Place and Duration of Study: The study utilizes secondary financial data from major global equity indices, namely NIFTY 50 (India), S&P 500 (USA), and Nikkei 225 (Japan), over the period from January 2020 to January 2026. Methodology: Daily log returns were computed from adjusted closing prices. A MAD-based standardized score was used to classify market regimes into five categories. Two benchmark methods, namely standard deviation-based and quantile-based classification, were implemented for comparison. Robustness was evaluated using Regime Balance Index (RBI), Extreme Sensitivity Score (ESS), and Label Stability Ratio (LSR) under controlled outlier contamination. Statistical validation was performed using bootstrap resampling to compute 95% confidence intervals, along with paired t-tests and Wilcoxon signed-rank tests to assess significance. Results: The MAD-based method consistently achieved superior robustness across all datasets. For NIFTY 50, the LSR was 0.9856 compared to 0.9142 (SD-based) and 0.9738 (quantile-based). Similar improvements were observed for S&P 500 (0.9862 vs 0.8967 and 0.9750) and Nikkei 225 (0.9860 vs 0.8876 and 0.9743). The ESS was significantly lower for the MAD method (≈0.014) compared to SD-based methods (up to 0.1124). Bootstrap confidence intervals were narrow, and all statistical tests yielded p-values < 0.001, confirming the significance of the results. The findings have important implications for investors, portfolio managers, and financial analysts, as the proposed framework enables more reliable identification of market risk regimes under extreme volatility conditions. Conclusion: The MAD-based classification framework provides a robust and statistically reliable alternative for stock market regime detection, particularly in environments characterized by extreme volatility and non-normal return distributions.
Majumder et al. (Tue,) studied this question.