Does Adaptive Weighting Improve Equity Market Stress Measurement? Evidence from a GARCH–HMM–EVT Composite Index

This paper investigates whether combining conditional volatility, filtered market-regime probabilities, and extreme-loss severity through regime-conditioned entropy weights improves equity-market stress measurement. An Adaptive Composite Market Stress Index (A-CMSI) is constructed for AAPL, MSFT, and SPY from ARIMA–conditional-variance estimates, forward-filtered five-state Gaussian hidden Markov probabilities, and rolling peaks-over-threshold generalized Pareto expected shortfall. An optional specification adds cross-asset correlation. A chronological expanding-window design uses 2,765 adjusted-price observations from 2015 through 2025, monthly model refits, and mature-label forecast calibration. Across 1,810 held-out 30-day volatility forecasts, Adaptive yields RMSE 0.10532, compared with 0.10457 for equal weighting and 0.10411 for the NoHMM ablation. The Adaptive–Equal Diebold–Mariano test does not reject equal predictive accuracy (p = 0.217). Adaptive achieves a future 30-day crisis ROC AUC of 0.658 and an after-close same-day crisis-detection F1 of 0.300 at an expanding 90th-percentile signal threshold; these are distinct evaluation tasks. Rolling EVT and wavelet diagnostics characterize tails and timescale dependence, while external-index comparisons remain exploratory because revised observations and assumed publication lags are used. The findings support a reproducible stress-measurement framework but do not establish that adaptive weighting outperforms simpler composites.