Distributional Regime Persistence: Geometric Market Memory and Its Forecasting Limits

Abstract

We define distributional regime persistence as the duration for which a rolling empirical return distribution remains geometrically aligned with a high-volatility prototype. Building on Wasserstein market-regime clustering, we estimate low- and high-volatility barycenters from rolling return distributions and locate each window between them using a normalized relative-distance score. This score yields distributional recovery times and cumulative excess memory that can be compared with filtered high-state probabilities from an ordered, variance-targeted Markov-switching GJR-GARCH model. Daily returns for the S&P 500, FTSE 100, Nikkei 225, and Hang Seng from January 2000 through June 2026 produce three main findings. First, raw distributional persistence is strongly scale-related: log realized volatility explains 59.5%–74.3% of its in-sample variation, while a conditional shape-only score retains modest residual information. Second, FTSE and Nikkei produce negative recovery gaps across alternative thresholds and geometries, but their bootstrap intervals include zero; the negative direction appears in 82%–85% of replications. S&P 500 COVID provides the strongest inferential result: its distribution-lagging gap has a 95% bootstrap interval of 4–94 trading days and is positive in 98.5% of replications. Hang Seng Markov-switching estimates are weakly identified and excluded from parametric inference. Third, observed DRP persistence exceeds an overlapping-window IID Student- t null. In a realtime forecast design with pre-2007 fixed prototypes, a multi-horizon volatility benchmark, expanding and rolling estimation, and MSE, MAE, and QLIKE losses, however, DRP produces no stable incremental forecast gain. A separate frozen-cutoff replacement race also rejects a stronger claim that DRP can substitute for the Markov-switching state: DRP loses all three predefined axes—crisis timing, controlled misspecification, and source-market transfer—and therefore does not qualify as an independent portability result. The evidence supports DRP as a measurement and model-diagnostic framework—not as a new clustering claim or a universal forecasting improvement. The negative forecast result is an informational boundary: geometric alignment describes the realized state and model disagreement, but it is not an omitted volatility factor once multi-horizon volatility history is observed.

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