Regime-conditional resampling for Monte Carlo (volatility clustering)

[MDUYN]

Context

Current Monte Carlo / permutation testing implicitly assumes returns are i.i.d. when shuffling. Real markets exhibit:

• Volatility clustering (GARCH-like behavior)
• Regime shifts (trending vs. mean-reverting, low-vol vs. high-vol)
• Fat tails concentrated in specific regimes

Naive resampling destroys these properties and produces optimistic tail-risk estimates.

Goal

Add a regime-aware resampling mode for both single-strategy and portfolio-level Monte Carlo (see #530) that respects volatility clustering and regime structure.

Approaches to evaluate

1. Block bootstrap with adaptive block length (preserves local volatility structure)
2. Markov-switching regime detection (e.g. 2–3 state HMM on volatility) → resample within regime, preserve regime transition matrix
3. GARCH-filtered resampling: fit GARCH, resample standardized residuals, reconstruct returns
4. Volatility-bucketed resampling: classify bars into vol quantiles, resample within bucket

Acceptance criteria

• New resampling option on existing MC / permutation API
• At least one regime-aware method implemented (block bootstrap with adaptive block length is the pragmatic starting point)
• Diagnostic output: detected regimes / block length / GARCH fit quality
• Docs section explaining when regime-conditional MC matters and which method to pick

Related

• Portfolio-level Monte Carlo with correlated drawdowns #530 Portfolio-level Monte Carlo with correlated drawdowns

Notes

Driven by community discussion on the 1k-stars LinkedIn post. Practitioners running large EA parameter sweeps (millions of combinations on tick data) consistently report that i.i.d. MC underestimates real-world drawdowns.