Regime-Arrival Uncertainty in Generalization Bounds under Distribution Shift

Battle Count: 79

Highly relevant to quantitative trading as it directly addresses model deployment risk under regime shifts in financial markets. The paper validates on 25 years of global equity indices and demonstrates that regime composition mismatch (not model architecture) drives deployment failures. The finding that regime geometry is detectable (½d̂=0.93) but temporal arrival is not (ρ=0.084 for training-only penalty) is crucial for practitioners. The framework provides a rigorous post-hoc auditing tool analogous to VaR, enabling stress-testing of trading strategies under hypothetical regime transitions. However, it is diagnostic rather than predictive, limiting direct trading signal generation.

The theoretical framework involves advanced concepts: H∆H-divergence estimation via domain classifiers, beta-mixing effective sample size calculations, spectral gap corrections, and rolling-origin validation with window-clustered bootstrap. The empirical pipeline requires HMM fitting for regime inference, domain classifier training, and careful statistical validation. The mathematical derivations are complex but the practical implementation (fitting HMMs, training classifiers, computing correlations) is moderate. The main challenge is the conceptual framework rather than code complexity.

The paper provides detailed mathematical derivations, explicit proofs in the appendix, and describes the empirical procedure thoroughly (rolling-origin design, window-clustered bootstrap, domain classifier estimation). However, no code repository is mentioned, and the synthetic data generation parameters, while described, would need to be reconstructed. The real data (equity indices) are publicly available. The HMM fitting procedure is described but implementation details are limited.