RC-Mamba: regime-conditioned selective state-space models for probabilistic time-series forecasting.

Selective state-space models (SSMs) such as Mamba achieve linear-time sequence modeling through input-dependent recurrence, yet they apply the same dynamics regardless of the latent regime generating the data-a structural mismatch for non-stationary signals whose statistics shift abruptly between regimes. We introduce RC-Mamba, a probabilistic forecaster whose selective-SSM backbone is dynamically conditioned on the posterior over a latent regime variable. Regime posteriors from a Student-t emission Hidden Markov Model with a sticky Dirichlet prior modulate the SSM discretisation step Δ t together with the input and readout matrices B t and C t , so the recurrence adapts its memory decay, input sensitivity, and output emphasis to the prevailing market state. An entropy-based scale-modulation component, the Regime Uncertainty Gate, is evaluated as a route from posterior sharpness to interval width, but matched controls do not identify a performance gain for it over posterior-independent scaling. A hierarchical Feature-wise Linear Modulation (FiLM) embedding captures asset-specific and sector-level structure without an explicit asset-class prediction objective. Evaluated on 18 US-listed ETFs spanning five asset classes under five calendar-aligned expanding-window walk-forward folds (test years 2021-2025), RC-Mamba achieves a mean Continuous Ranked Probability Score (CRPS) of 0.00532, improving on the Vanilla Temporal Fusion Transformer by 4.7 %, DeepAR by 8.9 %, S-Mamba by 15.2 %, and an HMM-conditioned DeepAR by 18.5 %. All models share robust-MAD preprocessing, a common ceiling of 11,450 optimizer updates with validation-based early stopping, and a 30-business-day origin embargo equal to the maximum forecast horizon, so neither preprocessing nor training budget confounds the architectural comparison. Significance is assessed on 1,110 synchronized forecast origins using a moving-block bootstrap that respects serial and cross-sectional dependence rather than treating overlapping horizons as independent; every comparison remains significant after Holm correction (p Holm = 0.006). RC-Mamba also attains the best Winkler80 score (0.0364) with PICP80 = 0.781 and PINAW80 = 0.024, and recovers three interpretable regimes (Calm, Transition, Stress) that assign every one of the 25 observed April 2025 trading days to the Stress state. Matched single-fold ablations show that removing regime conditioning degrades CRPS by 2.05 % in the most volatile test year, although several component contrasts change sign across folds and are therefore reported as design trade-offs rather than identified causal effects. A one-day-lagged long-only backtest over 1,255 out-of-sample trading days returns 8.89 % annualized against 6.56 % for an equal-weight benchmark, but its annualized alpha of 1.18 % is not statistically significant (p = 0.506) and remains insignificant under 1-10 basis-point costs; the economic evidence is therefore suggestive rather than conclusive. Transfer to non-financial domains is left to future work.