Decay-Weighted Survivability Estimators: A Nonparametric Class of Regime Detectors with Bounded Forgetting and Reactivation

Tracking regime shifts in non-stationary time series is difficult because standard filtering and changepoint detection algorithms typically discard inactive hypotheses to remain computationally efficient. When the environment shifts abruptly, or reverts to a regime seen before, these models are forced to reconstruct state estimates from limited recent observations. We introduce Decay-Weighted Survivability Estimators (DWSE), a class of nonparametric regime detectors that instead retain inactive hypotheses through a decay-plus-floor trust recurrence: rather than deleting a hypothesis, its trust decays toward a small but nonzero floor, allowing rapid reactivation if the regime it describes recurs. This guarantee is distinct in kind from forgetting-factor results in adaptive filtering, which bound convergence of a parameter estimate; DWSE instead bounds the dynamics of hypothesis selection itself. We instantiate the class in three ways: DWSE-Mean and DWSE-Vol, targeted to shifts in the first and second moments respectively, and DWSE-Rank, an omnibus detector sensitive to distributional change more broadly.We prove finite-sample bounds on hypothesis forgetting time ($T_{\text{forget}}$), reactivation time ($T_{\text{recover}}$), and worst-case detection delay ($T_{\text{detect}}$), alongside a non-asymptotic concentration guarantee. Under stable regime conditions, we further show the centered trust process satisfies a functional central limit theorem, converging weakly to a scaled Brownian motion, giving a principled basis for threshold calibration. On Bitcoin and non-stationary climate data, all three DWSE instances achieve strong recall on labelled regime shifts, performing comparably to or better than classical baselines such as CUSUM, EWMA control charts, directional change, Kalman filtering, and particle filtering, all with the same fixed parameters across domains.