A Time-Varying-Parameter State-Space Approach to Sparse-Event Survival Modelling: Methodological Design, Out-of-Sample Performance, and Application to Hydrogen Project Implementation-Risk

We propose a time-varying-parameter (TVP) state-space approach to survival modelling under sparse-event data conditions, in which the conditional hazard depends on a generative-process parameter whose evolution is driven by the score of the predictive likelihood. The score-driven Generalized Autoregressive Score (GAS) specification provides a parsimonious and asymptotically optimal mechanism for parameter time-variation, requiring only the score and a one-parameter persistence specification. The methodology is motivated by, and applied to, the empirical setting of irreversible clean-technology investments under transition uncertainty, where the policy-conditional hazard of project cancellation is plausibly regime-dependent rather than constant - a setting in which constant-parameter survival models systematically under-estimate the time-variation of the operating economic mechanism. Three rival TVP specifications are compared: M1 with constant parameter, M2 with parameter-driven block-step transitions, and M3 with observation-driven GAS persistence. The three are tested for out-of-sample forecast accuracy via three independent designs - a 75-25 time split, 5-fold within-project block cross-validation, and rolling one-step-ahead full-sample prediction. Significance is assessed by the Diebold-Mariano-Harvey-Leybourne-Newbold test on per-observation Bernoulli log-loss. The score-driven specification wins uniformly in point estimates across all three designs and is the unique element of the Hansen-Lunde-Nason Model Confidence Set at alpha = 0.10 under the rolling-one-step design. The DM-HLN test statistics for M3 versus M1 and M3 versus M2 are +5.59 and +4.80 respectively (p