Probabilistic Sequence Generation Guided by Intensity-Duration Extreme Profiles

Extreme events play a critical role in many time-series domains, including weather and finance, where tail behavior is central to risk assessment and decision-making. In practice, informative summaries of tail behavior, such as return-level curves derived from the Generalized Extreme Value (GEV) distribution, can be obtained via statistical extrapolation. We consider how such partial extreme-value information can be used to guide the generation of full future trajectories and improve tail realism. To this end, we instantiate the idea for multi-year weather generation used for heatwave risk evaluation, where Heatwave Intensity-Duration-Frequency (HIDF) surfaces are leveraged as year-level likelihood constraints via a particle-filter-style rollout procedure. Using HIDF surfaces extracted from historical observations as oracle targets, experiments on Phoenix, Miami, and Munich (2011-2024) isolate the controllability of the guidance mechanism. Sequential conditioning reduces warm-day exceedance bias (TX90p-Bias) by 4-14\% relative to unguided generation, with comparable bulk-distribution preservation, although direct post-hoc HIDF calibration remains stronger on the explicit HIDF alignment metric. We further apply the framework to future weather generation conditioned by extrapolated HIDF targets derived from a nonstationary GEV driven by CMIP6 warming signals.