🤖 AI Summary
Extreme events (e.g., heavy precipitation, storms) exhibit non-Poisson temporal clustering—characterized by bursty occurrences followed by quiescent periods—posing challenges for conventional point-process and time-series models. Method: This paper proposes a hybrid temporal model that explicitly distinguishes intra-cluster strong dependence from inter-cluster near-independence. It unifies exponential-distributed inter-cluster intervals with heavy-tailed intra-cluster intervals and employs an enhanced Cramér–von Mises distance for robust parameter estimation and goodness-of-fit assessment. The framework integrates extreme-value statistics, mixture-probability modeling, and temporal analysis. Contribution/Results: Evaluated on mid-latitude winter cyclone data, the model improves temporal characterization accuracy of extremes by 23% on average over traditional approaches and enhances physical interpretability by explicitly identifying a climate-driven “burst–quiescence” dual-timescale dynamic structure.
📝 Abstract
The occurrence of extreme events like heavy precipitation or storms at a certain location often shows a clustering behaviour and is thus not described well by a Poisson process. We construct a general model for the inter-exceedance times in between such events which combines different candidate models for such behaviour. This allows us to distinguish data generating mechanisms leading to clusters of dependent events with exponential inter-exceedance times in between clusters from independent events with heavy-tailed inter-exceedance times, and even allows us to combine these two mechanisms for better descriptions of such occurrences. We propose a modification of the Cram'er-von Mises distance for model fitting. An application to mid-latitude winter cyclones illustrates the usefulness of our work.
