Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights

The peaks-over-threshold (POT) method has a long tradition in modelling extremes environmental variables. However, it originally been introduced under the assumption of independently and identically distributed (iid) data. Since data often exhibits time series structure, this is likely to be violated due short- long-term dependencies practical settings, leading clustering high-threshold exceedances. In paper, we first review popular approaches that either focus on or long-range dynamics explicitly. particular, consider conditional POT variants Mittag–Leffler distribution waiting times between Further, propose new two-step approach capturing both correlations simultaneously. We suggest autoregressive fractionally integrated moving average (ARFIMA-POT) approach, which step fits an ARFIMA model original then second utilises classical for residuals. Applying these models oceanographic significant wave heights measured Sefton coast (UK), find neither solely nor satisfactorily explains extremes. ARFIMA-POT however, provides improvement terms fit, underlining need jointly incorporate dependence address extremal clustering, their theoretical justification.