Analysis of rare-event time series with application to Caribbean hurricane data

Max-Planck-Institut für Plasmaphysik, EURATOM-Association - Boltzmannstr. 2, D-85748 Garching bei München, Germany, EU

Corresponding author: vod@ipp.mpg.de

Received: 19 December 2008
Accepted: 9 February 2009

Abstract

A Bayesian analysis of rare-event time series is presented. The model space for the description of the time series of Caribbean hurricanes includes a constant Poisson rate, a rate varying linearly in time and a rate described by a change point function. Bayesian model probabilities for the tropical systems of the Bermudas, Bahamas, and East and West Caribbean regions are calculated. For the Bahamas data also model probabilities for the three different hurricane intensity classes , and tropical storms are obtained. All results show that inclusion of a nonlinear not necessarily monotonic model function is mandatory for proper data representation. For the Bahamas we calculate also predictive distributions of the Poisson rate from which the probabilities of H events in the years 2008 and 2015 are deduced. These data find application in future risk assessment in the insurance industry.