Simulation and Estimation Procedures for Stress Release Model

The stress release model is a piecewise linear Markov Process similar to the collective risk model,in which the observations consist of the times and sizes of the Jumps, which are taken to represent the times and sizes of large earthquakes. Earlier studies have shown that the asymptotic behaviour of the likelyhood-based tests for this process against a Poisson null hypothesis show anomalous behaviour. The present paper develops simulation methods for the process and uses them to investigate quantitatively some of the qualitative predictions of theoretical studies. In particular it is confirmed that the distribution of the likelyhood ratio statistic is non-standard.