A nonparametric approach to forecast a geophysical system of Poisson type
|Location||International Geological Congress,oslo 2008|
|Holding Date||21 September 2008|
A nonhomogeneous Poisson process (NHPP) is often appropriate for the modeling of a series of events that occur over time in a non-stationary fashion. NHPPs have been used to model event occurrences in a variety of applications in earth sciences, ranging from mining accidents to volcanic hazard and risk assessment studies. A major difficulty with the NHPP is that it has infinitely many forms for the intensity function. This presentation proposes a linking bridge between a point process and the classical time series via a sequence of the empirical recurrence rates, calculated sequentially at equidistant time intervals. The distinctive technique is demonstrated with an empirical recurrence rate plot, designed to fingerprint the temporal pattern of a point process.
Moreover, Autoregressive Integrated Moving Average (ARIMA) models are presented to find the best fitting model to predict the future recurrence rates that in turn, are used to estimate the mean function associated with the underlying NHPP. Valuable modeling and computing techniques are demonstrated based on real data related to Poisson processes. Model validation results, extended to those obtained using the conventional statistical inference procedures, are compared. The interaction between Poisson processes and time series, created in this work, provides additional opportunities for the application of time series methods to the geosciences. Based on the foundation laid, further studies can be carried out to address the applicability of the proposed method to a wide range of geophysical systems including processes with non-monotonic or somewhat periodic recurrence rates, and, in particular, processes with several regimes.