Forecasting a point process with an ARIMA model

In fitting a power-law process, we show that the construction of the empirical recurrence rate time series either simplifies the modeling task, or liberates a point process restrained by a key parametric model assumption such as the monotonicity requirement of the intensity function. The technique can be applied to seasonal events occurring in spurts or clusters, because the autoregressive integrated moving average (ARIMA) procedure provides a comprehensive set of tools with great flexibility. Essentially, we consolidate two of the most powerful modeling tools for the stochastic process and time series in the statistical literature to handle counts of events in a Poisson or Poisson-like process.