Nonparametric modeling and break point detection for time series signal of counts

This paper considers the problem of flexible modeling as well as break point detection for time series signal of counts. In particular, the Poisson Generalized Autoregressive Moving Average (GARMA) models paired with radial basis expansions are used to fit such signals. A genetic algorithm is developed to find the possible breaks and the best fitting model derived from the minimum description length principle. The empirical performance of the proposed methodology is illustrated via a simulation study and a practical analysis of the bursts in the BATSE gamma ray data. Lastly, the consistency of the estimated break points and the model parameters is established under some regularity conditions.