Sequential change-point detection in Poisson autoregressive models

Abstract

We consider the sequential change-point detection in a general class of Poisson autoregressive models. The conditional mean of the process depends on a parameter theta*_0 in Theta include in R^d which may change over time as and when data are observed. We propose a closed and open-end procedure based on the maximum likelihood estimator of the parameter. Under the null hypothesis of no change, it is shown that the detector converges to a well know distribution. The (empirical) power and the efficiency in terms of the detection delay are assessed through a simulation study and a real data example is provided.