Multiple-change-point Detection For Integer-valued Auto-regressive Conditional Heteroscedastic Processes

Integer-valued time series occur in many situations. To model such time series, we can use integer-valued auto-regressive conditional heteroscedastic processes. However, it is unlikely that the data should stay stationary over long time intervals, in another words, there could be some change points. Our aim in this paper is to devise a statistically rigorous, well performing and fast technique for multiple-change-point detection in the INARCH model with piecewise constant parameters, where neither the number nor the amplitudes of the changes are assumed to be known. Our method, termed BASTINA (binary segmentation for transformed inter-valued auto-regressive conditional heteroscedasticity), proceeds in two stages:the process transforma-tion and the binary segmentation stage. The process transformation decorrelates the original process, and the binary segmentation consistently estimates the change points. We use simula-tion to illustrate good performance as well as fine-tune their parameters. At last, we apply our methods to the the number of cases of campylobacterosis infections and reveals an interesting correspondence between the estimated change points and real events.The contents of the paper are as follows. Section 1 is the background of integer-valued time series and some previous research outcomes. Section 2, we will introduce some basis of the model and basic knowledge involved in this paper. Section 3 describes the problem of multiple-change-point detection for integer-valued auto-regressive conditional heteroscedastic processes and provides a computation algorithm for solving the problem. Section 4 provides the outcome of simulations. Section 5, we apply the proposed method to the number of cases of campylobacterosis infections from 1990 to 2000 in Quebec, Canada. Section 6 ends the paper with a brief discussion.