ABSTRACT
There has recently been a renewed interest in statistical procedures concerned with the detection of structural breaks in time series, for example, the recent review articles by Aue and Horváth [2] and Horváth and Rice [16]. The literature contains statistics to detect simple mean changes, changes in linear regression, changes in generalized autoregressive conditionally heteroscedastic (GARCH) models; from likelihood ratio to robust M methods (see, e.g., Berkes et al. [3], Davis et al. [6], Hušková and Marušiaková [26], and Robbins et al. [31]). While at first sight, the corresponding statistics appear very different, most of them are derived using the same principles. In this chapter, we shed light on those principles, explaining how corresponding statistics and their respective asymptotic behavior under both the null and alternative hypotheses can be derived. This enables us to give a unified presentation of change point procedures for integer-valued time series. Because the methodology considered in this chapter is by no means limited to these situations, it allows for future extensions in a standardized way.
