A0809
Title: A change point test for Poisson INARCH(1) processes with logistic intensity
Authors: Florian Schirra - Fraunhofer ITWM (Germany) [presenting]
Joern Sass - RPTU Kaiserslautern-Landau (Germany)
Stefanie Schwaar - University of Kaiserslautern (Germany)
Abstract: Change point detection methods are a common tool to identify structural changes in the distribution of time series. In recent years, there has been progress in detecting changes within times series in countable spaces, e.g. the natural numbers. For a number of applications, such as outbreak detection of infectious diseases, the theory still needs to be extended. Such time series can be modelled by using Poisson INARCH processes. A common assumption is a contraction property on the autoregressive part of the process, which leads to helpful properties concerning stability and regularity. A downside of this approach is that exponential growth is not possible, although this is essential for modelling outbreaks of infectious diseases. Hence, this contraction property is replaced by an assumption that the function describing the autoregression must be bounded as well as its derivative. This is, in particular, fulfilled for a logistic function as the intensity of the process. It is shown that the process still fulfils important properties like having a stationary distribution and alpha-mixing. The quality of the model is then analysed based on a comparative simulation study.
