Change-point detection in an AR(1) process via the cross-entropy method

In time series analysis, it is essential to check whether the observations are obtained by one or by several different mechanisms of data generation. In recent years, this problem, which is known as a change-point or break-point detection problem, has become a question of renewed interest for many researchers. Problems of this type arise in a wide range of applications, including financial time series analysis (e.g. changing volatility), signal processing (e.g.structural analysis of EEG signals), geology data analysis (e.g. analysis of volcanic eruption series) and environmental applications (e.g. detecting changes in ecological systems due to climatic conditions crossing some critical thresholds). This thesis focuses on detecting the changes in the mean level of autoregressive processes. We develop the Cross Entropy method for estimating the locations of change-points as well as parameters of the process in each segment. In order to identify the number of change-points, we use the Minimum Description Length information criterion. We apply the proposed method to simulated and real data to illustrate the usefulness of the approach.