Change-point detection in time series data via the cross-entropy method

In many applications data are collected over time and very often the statistical properties, such as mean or variance, of the data will change along data. In recent years, there has been an increasing interest to the problem, which is known as a change-point problem, where it is necessary to detect the number and locations of change-points of time series processes. The change-point detection problem, which may also be called a segmentation or break-point problem, can be found in a wide range of applications, such as 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). For example, many macroeconomic variables such as inflation may be subject to changes in government policy that may cause structural breaks in the data and make highly persistent impacts. An awareness of those changes can assist people to eliminate and manage unnecessary risk and further improve the decision-making.
The main concern of change-point problem is the complexity to build a flexible and effective model to estimate the unknown number and locations of break points in time series. In this paper, we develop an innovative methodology to tackle this problem. We compare the statistical performance of a number of computational methods for estimating unknown parameters of autoregressive data with structural breaks. Specifically, we consider the Cross Entropy method for modelling break points using minimum description length (MDL) information criterion to estimate change-points as well as parameters of the process on each segment. Numerical experiments illustrate the robustness of this approach. We obtain estimates for the locations of change-points in artificially generated sequences and compare the accuracy of these estimates to those obtained with other methods. Finally, we use the proposed method to detect the potential location of change-points in the Australian annual inflation rate data from 1960 to 2016.