Abstract
It is very often the case that at some moment a time series process abruptly changes its underlying structure and, therefore, it is very important to accurately detect such change-points. In this problem, which is called a change-point (or break-point) detection problem, we need to find a method that divides the original nonstationary time series into a piecewise stationary segments. In this paper, we develop a flexible method to estimate the unknown number and the locations of change-points in autoregressive time series. In order to find the optimal value of a performance function, which is based on the Minimum Description Length principle, we develop a Cross-Entropy algorithm for the combinatorial optimization problem. Our numerical experiments show that the proposed approach is very efficient in detecting multiple change-points when the underlying process has moderate to substantial variations in the mean and the autocorrelation coefficient. We also apply the proposed method to real data of daily AUD/CNY exchange rate series from 2 January 2018 to 24 March 2020.
Highlights
Change-point detection in time series processes, or time series segmentation, has been discussed by many authors in the fields of statistics, computer science, and data mining for several decades [1].Change-point detection has a broad range of applications, including financial time series analysis [2,3], econometrics [4,5], and science and engineering [6,7,8]
A change-point is defined when at least one statistical parameter in a given time series process suddenly changes, which may be caused by the variation in the mean, trend, or other internal parameters
We introduce the two-stage minimum description length (MDL) for our change-point problem based on model (1); the superior flexibility is one strength of MDL
Summary
Change-point detection in time series processes, or time series segmentation, has been discussed by many authors in the fields of statistics, computer science, and data mining for several decades [1].Change-point detection has a broad range of applications, including financial time series analysis [2,3], econometrics [4,5], and science and engineering [6,7,8]. Change-point detection in time series processes, or time series segmentation, has been discussed by many authors in the fields of statistics, computer science, and data mining for several decades [1]. Change-point problems are traditionally divided into two large categories: posterior (off-line) and sequential (on-line) problems; see, for example, [9]. The former is often referred to as segmentation of a signal or time series when all data are observed, while the latter assumes a stream of data coming in real-time. Following the assumption of [10] and [7], a non-stationary time series process is assumed to be segmented by change-points into a sequence of piecewise stationary processes. We are interested in modeling the non-stationary autoregressive AR (p) process and estimating the unknown number of segments and the locations of change points
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