{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:52:12Z","timestamp":1760237532538,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T00:00:00Z","timestamp":1589932800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/a13050128","type":"journal-article","created":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T10:37:38Z","timestamp":1589971058000},"page":"128","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Change-Point Detection in Autoregressive Processes via the Cross-Entropy Method"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6892-3790","authenticated-orcid":false,"given":"Lijing","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Macquarie University, Sydney, NSW 2109, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5342-7559","authenticated-orcid":false,"given":"Georgy","family":"Sofronov","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Macquarie University, Sydney, NSW 2109, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s10115-016-0987-z","article-title":"A survey of methods for time series change point detection","volume":"51","author":"Aminikhanghahi","year":"2017","journal-title":"Knowl. 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