{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:23:40Z","timestamp":1760149420431,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T00:00:00Z","timestamp":1691020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper introduces a novel approach, called causal relation quantification, based on change-point detection to address the issue of harmonic responsibility division in power systems. The proposed method focuses on determining the causal effect of chronological continuous treatment, enabling the identification of crucial treatment intervals. Within each interval, three propensity-score-based algorithms are executed to assess their respective causal effects. By integrating the results from each interval, the overall causal effect of a chronological continuous treatment variable can be calculated. This calculated overall causal effect represents the causal responsibility of each harmonic customer. The effectiveness of the proposed method is evaluated through a simulation study and demonstrated in an empirical harmonic application. The results of the simulation study indicate that our method provides accurate and robust estimates, while the calculated results in the harmonic application align closely with the real-world scenario as verified by on-site investigations.<\/jats:p>","DOI":"10.3390\/e25081164","type":"journal-article","created":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T11:08:43Z","timestamp":1691060923000},"page":"1164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Causal Responsibility Division of Chronological Continuous Treatment Based on Change-Point Detection"],"prefix":"10.3390","volume":"25","author":[{"given":"Hang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiefeng","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Conan","family":"Liu","sequence":"additional","affiliation":[{"name":"Business School, University of New South Wales, Sydney, NSW 2052, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuangzhe","family":"Liu","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, University of Canberra, Bruce, ACT 2617, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1080\/01621459.1986.10478354","article-title":"Statistics and causal inference","volume":"81","author":"Holland","year":"1986","journal-title":"J. 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