{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T14:17:51Z","timestamp":1774966671483,"version":"3.50.1"},"reference-count":23,"publisher":"Emerald","issue":"1","license":[{"start":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T00:00:00Z","timestamp":1655856000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["GS"],"published-print":{"date-parts":[[2023,1,25]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>The cumulative sum (Cusum) operator, also referred to as accumulating generation operator, is the fundamental of grey system models and proves to be successful in various real-world applications. This paper aims to uncover the advantages of the Cusum operator from a parameter estimation perspective, i.e. comparing integral matching with classical gradient matching.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>Grey system models are represented as a state space form to investigate the effect of measurement errors on estimation performance; subsequently, gradient matching and integral matching are respectively formulated to estimate parameters from noisy observations and, then, their quantitative relationships are established by using matrix computation tricks.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>Extensive simulations, which are conducted on both linear and non-linear models under different sample size and noise level combinations, show that integral matching is superior to gradient matching, and, also the former is less sensitive to measurement error.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>This paper explains why the Cusum operator is widely utilized in grey system models, thereby further solidifying the mathematical fundamentals of grey system models.<\/jats:p><\/jats:sec>","DOI":"10.1108\/gs-03-2022-0029","type":"journal-article","created":{"date-parts":[[2022,6,21]],"date-time":"2022-06-21T11:36:05Z","timestamp":1655811365000},"page":"125-140","source":"Crossref","is-referenced-by-count":4,"title":["Parameter estimation for grey system models: gradient matching versus integral 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