{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T22:11:42Z","timestamp":1779315102422,"version":"3.51.4"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T00:00:00Z","timestamp":1731628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi","award":["2022L415"],"award-info":[{"award-number":["2022L415"]}]},{"name":"Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi","award":["2022Q15"],"award-info":[{"award-number":["2022Q15"]}]},{"name":"Shanxi Datong University Project","award":["2022L415"],"award-info":[{"award-number":["2022L415"]}]},{"name":"Shanxi Datong University Project","award":["2022Q15"],"award-info":[{"award-number":["2022Q15"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the study of uncertain autoregressive models, how to estimate the unknown parameters and uncertain disturbance term in the models is always a key problem. In view of this, this paper proposes a statistical inference method based on the principle of least squares to determine the unknown parameters and uncertain disturbance term in an uncertain autoregressive model, and designs a numerical algorithm to calculate the numerical solutions of the corresponding estimators. Then, the uncertain hypothesis test is used to verify the applicability of the estimated uncertain autoregressive model, and point forecast and interval forecast are also made for the time series of future moments. Finally, a case study of the Consumer Price Index for all items in U.S. cities is provided to illustrate the effectiveness of the approach proposed in this paper.<\/jats:p>","DOI":"10.3390\/axioms13110789","type":"journal-article","created":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T06:59:13Z","timestamp":1731653953000},"page":"789","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Statistical Inference of Uncertain Autoregressive Model via the Principle of Least Squares"],"prefix":"10.3390","volume":"13","author":[{"given":"Han","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics Science, Shanxi Datong University, Datong 037009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0780-8267","authenticated-orcid":false,"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5719-8893","authenticated-orcid":false,"given":"Haiyan","family":"Shi","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics Science, Shanxi Datong University, Datong 037009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1098\/rsta.1927.0007","article-title":"On a method of investigating periodicities disturbed series, with special reference to Wolfer\u2019s sunspot numbers","volume":"226","author":"Yule","year":"1927","journal-title":"Philos. 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