{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T23:08:22Z","timestamp":1788822502150,"version":"build-2803163510"},"reference-count":29,"publisher":"Wiley","issue":"13","license":[{"start":{"date-parts":[[2024,5,1]],"date-time":"2024-05-01T00:00:00Z","timestamp":1714521600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01161303"],"award-info":[{"award-number":["R01161303"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01DK117208"],"award-info":[{"award-number":["R01DK117208"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01DK130067"],"award-info":[{"award-number":["R01DK130067"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["UL1TR001878"],"award-info":[{"award-number":["UL1TR001878"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2024,6,15]]},"abstract":"<jats:p>In this paper, we aim to both borrow information from existing units and incorporate the target unit's history data in time series forecasting. We consider a situation when we have time series data from multiple units that share similar patterns when aligned in terms of an internal time. The internal time is defined as an index according to evolving features of interest. When mapped back to the calendar time, these time series can span different time intervals that can include the future calendar time of the targeted unit, over which we can borrow the information from other units in forecasting the targeted unit. We first build a hierarchical state space model for the multiple time series data in terms of the internal time, where the shared components capture the similarities among different units while allowing for unit\u2010specific deviations. A conditional state space model is then constructed to incorporate the information of existing units as the prior information in forecasting the targeted unit. By running the Kalman filtering based on the conditional state space model on the targeted unit, we incorporate both the information from the other units and the history of the targeted unit. The forecasts are then transformed from internal time back into calendar time for ease of interpretation. A simulation study is conducted to evaluate the finite sample performance. Forecasting state\u2010level new COVID\u201019 cases in United States is used for illustration.<\/jats:p>","DOI":"10.1002\/sim.10097","type":"journal-article","created":{"date-parts":[[2024,5,1]],"date-time":"2024-05-01T23:34:20Z","timestamp":1714606460000},"page":"2655-2671","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dynamic hierarchical state space forecasting"],"prefix":"10.1002","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-8312-6608","authenticated-orcid":false,"given":"Ziyue","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Health Data Science Indiana University School of Medicine  Indianapolis Indiana"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wensheng","family":"Guo","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology and Informatics University of Pennsylvania  Philadelphia 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