{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,26]],"date-time":"2026-07-26T14:00:38Z","timestamp":1785074438208,"version":"3.55.0"},"reference-count":49,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computational Statistics & Data Analysis"],"published-print":{"date-parts":[[2026,12]]},"DOI":"10.1016\/j.csda.2026.108444","type":"journal-article","created":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T23:58:51Z","timestamp":1781827131000},"page":"108444","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Online estimation and dynamic forecasting of multivariate time series streams"],"prefix":"10.1016","volume":"224","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0668-862X","authenticated-orcid":false,"given":"Mingxue","family":"Quan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yonghong","family":"Long","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miao","family":"Tian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/j.csda.2026.108444_bib0001","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1002\/wics.101","article-title":"Principal component analysis","volume":"2","author":"Abdi","year":"2010","journal-title":"Wiley Interdiscip. Rev.: Comput. Stat."},{"issue":"4","key":"10.1016\/j.csda.2026.108444_bib0002","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1007\/s10994-022-06129-4","article-title":"Unsupervised anomaly detection in multivariate time series with online evolving spiking neural networks","volume":"111","author":"B\u00e4\u00dfler","year":"2022","journal-title":"Mach. Learn."},{"issue":"3\u20134","key":"10.1016\/j.csda.2026.108444_bib0003","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1177\/0008068319860302","article-title":"On some asymptotic results for multivariate autoregressive models with estimated parameters","volume":"35","author":"Basu","year":"1986","journal-title":"Calcutta Stat. Assoc. Bull."},{"issue":"15","key":"10.1016\/j.csda.2026.108444_bib0004","doi-asserted-by":"crossref","first-page":"3854","DOI":"10.1109\/TSP.2016.2546225","article-title":"Online censoring for large-scale regressions with application to streaming big data","volume":"64","author":"Berberidis","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/j.csda.2026.108444_bib0005","article-title":"Robust regression via hard thresholding","volume":"28","author":"Bhatia","year":"2015","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"1","key":"10.1016\/j.csda.2026.108444_bib0006","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1111\/insr.12220","article-title":"Online principal component analysis in high dimension: which algorithm to choose?","volume":"86","author":"Cardot","year":"2018","journal-title":"Int. Stat. Rev."},{"key":"10.1016\/j.csda.2026.108444_bib0007","series-title":"Time series: applications to finance","author":"Chan","year":"2004"},{"issue":"6","key":"10.1016\/j.csda.2026.108444_bib0008","doi-asserted-by":"crossref","first-page":"3244","DOI":"10.1214\/18-AOS1777","article-title":"Quantile regression under memory constraint","volume":"47","author":"Chen","year":"2019","journal-title":"Ann. Stat."},{"issue":"3","key":"10.1016\/j.csda.2026.108444_bib0009","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0165-1765(95)00680-E","article-title":"The dynamic effects of aggregate demand and supply disturbances: another look","volume":"49","author":"Crowder","year":"1995","journal-title":"Econ. Lett."},{"key":"10.1016\/j.csda.2026.108444_bib0010","first-page":"145","article-title":"Detection of events in multiple streams of surveillance data: multivariate, multi-stream and multi-dimensional approaches","author":"Dubrawski","year":"2010","journal-title":"Infect. Dis. Inform. Biosurveillance"},{"issue":"3","key":"10.1016\/j.csda.2026.108444_bib0011","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1017\/S0266466600011270","article-title":"Unbiasedness of predictions from etimated vector autoregressions","volume":"1","author":"Dufour","year":"1985","journal-title":"Econom. Theory"},{"issue":"1","key":"10.1016\/j.csda.2026.108444_bib0012","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1080\/00224065.2020.1805377","article-title":"Monitoring and root-cause diagnostics of high-dimensional data streams","volume":"54","author":"Ebrahimi","year":"2021","journal-title":"J. Qual. Technol."},{"key":"10.1016\/j.csda.2026.108444_bib0013","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.eneco.2016.09.008","article-title":"Common long-range dependence in a panel of hourly nord pool electricity prices and loads","volume":"60","author":"Ergemen","year":"2016","journal-title":"Energy Econ."},{"issue":"1","key":"10.1016\/j.csda.2026.108444_bib0014","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.ijforecast.2021.12.004","article-title":"Estimation of a dynamic multi-level factor model with possible long-range dependence","volume":"39","author":"Ergemen","year":"2023","journal-title":"Int. J. Forecast."},{"issue":"5","key":"10.1016\/j.csda.2026.108444_bib0015","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1016\/j.eneco.2010.02.012","article-title":"A vector autoregressive model for electricity prices subject to long memory and regime switching","volume":"32","author":"Haldrup","year":"2010","journal-title":"Energy Econ."},{"issue":"1\u20132","key":"10.1016\/j.csda.2026.108444_bib0016","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.jeconom.2005.07.021","article-title":"A regime switching long memory model for electricity prices","volume":"135","author":"Haldrup","year":"2006","journal-title":"J. Econom."},{"issue":"3","key":"10.1016\/j.csda.2026.108444_bib0017","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1017\/S0266466609090707","article-title":"A simple efficient instrumental variable estimator for panel AR (p) models when both n and t are large","volume":"25","author":"Hayakawa","year":"2009","journal-title":"Econom. Theory"},{"key":"10.1016\/j.csda.2026.108444_bib0018","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.csda.2015.05.004","article-title":"Improved GMM estimation of panel VAR models","volume":"100","author":"Hayakawa","year":"2016","journal-title":"Comput. Stat. Data Anal."},{"key":"10.1016\/j.csda.2026.108444_bib0019","doi-asserted-by":"crossref","first-page":"1371","DOI":"10.2307\/1913103","article-title":"Estimating vector autoregressions with panel data","author":"Holtz-Eakin","year":"1988","journal-title":"Econom.: J. Econom. Soc."},{"issue":"1","key":"10.1016\/j.csda.2026.108444_bib0020","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0304-4076(01)00143-9","article-title":"Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods","volume":"109","author":"Hsiao","year":"2002","journal-title":"J. Econom."},{"key":"10.1016\/j.csda.2026.108444_bib0021","series-title":"Breakthroughs in Statistics: Methodology and Distribution","first-page":"492","article-title":"Robust estimation of a location parameter","author":"Huber","year":"1992"},{"key":"10.1016\/j.csda.2026.108444_bib0022","series-title":"Proceedings of the 37Th Annual ACM Symposium on Theory of Computing","first-page":"202","article-title":"Optimal approximations of the frequency moments of data streams","author":"Indyk","year":"2005"},{"issue":"1","key":"10.1016\/j.csda.2026.108444_bib0023","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1109\/MCI.2021.3129962","article-title":"A multivariate time series streaming classifier for predicting hard drive failures application notes","volume":"17","author":"Ircio","year":"2022","journal-title":"IEEE Comput. Intell. Mag."},{"issue":"1","key":"10.1016\/j.csda.2026.108444_bib0024","first-page":"185","article-title":"On the efficiency of online approach to nonparametric smoothing of big data","volume":"29","author":"Kong","year":"2019","journal-title":"Stat. Sin."},{"issue":"4","key":"10.1016\/j.csda.2026.108444_bib0025","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1561\/0800000013","article-title":"Bayesian multivariate time series methods for empirical macroeconomics","volume":"3","author":"Koop","year":"2010","journal-title":"Found. Trends\/textregistered Econom."},{"key":"10.1016\/j.csda.2026.108444_bib0026","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.inffus.2022.10.008","article-title":"Deep learning for anomaly detection in multivariate time series: approaches, applications, and challenges","volume":"91","author":"Li","year":"2023","journal-title":"Inf. Fusion"},{"key":"10.1016\/j.csda.2026.108444_bib0027","doi-asserted-by":"crossref","DOI":"10.1016\/j.jmva.2022.105017","article-title":"Online statistical inference for parameters estimation with linear-equality constraints","volume":"191","author":"Liu","year":"2022","journal-title":"J. Multivar. Anal."},{"key":"10.1016\/j.csda.2026.108444_bib0028","unstructured":"Luan, Z., Sun, D., Wang, H., Zhang, L., 2024. Efficient online prediction for high-dimensional time series via joint tensor tucker decomposition. arXiv: 2403.18320."},{"issue":"4","key":"10.1016\/j.csda.2026.108444_bib0029","first-page":"361","article-title":"Statistical inference for streamed longitudinal data","volume":"110","author":"Luo","year":"1988","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2026.108444_bib0030","first-page":"1","article-title":"Bayesian inference of vector autoregressions with tensor decompositions","author":"Luo","year":"2025","journal-title":"J. Bus. Econ. Stat."},{"key":"10.1016\/j.csda.2026.108444_bib0031","series-title":"New introduction to multiple time series analysis","author":"L\u00fctkepohl","year":"2005"},{"key":"10.1016\/j.csda.2026.108444_bib0032","series-title":"New Introduction to Multiple Time Series Analysis","first-page":"135","article-title":"Var order selection and checking the model adequacy","author":"L\u00fctkepohl","year":"2005"},{"key":"10.1016\/j.csda.2026.108444_bib0033","series-title":"Symposium on Experimental and Efficient Algorithms","first-page":"430","article-title":"Online distribution estimation for streaming data: framework and applications","author":"Palpanas","year":"2007"},{"issue":"545","key":"10.1016\/j.csda.2026.108444_bib0034","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1080\/01621459.2022.2115374","article-title":"Optimal one-pass nonparametric estimation under memory constraint","volume":"119","author":"Quan","year":"2024","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"10.1016\/j.csda.2026.108444_bib0035","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1111\/j.2517-6161.1980.tb01116.x","article-title":"Order determination for a multivariate autoregression","volume":"42","author":"Quinn","year":"1980","journal-title":"J. R. Stat. Soc. B: Stat. Methodol."},{"key":"10.1016\/j.csda.2026.108444_bib0036","series-title":"Conference on Learning Theory","first-page":"1232","article-title":"Online non-parametric regression","author":"Rakhlin","year":"2014"},{"issue":"1","key":"10.1016\/j.csda.2026.108444_bib0037","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1080\/10618600.2021.1950005","article-title":"Fast and scalable algorithm for detection of structural breaks in big VAR models","volume":"31","author":"Safikhani","year":"2022","journal-title":"J. Comput. Graph. Stat."},{"issue":"4","key":"10.1016\/j.csda.2026.108444_bib0038","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1111\/j.1467-9892.1988.tb00477.x","article-title":"Properties of predictors for multivariate autoregressive models with estimated parameters","volume":"9","author":"Samaranayake","year":"1988","journal-title":"J. Time Ser. Anal."},{"key":"10.1016\/j.csda.2026.108444_bib0039","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1912017","article-title":"Macroeconomics and reality","author":"Sims","year":"1980","journal-title":"Econom.: J. Econom. Soc."},{"key":"10.1016\/j.csda.2026.108444_bib0040","doi-asserted-by":"crossref","first-page":"949","DOI":"10.2307\/2527347","article-title":"Bayesian methods for dynamic multivariate models","author":"Sims","year":"1998","journal-title":"Int. Econ. Rev."},{"key":"10.1016\/j.csda.2026.108444_bib0041","doi-asserted-by":"crossref","DOI":"10.1016\/j.csda.2023.107781","article-title":"Online renewable smooth quantile regression","volume":"185","author":"Sun","year":"2023","journal-title":"Comput. Stat. Data Anal."},{"issue":"5","key":"10.1016\/j.csda.2026.108444_bib0042","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1080\/02331888.2024.2398057","article-title":"Online updating huber robust regression for big data streams","volume":"58","author":"Tao","year":"2024","journal-title":"Statistics"},{"key":"10.1016\/j.csda.2026.108444_bib0043","series-title":"Asymptotic Statistics","author":"Van der Vaart","year":"2000"},{"issue":"3","key":"10.1016\/j.csda.2026.108444_bib0044","doi-asserted-by":"crossref","first-page":"786","DOI":"10.2307\/2111654","article-title":"Concepts and suggestions for robust regression analysis","volume":"39","author":"Western","year":"1995","journal-title":"Am. J. Polit. Sci."},{"issue":"541","key":"10.1016\/j.csda.2026.108444_bib0045","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1080\/01621459.2021.1942013","article-title":"Sparse identification and estimation of large-scale vector autoregressive moving averages","volume":"118","author":"Wilms","year":"2023","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"10.1016\/j.csda.2026.108444_bib0046","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/JSTSP.2012.2234082","article-title":"Change-point detection for high-dimensional time series with missing data","volume":"7","author":"Xie","year":"2012","journal-title":"IEEE J. Sel. Top. Signal Process."},{"issue":"3","key":"10.1016\/j.csda.2026.108444_bib0047","first-page":"1363","article-title":"Dynamic penalized splines for streaming data","volume":"32","author":"Xue","year":"2022","journal-title":"Stat. Sin."},{"issue":"543","key":"10.1016\/j.csda.2026.108444_bib0048","doi-asserted-by":"crossref","first-page":"1630","DOI":"10.1080\/01621459.2021.2002158","article-title":"Online estimation for functional data","volume":"118","author":"Yang","year":"2023","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"10.1016\/j.csda.2026.108444_bib0049","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1080\/07350015.2023.2174124","article-title":"On the least squares estimation of multiple-threshold-variable autoregressive models","volume":"42","author":"Zhang","year":"2024","journal-title":"J. Bus. Econ. Stat."}],"container-title":["Computational Statistics & Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947326001131?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167947326001131?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,26]],"date-time":"2026-07-26T13:16:27Z","timestamp":1785071787000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167947326001131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,12]]},"references-count":49,"alternative-id":["S0167947326001131"],"URL":"https:\/\/doi.org\/10.1016\/j.csda.2026.108444","relation":{},"ISSN":["0167-9473"],"issn-type":[{"value":"0167-9473","type":"print"}],"subject":[],"published":{"date-parts":[[2026,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Online estimation and dynamic forecasting of multivariate time series streams","name":"articletitle","label":"Article Title"},{"value":"Computational Statistics & Data Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.csda.2026.108444","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"108444"}}