{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T11:43:26Z","timestamp":1791546206946,"version":"4.3.4"},"reference-count":60,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T00:00:00Z","timestamp":1680307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"crossref","award":["45723897"],"award-info":[{"award-number":["45723897"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"name":"NSERC of Canada","award":["489079"],"award-info":[{"award-number":["489079"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,5,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we develop statistical inference tools for high-dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis decomposition of functional data in these spaces, and derive Gaussian and multiplier bootstrap approximations for sums of high-dimensional functional time series. These results have numerous important statistical consequences. Exemplarily, we consider the development of joint simultaneous confidence bands for the mean functions and the construction of tests for the hypotheses that the mean functions in the panel dimension are parallel. The results are illustrated by means of a small simulation study and in the analysis of Canadian temperature data.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad015","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T05:53:24Z","timestamp":1680501204000},"page":"523-549","source":"Crossref","is-referenced-by-count":13,"title":["Statistical inference for high-dimensional panel functional time series"],"prefix":"10.1093","volume":"85","author":[{"given":"Zhou","family":"Zhou","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Toronto , Toronto , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Holger","family":"Dette","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Ruhr-Universit\u00e4t Bochum , Universit\u00e4tsstrasse 150, D-44801 Bochum , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,4,3]]},"reference":[{"key":"2023051203365939500_qkad015-B1","volume-title":"Econometric analysis of panel data","author":"Baltagi","year":"2005","edition":"3rd ed."},{"issue":"4","key":"2023051203365939500_qkad015-B2","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1080\/07350015.2015.1102733","article-title":"Inference in high-dimensional panel models with an application to gun control","volume":"34","author":"Belloni","year":"2016","journal-title":"Journal of Business & Economic Statistics"},{"key":"2023051203365939500_qkad015-B3","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1154-9","volume-title":"Linear processes in function spaces","author":"Bosq","year":"2000"},{"issue":"3","key":"2023051203365939500_qkad015-B4","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1023\/A:1021279131053","article-title":"Estimation of mean and covariance operator of autoregressive processes in Banach spaces","volume":"5","author":"Bosq","year":"2002","journal-title":"Statistical Inference for Stochastic Processes"},{"key":"2023051203365939500_qkad015-B5","volume-title":"Introduction to strong mixing conditions, Vols. 1, 2, 3","author":"Bradley","year":"2007"},{"issue":"4","key":"2023051203365939500_qkad015-B6","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1080\/07350015.2017.1421545","article-title":"Testing for slope heterogeneity bias in panel data models","volume":"37","author":"Campello","year":"2019","journal-title":"Journal of Business & Economic Statistics"},{"issue":"1","key":"2023051203365939500_qkad015-B7","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1111\/rssb.12160","article-title":"Modelling function-valued stochastic processes, with applications to fertility dynamics","volume":"79","author":"Chen","year":"2017","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"540","key":"2023051203365939500_qkad015-B8","first-page":"1","article-title":"Inference of breakpoints in high-dimensional time series","volume":"117","author":"Chen","year":"2021","journal-title":"Journal of the American Statistical Association"},{"issue":"526","key":"2023051203365939500_qkad015-B9","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1080\/01621459.2018.1456935","article-title":"Testing for trends in high-dimensional time series","volume":"114","author":"Chen","year":"2019","journal-title":"Journal of the American Statistical Association"},{"issue":"6","key":"2023051203365939500_qkad015-B10","doi-asserted-by":"crossref","first-page":"2786","DOI":"10.1214\/13-AOS1161","article-title":"Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors","volume":"41","author":"Chernozhukov","year":"2013","journal-title":"Annals of Statistics"},{"key":"2023051203365939500_qkad015-B11","volume-title":"The Oxford handbook of panel data","author":"Chudik","year":"2015"},{"issue":"3","key":"2023051203365939500_qkad015-B12","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1109\/TSP.2011.2177831","article-title":"Testing for parallelism among trends in multiple time series","volume":"60","author":"Degras","year":"2012","journal-title":"IEEE Transactions on Signal Processing"},{"issue":"3\u20134","key":"2023051203365939500_qkad015-B13","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1002\/env.1003","article-title":"Statistics for spatial functional data: Some recent contributions","volume":"21","author":"Delicado","year":"2010","journal-title":"Environmetrics"},{"issue":"2","key":"2023051203365939500_qkad015-B14","doi-asserted-by":"crossref","first-page":"2578","DOI":"10.1214\/18-EJS1464","article-title":"Relevant change points in high dimensional time series","volume":"12","author":"Dette","year":"2018","journal-title":"Electronic Journal of Statistics"},{"issue":"4","key":"2023051203365939500_qkad015-B15","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1175\/BAMS-D-12-00170.1","article-title":"U.S. climate reference network after one decade of operations: Status and assessment","volume":"94","author":"Diamond","year":"2013","journal-title":"Bulletin of the American Meteorological Society"},{"issue":"4","key":"2023051203365939500_qkad015-B16","doi-asserted-by":"crossref","first-page":"1497","DOI":"10.3982\/ECTA12749","article-title":"Power enhancement in high-dimensional cross-sectional tests","volume":"83","author":"Fan","year":"2015","journal-title":"Econometrica"},{"issue":"5","key":"2023051203365939500_qkad015-B17","doi-asserted-by":"crossref","first-page":"2296","DOI":"10.1214\/15-AOS1346","article-title":"Functional additive regression","volume":"43","author":"Fan","year":"2015","journal-title":"The Annals of Statistics"},{"key":"2023051203365939500_qkad015-B18","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.ecosta.2016.08.001","article-title":"High-dimensional adaptive function-on-scalar regression","volume":"1","author":"Fan","year":"2017","journal-title":"Econometrics and Statistics"},{"issue":"1","key":"2023051203365939500_qkad015-B19","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1214\/21-EJS1960","article-title":"Finite sample theory for high-dimensional functional\/scalar time series with applications","volume":"16","author":"Fang","year":"2022","journal-title":"Electronic Journal of Statistics"},{"key":"2023051203365939500_qkad015-B20","volume-title":"Nonparametric functional data analysis","author":"Ferraty","year":"2010"},{"issue":"11","key":"2023051203365939500_qkad015-B21","doi-asserted-by":"crossref","first-page":"3476","DOI":"10.1016\/j.jspi.2010.05.008","article-title":"Penalized quantile regression for dynamic panel data","volume":"140","author":"Galvao","year":"2010","journal-title":"Journal of Statistical Planning and Inference"},{"key":"2023051203365939500_qkad015-B22","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.jmva.2018.10.003","article-title":"High-dimensional functional time series forecasting: An application to age-specific mortality rates","volume":"170","author":"Gao","year":"2019","journal-title":"Journal of Multivariate Analysis"},{"key":"2023051203365939500_qkad015-B23","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.1214\/10-EJS575","article-title":"Longitudinal functional principal component analysis","volume":"4","author":"Greven","year":"2010","journal-title":"Electronic Journal of Statistics"},{"issue":"1","key":"2023051203365939500_qkad015-B24","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1111\/rssb.12156","article-title":"Detection of change in the spatiotemporal mean function","volume":"79","author":"Gromenko","year":"2017","journal-title":"Journal of the Royal Statistical Society Series B: Statistical Methodology"},{"key":"2023051203365939500_qkad015-B25","author":"Guo","year":"2020"},{"key":"2023051203365939500_qkad015-B26","author":"Guo","year":"2021"},{"issue":"3","key":"2023051203365939500_qkad015-B27","doi-asserted-by":"crossref","first-page":"1845","DOI":"10.1214\/09-AOS768","article-title":"Weakly dependent functional data","volume":"38","author":"H\u00f6rmann","year":"2010","journal-title":"Annals of Statistics"},{"key":"2023051203365939500_qkad015-B28","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-3655-3","volume-title":"Inference for functional data with applications","author":"Horv\u00e1th","year":"2012"},{"key":"2023051203365939500_qkad015-B29","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511754203","volume-title":"Analysis of panel data","author":"Hsiao","year":"2003","edition":"2nd ed."},{"key":"2023051203365939500_qkad015-B30","doi-asserted-by":"crossref","DOI":"10.1002\/9781118762547","volume-title":"Theoretical foundations of functional data analysis, with an introduction to linear operators","author":"Hsing","year":"2015"},{"key":"2023051203365939500_qkad015-B31","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/3-540-27373-5_42","volume-title":"New developments in classification and data analysis","author":"Ingrassia","year":"2005"},{"issue":"6","key":"2023051203365939500_qkad015-B32","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1214\/15-AOS1347","article-title":"Uniform change point tests in high dimension","volume":"43","author":"Jirak","year":"2015","journal-title":"The Annals of Statistics"},{"issue":"1","key":"2023051203365939500_qkad015-B33","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.jeconom.2016.06.001","article-title":"Oracle inequalities, variable selection and uniform inference in high-dimensional correlated random effects panel data models","volume":"195","author":"Kock","year":"2016","journal-title":"Journal of Econometrics"},{"issue":"3","key":"2023051203365939500_qkad015-B34","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.3982\/ECTA15844","article-title":"Power in high-dimensional testing problems","volume":"87","author":"Kock","year":"2019","journal-title":"Econometrica"},{"issue":"2","key":"2023051203365939500_qkad015-B35","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1017\/S0266466618000087","article-title":"Uniform inference in high-dimensional dynamic panel data models with approximately sparse fixed effects","volume":"35","author":"Kock","year":"2019","journal-title":"Econometric Theory"},{"issue":"1","key":"2023051203365939500_qkad015-B36","doi-asserted-by":"crossref","first-page":"101","DOI":"10.15446\/rce.v42n1.77058","article-title":"Some recent developments in inference for geostatistical functional data","volume":"42","author":"Kokoszka","year":"2019","journal-title":"Revista Colombiana de Estad\u00edstica"},{"issue":"1","key":"2023051203365939500_qkad015-B37","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1093\/biomet\/asv062","article-title":"Partially functional linear regression in high dimensions","volume":"103","author":"Kong","year":"2016","journal-title":"Biometrika"},{"issue":"3","key":"2023051203365939500_qkad015-B38","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1080\/10618600.2019.1710837","article-title":"Bayesian function-on-scalars regression for high-dimensional data","volume":"29","author":"Kowal","year":"2020","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"524","key":"2023051203365939500_qkad015-B39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/01621459.2017.1356726","article-title":"A nonparametric graphical model for functional data with application to brain networks based on FMRI","volume":"113","author":"Li","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023051203365939500_qkad015-B40","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.jeconom.2015.09.005","article-title":"Shrinkage estimation of dynamic panel data models with interactive fixed effects","volume":"190","author":"Lu","year":"2016","journal-title":"Journal of Econometrics"},{"key":"2023051203365939500_qkad015-B41","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.jmva.2016.05.004","article-title":"A local factor nonparametric test for trend synchronism in multiple time series","volume":"150","author":"Lyubchich","year":"2016","journal-title":"Journal of Multivariate Analysis"},{"key":"2023051203365939500_qkad015-B42","author":"Nisol","year":"2019"},{"issue":"2","key":"2023051203365939500_qkad015-B43","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1214\/13-AOS1086","article-title":"Fourier analysis of stationary time series in function space","volume":"41","author":"Panaretos","year":"2013,","journal-title":"The Annals of Statistics"},{"issue":"1","key":"2023051203365939500_qkad015-B44","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1002\/sta4.89","article-title":"Longitudinal functional data analysis","volume":"4","author":"Park","year":"2015","journal-title":"Statistics"},{"issue":"1","key":"2023051203365939500_qkad015-B45","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.jeconom.2007.05.010","article-title":"Testing slope homogeneity in large panels","volume":"142","author":"Pesaran","year":"2008","journal-title":"Journal of Econometrics"},{"key":"2023051203365939500_qkad015-B46","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1554-7","volume-title":"Subsampling","author":"Politis","year":"1999"},{"issue":"525","key":"2023051203365939500_qkad015-B47","first-page":"1","article-title":"Functional graphical models","volume":"114","author":"Qiao","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"2023051203365939500_qkad015-B48","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1093\/biomet\/asz072","article-title":"Doubly functional graphical models in high dimensions","volume":"107","author":"Qiao","year":"2020,","journal-title":"Biometrika"},{"key":"2023051203365939500_qkad015-B49","doi-asserted-by":"crossref","DOI":"10.1007\/b98888","volume-title":"Functional data analysis","author":"Ramsay","year":"2005","edition":"2nd ed."},{"issue":"10","key":"2023051203365939500_qkad015-B50","doi-asserted-by":"crossref","first-page":"3405","DOI":"10.1016\/j.jspi.2009.03.001","article-title":"Partial functional linear regression","volume":"139","author":"Shin","year":"2009","journal-title":"Journal of Statistical Planning and Inference"},{"issue":"36","key":"2023051203365939500_qkad015-B51","doi-asserted-by":"crossref","first-page":"12837","DOI":"10.1073\/pnas.0504609102","article-title":"Significance analysis of time course microarray experiments","volume":"102","author":"Storey","year":"2005","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"8","key":"2023051203365939500_qkad015-B52","doi-asserted-by":"crossref","DOI":"10.3390\/jrfm14080343","article-title":"Forecasting high-dimensional financial functional time series: An application to constituent stocks in Dow Jones index","volume":"14","author":"Tang","year":"2021","journal-title":"Journal of Risk and Financial Management"},{"issue":"3","key":"2023051203365939500_qkad015-B53","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1109\/TITS.2017.2706143","article-title":"A functional data analysis approach to traffic volume forecasting","volume":"19","author":"Wagner-Muns","year":"2018","journal-title":"IEEE Transactions on Intelligent Transportation Systems"},{"key":"2023051203365939500_qkad015-B54","volume-title":"Econometric analysis of cross section and panel data","author":"Wooldridge","year":"2010","edition":"2nd ed."},{"issue":"40","key":"2023051203365939500_qkad015-B55","doi-asserted-by":"crossref","first-page":"14150","DOI":"10.1073\/pnas.0506715102","article-title":"Nonlinear system theory: Another look at dependence","volume":"102","author":"Wu","year":"2005","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"issue":"5","key":"2023051203365939500_qkad015-B56","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1214\/16-AOS1512","article-title":"Gaussian approximation for high dimensional time series","volume":"45","author":"Zhang","year":"2017","journal-title":"Annals of Statistics"},{"key":"2023051203365939500_qkad015-B57","doi-asserted-by":"crossref","first-page":"2640","DOI":"10.3150\/17-BEJ939","article-title":"Gaussian approximation for high dimensional vector under physical dependence","volume":"24","author":"Zhang","year":"2018","journal-title":"Bernoulli"},{"issue":"539","key":"2023051203365939500_qkad015-B58","first-page":"1","article-title":"High-dimensional spatial quantile function-on-scalar regression","volume":"117","author":"Zhang","year":"2021","journal-title":"Journal of the American Statistical Association"},{"issue":"502","key":"2023051203365939500_qkad015-B59","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1080\/01621459.2013.787184","article-title":"Heteroscedasticity and autocorrelation robust structural change detection","volume":"108","author":"Zhou","year":"2013","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023051203365939500_qkad015-B60","first-page":"7157","article-title":"Bayesian graphical models for multivariate functional data","volume":"17","author":"Zhu","year":"2016","journal-title":"The Journal of Machine Learning Research"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/2\/523\/50285756\/qkad015.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/2\/523\/50285756\/qkad015.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,7]],"date-time":"2023-12-07T22:24:00Z","timestamp":1701987840000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/85\/2\/523\/7099701"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,1]]},"references-count":60,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,4,3]]},"published-print":{"date-parts":[[2023,5,4]]}},"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkad015","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,4,1]]},"published":{"date-parts":[[2023,4,1]]}}}