{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T15:28:03Z","timestamp":1770996483773,"version":"3.50.1"},"reference-count":67,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,8]],"date-time":"2023-06-08T00:00:00Z","timestamp":1686182400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Time-series data are widespread and have inspired numerous research works in machine learning and data analysis fields for the classification and clustering of temporal data. While there are several clustering methods for univariate time series and a few for multivariate series, most methods are based on distance and\/or dissimilarity measures that do not fully utilize the time-dependency information inherent to time-series data. To highlight the main dynamic structure of a set of multivariate time series, this study extends the use of standard variance\u2013covariance matrices in principal component analysis to cross-autocorrelation matrices at time lags k=1,2,\u2026. This results in \u201cprincipal component time series\u201d. Simulations and a sign language dataset are used to demonstrate the effectiveness of the proposed method and its benefits in exploring the main structural features of multiple time series.<\/jats:p>","DOI":"10.3390\/axioms12060570","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T02:03:18Z","timestamp":1686276198000},"page":"570","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Exploring Dynamic Structures in Matrix-Valued Time Series via Principal Component Analysis"],"prefix":"10.3390","volume":"12","author":[{"given":"Lynne","family":"Billard","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Georgia, Athens, GA 30602, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahlame","family":"Douzal-Chouakria","sequence":"additional","affiliation":[{"name":"Centre National de Recherche Scientifique\u2014Laboratoire d\u2019Informatique de Grenoble, Universit\u00e9 Grenoble Alpes, 38401 Saint-Martin-d\u2019H\u00e8res, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6121-0234","authenticated-orcid":false,"given":"S. Yaser","family":"Samadi","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Georgia, Athens, GA 30602, USA"},{"name":"School of Mathematical and Statistical Sciences, Southern Illinois University, Carbondale, IL 62901, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,8]]},"reference":[{"key":"ref_1","first-page":"4188","article-title":"Regularized estimation and testing for high-dimensional multi- block vector-autoregressive models","volume":"18","author":"Lin","year":"2017","journal-title":"J. Mach. Learn. Res."},{"key":"ref_2","unstructured":"Mills, T.C. (1993). The Econometric Modelling of Financial Time Series, Cambridge University Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"104817","DOI":"10.1016\/j.jmva.2021.104817","article-title":"Analysis of dependent data aggregated into intervals","volume":"186","author":"Samadi","year":"2021","journal-title":"J. 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