{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T02:22:21Z","timestamp":1776738141627,"version":"3.51.2"},"reference-count":67,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,31]],"date-time":"2019-12-31T00:00:00Z","timestamp":1577750400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1752614"],"award-info":[{"award-number":["DMS-1752614"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1405410"],"award-info":[{"award-number":["DMS-1405410"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"UIUC Research Board Award","award":["RB18099"],"award-info":[{"award-number":["RB18099"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified on the basis of comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered on the basis of a kernelized time-varying constrained     L 1    -minimization for inverse matrix estimation (CLIME) estimator on each segment. We derive the rates of convergence for estimating the change points and precision matrices under mild moment and dependence conditions. In particular, we show that this two-step approach is consistent in estimating the change points and the piecewise smooth precision matrix function, under a certain high-dimensional scaling limit. The method is applied to the analysis of network structure of the S&amp;P 500 index between 2003 and 2008.<\/jats:p>","DOI":"10.3390\/e22010055","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T03:28:53Z","timestamp":1578022133000},"page":"55","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Estimation of Dynamic Networks for High-Dimensional Nonstationary Time Series"],"prefix":"10.3390","volume":"22","author":[{"given":"Mengyu","family":"Xu","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL 32816, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohui","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Illinois at Urbana-Champaign, S. Wright Street, Champaign, IL 61820, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei Biao","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Chicago, 5747 S. Ellis Avenue, Jones 311, Chicago, IL 60637, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lauritzen, S. (1996). Graphical Models, Clarendon Press.","DOI":"10.1093\/oso\/9780198522195.001.0001"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1198\/jasa.2009.0126","article-title":"Partial Correlation Estimation by Joint Sparse Regression Models","volume":"104","author":"Peng","year":"2009","journal-title":"J. Am. Stat. 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