{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T15:25:04Z","timestamp":1726413904643},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T00:00:00Z","timestamp":1710115200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T00:00:00Z","timestamp":1710115200000},"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-2152746"],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2024,4]]},"abstract":"Abstract<\/jats:title>A Bayesian method is proposed for variable selection in high-dimensional matrix autoregressive models which reflects and exploits the original matrix structure of data to (a) reduce dimensionality and (b) foster interpretability of multidimensional relationship structures. A compact form of the model is derived which facilitates the estimation procedure and two computational methods for the estimation are proposed: a Markov chain Monte Carlo algorithm and a scalable Bayesian EM algorithm. Being based on the spike-and-slab framework for fast posterior mode identification, the latter enables Bayesian data analysis of matrix-valued time series at large scales. The theoretical properties, comparative performance, and computational efficiency of the proposed model is investigated through simulated examples and an application to a panel of country economic indicators.<\/jats:p>","DOI":"10.1007\/s11222-024-10402-y","type":"journal-article","created":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T08:02:17Z","timestamp":1710144137000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Bayesian variable selection for matrix autoregressive models"],"prefix":"10.1007","volume":"34","author":[{"given":"Alessandro","family":"Celani","sequence":"first","affiliation":[]},{"given":"Paolo","family":"Pagnottoni","sequence":"additional","affiliation":[]},{"given":"Galin","family":"Jones","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,3,11]]},"reference":[{"key":"10402_CR1","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1002\/jae.2443","volume":"31","author":"D Ahelegbey","year":"2016","unstructured":"Ahelegbey, D., Billio, M., Casarin, R.: Bayesian graphical models for structural vector autoregressive processes. J. Appl. Econom. 31, 357\u2013386 (2016). (https:\/\/onlinelibrary.wiley.com\/doi\/abs\/10.1002\/jae.2443)","journal-title":"J. Appl. Econom."},{"key":"10402_CR2","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1145\/1186785.1186794","volume":"32","author":"B Bader","year":"2006","unstructured":"Bader, B., Kolda, T.: Algorithm 862: Matlab tensor classes for fast algorithm prototyping. ACM Trans. Math. Softw. 32, 635\u2013653 (2006). https:\/\/doi.org\/10.1145\/1186785.1186794","journal-title":"ACM Trans. Math. Softw."},{"key":"10402_CR3","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1111\/1468-0262.00273","volume":"70","author":"J Bai","year":"2002","unstructured":"Bai, J., Ng, S.: Determining the number of factors in approximate factor models. Econometrica 70, 191\u2013221 (2002). https:\/\/doi.org\/10.1111\/1468-0262.00273","journal-title":"Econometrica"},{"key":"10402_CR4","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1002\/jae.1137","volume":"25","author":"M Ba\u0144bura","year":"2010","unstructured":"Ba\u0144bura, M., Giannone, D., Reichlin, L.: Large Bayesian vector auto regressions. J. Appl. Econom. 25, 71\u201392 (2010). https:\/\/doi.org\/10.1002\/jae.1137","journal-title":"J. Appl. Econom."},{"key":"10402_CR5","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/BF00142572","volume":"4","author":"BE Barrett","year":"1994","unstructured":"Barrett, B.E., Gray, J.B.: A computational framework for variable selection in multivariate regression. Stat. Comput. 4, 203\u2013212 (1994)","journal-title":"Stat. Comput."},{"key":"10402_CR6","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2022.2032721","author":"M Billio","year":"2022","unstructured":"Billio, M., Casarin, R., Iacopini, M., Kaufmann, S.: Bayesian dynamic tensor regression. J. Bus. Econ. Stat. (2022). https:\/\/doi.org\/10.1080\/07350015.2022.2032721","journal-title":"J. Bus. Econ. Stat."},{"key":"10402_CR7","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/s11222-022-10157-4","volume":"32","author":"A Bucci","year":"2022","unstructured":"Bucci, A., Ippoliti, L., Valentini, P.: Comparing unconstrained parametrization methods for return covariance matrix prediction. Stat. Comput. 32, 90 (2022)","journal-title":"Stat. Comput."},{"key":"10402_CR8","first-page":"66","volume":"6","author":"A Camehl","year":"2022","unstructured":"Camehl, A.: Penalized estimation of panel vector autoregressive models: a panel lasso approach. Int. J. Forecast. 6, 66 (2022)","journal-title":"Int. J. Forecast."},{"key":"10402_CR9","doi-asserted-by":"publisher","first-page":"929","DOI":"10.1111\/j.1468-2354.2009.00554.x","volume":"50","author":"F Canova","year":"2009","unstructured":"Canova, F., Ciccarelli, M.: Estimating multicountry VAR models. Int. Econ. Rev. 50, 929\u2013959 (2009). (https:\/\/onlinelibrary.wiley.com\/doi\/abs\/10.1111\/j.1468-2354.2009.00554.x)","journal-title":"Int. Econ. Rev."},{"key":"10402_CR10","first-page":"66","volume":"31","author":"F Canova","year":"2013","unstructured":"Canova, F., Ciccarelli, M.: Panel vector autoregressive models: a survey. Adv. Econom. 31, 66 (2013)","journal-title":"Adv. Econom."},{"key":"10402_CR11","doi-asserted-by":"publisher","first-page":"2069","DOI":"10.1214\/12-AOS1029","volume":"40","author":"I Castillo","year":"2012","unstructured":"Castillo, I., van der Vaart, A.: Needles and Straw in a Haystack: posterior concentration for possibly sparse sequences. Ann. Stat. 40, 2069\u20132101 (2012). https:\/\/doi.org\/10.1214\/12-AOS1029","journal-title":"Ann. Stat."},{"key":"10402_CR12","first-page":"1","volume":"66","author":"EY Chen","year":"2021","unstructured":"Chen, E.Y., Fan, J.: Statistical inference for high-dimensional matrix-variate factor models. J. Am. Stat. Assoc. 66, 1\u201318 (2021)","journal-title":"J. Am. Stat. Assoc."},{"key":"10402_CR13","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/s11222-014-9517-6","volume":"26","author":"L Chen","year":"2016","unstructured":"Chen, L., Huang, J.Z.: Sparse reduced-rank regression with covariance estimation. Stat. Comput. 26, 461\u2013470 (2016)","journal-title":"Stat. Comput."},{"key":"10402_CR14","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1016\/j.jeconom.2020.07.015","volume":"222","author":"RHX Chen","year":"2021","unstructured":"Chen, R.H.X., Yang, D.: Autoregressive models for matrix-valued time series. J. Econom. 222, 539\u2013560 (2021)","journal-title":"J. Econom."},{"key":"10402_CR15","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1080\/01621459.2021.1912757","volume":"117","author":"R Chen","year":"2022","unstructured":"Chen, R., Yang, D., Zhang, C.-H.: Factor models for high-dimensional tensor time series. J. Am. Stat. Assoc. 117, 94\u2013116 (2022)","journal-title":"J. Am. Stat. Assoc."},{"key":"10402_CR16","doi-asserted-by":"publisher","first-page":"921","DOI":"10.1007\/s11045-017-0481-0","volume":"29","author":"A Cichocki","year":"2018","unstructured":"Cichocki, A.: Fundamental tensor operations for large-scale data analysis using tensor network formats. Multidimens. Syst. Signal Process. 29, 921\u2013960 (2018). https:\/\/doi.org\/10.1007\/s11045-017-0481-0","journal-title":"Multidimens. Syst. Signal Process."},{"key":"10402_CR17","doi-asserted-by":"publisher","first-page":"830","DOI":"10.1198\/016214504000002050","volume":"100","author":"M Forni","year":"2005","unstructured":"Forni, M., Hallin, M., Lippi, M., Reichlin, L.: The generalized dynamic factor model. J. Am. Stat. Assoc. 100, 830\u2013840 (2005). https:\/\/doi.org\/10.1198\/016214504000002050","journal-title":"J. Am. Stat. Assoc."},{"key":"10402_CR18","first-page":"66","volume":"6","author":"Z Gao","year":"2021","unstructured":"Gao, Z., Tsay, R.S.: A two-way transformed factor model for matrix-variate time series. Econom. Stat. 6, 66 (2021)","journal-title":"Econom. Stat."},{"key":"10402_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ijforecast.2013.04.004","volume":"30","author":"D Gefang","year":"2014","unstructured":"Gefang, D.: Bayesian doubly adaptive elastic-net lasso for VAR shrinkage. Int. J. Forecast. 30, 1\u201311 (2014). (https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0169207013000770)","journal-title":"Int. J. Forecast."},{"key":"10402_CR20","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1080\/01621459.1993.10476353","volume":"88","author":"EI George","year":"1993","unstructured":"George, E.I., McCulloch, R.E.: Variable selection via Gibbs sampling. J. Am. Stat. Assoc. 88, 881\u2013889 (1993)","journal-title":"J. Am. Stat. Assoc."},{"key":"10402_CR21","first-page":"339","volume":"66","author":"EI George","year":"1997","unstructured":"George, E.I., McCulloch, R.E.: Approaches for Bayesian variable selection. Stat. Sin. 66, 339\u2013373 (1997)","journal-title":"Stat. Sin."},{"key":"10402_CR22","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1016\/j.jeconom.2007.08.017","volume":"142","author":"EI George","year":"2008","unstructured":"George, E.I., Sun, D., Ni, S.: Bayesian stochastic search for VAR model restrictions. J. Econom. 142, 553\u2013580 (2008)","journal-title":"J. Econom."},{"key":"10402_CR23","doi-asserted-by":"crossref","unstructured":"Geyer, C.J.: Computation for the Introduction to MCMC Chapter of Handbook of Markov chain Monte Carlo (2010)","DOI":"10.1201\/b10905-2"},{"key":"10402_CR24","doi-asserted-by":"publisher","first-page":"684","DOI":"10.1080\/10618600.2015.1044092","volume":"25","author":"L Gong","year":"2016","unstructured":"Gong, L., Flegal, J.M.: A practical sequential stopping rule for high-dimensional Markov chain Monte Carlo. J. Comput. Graph. Stat. 25, 684\u2013700 (2016). https:\/\/doi.org\/10.1080\/10618600.2015.1044092","journal-title":"J. Comput. Graph. Stat."},{"key":"10402_CR25","volume-title":"Matrix Variate Distributions","author":"A Gupta","year":"1999","unstructured":"Gupta, A., Nagar, D.K.: Matrix Variate Distributions. Chapman & Hall\/CRC, London (1999)"},{"key":"10402_CR26","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1214\/11-BA606","volume":"6","author":"PD Hoff","year":"2011","unstructured":"Hoff, P.D.: Separable covariance arrays via the Tucker product, with applications to multivariate relational data. Bayesian Anal. 6, 179\u2013196 (2011). https:\/\/doi.org\/10.1214\/11-BA606","journal-title":"Bayesian Anal."},{"key":"10402_CR27","doi-asserted-by":"publisher","first-page":"1169","DOI":"10.1214\/15-AOAS839","volume":"9","author":"PD Hoff","year":"2015","unstructured":"Hoff, P.D.: Multilinear tensor regression for longitudinal relational data. Ann. Appl. Stat. 9, 1169\u20131193 (2015). https:\/\/doi.org\/10.1214\/15-AOAS839","journal-title":"Ann. Appl. Stat."},{"key":"10402_CR28","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1146\/annurev-statistics-040220-090158","volume":"9","author":"GL Jones","year":"2022","unstructured":"Jones, G.L., Qin, Q.: Markov chain Monte Carlo in practice. Annu. Rev. Stat. Appl. 9, 557\u2013578 (2022)","journal-title":"Annu. Rev. Stat. Appl."},{"key":"10402_CR29","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1016\/j.jeconom.2015.02.013","volume":"186","author":"A Kock","year":"2015","unstructured":"Kock, A., Callot, L.: Oracle inequalities for high dimensional vector autoregressions. J. Econom. 186, 325\u2013344 (2015)","journal-title":"J. Econom."},{"key":"10402_CR30","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51, 455\u2013500 (2009)","journal-title":"SIAM Rev."},{"key":"10402_CR31","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.euroecorev.2015.09.006","volume":"81","author":"G Koop","year":"2016","unstructured":"Koop, G., Korobilis, D.: Model uncertainty in panel vector autoregressive models. Eur. Econ. Rev. 81, 115\u2013131 (2016)","journal-title":"Eur. Econ. Rev."},{"key":"10402_CR32","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/0304-4076(95)01753-4","volume":"74","author":"G Koop","year":"1996","unstructured":"Koop, G., Pesaran, M., Potter, S.M.: Impulse response analysis in nonlinear multivariate models. J. Econom. 74, 119\u2013147 (1996). (https:\/\/www.sciencedirect.com\/science\/article\/pii\/0304407695017534)","journal-title":"J. Econom."},{"key":"10402_CR33","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.csda.2016.02.011","volume":"101","author":"D Korobilis","year":"2016","unstructured":"Korobilis, D.: Prior selection for panel vector autoregressions. Comput. Stat. Data Anal. 101, 110\u2013120 (2016). (https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0167947316300275)","journal-title":"Comput. Stat. Data Anal."},{"key":"10402_CR34","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1080\/07350015.2019.1677472","volume":"39","author":"D Korobilis","year":"2021","unstructured":"Korobilis, D.: High-dimensional macroeconomic forecasting using message passing algorithms. J. Bus. Econ. Stat. 39, 493\u2013504 (2021)","journal-title":"J. Bus. Econ. Stat."},{"key":"10402_CR35","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1093\/biomet\/asr048","volume":"98","author":"C Lam","year":"2011","unstructured":"Lam, C., Yao, Q., Bathia, N.: Estimation of latent factors for high-dimensional time series. Biometrika 98, 901\u2013918 (2011). https:\/\/doi.org\/10.1093\/biomet\/asr048","journal-title":"Biometrika"},{"key":"10402_CR36","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1111\/obes.12125","volume":"78","author":"M Lanne","year":"2016","unstructured":"Lanne, M., Nyberg, H.: Generalized forecast error variance decomposition for linear and nonlinear multivariate models. Oxf. Bull. Econ. Stat. 78, 595\u2013603 (2016). (https:\/\/onlinelibrary.wiley.com\/doi\/abs\/10.1111\/obes.12125)","journal-title":"Oxf. Bull. Econ. Stat."},{"key":"10402_CR37","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-27752-1","volume-title":"New Introduction to Multiple Time Series Analysis","author":"H L\u00fctkepohl","year":"2005","unstructured":"L\u00fctkepohl, H.: New Introduction to Multiple Time Series Analysis. Springer, Berlin (2005)"},{"key":"10402_CR38","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1093\/biomet\/80.2.267","volume":"80","author":"X-L Meng","year":"1993","unstructured":"Meng, X.-L., Rubin, D.B.: Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80, 267\u2013278 (1993). (http:\/\/www.jstor.org\/stable\/2337198)","journal-title":"Biometrika"},{"key":"10402_CR39","first-page":"107","volume":"29","author":"J Nakajima","year":"2011","unstructured":"Nakajima, J.: Time-varying parameter var model with stochastic volatility: an overview of methodology and empirical applications. Monet. Econ. Stud. 29, 107\u2013142 (2011)","journal-title":"Monet. Econ. Stud."},{"key":"10402_CR40","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.jmva.2011.05.015","volume":"113","author":"M Ohlson","year":"2013","unstructured":"Ohlson, M., Rauf Ahmad, M., von Rosen, D.: The multilinear normal distribution: introduction and some basic properties. J. Multivar. Anal. 113, 37\u201347 (2013). (https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0047259X11001047)","journal-title":"J. Multivar. Anal."},{"key":"10402_CR41","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1198\/016214508000000337","volume":"103","author":"T Park","year":"2008","unstructured":"Park, T., Casella, G.: The Bayesian Lasso. J. Am. Stat. Assoc. 103, 681\u2013686 (2008). https:\/\/doi.org\/10.1198\/016214508000000337","journal-title":"J. Am. Stat. Assoc."},{"key":"10402_CR42","doi-asserted-by":"publisher","unstructured":"Pesaran, M.H., Schuermann, T., Weiner, S.M.: Modeling regional interdependencies using a global error-correcting macroeconometric model. J. Bus. Econ. Stat. 22, 129\u2013162 (2004). https:\/\/doi.org\/10.1198\/073500104000000019","DOI":"10.1198\/073500104000000019"},{"key":"10402_CR43","doi-asserted-by":"crossref","unstructured":"Polson, N., Scott, J., Clarke, B., Severinski, C.: Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction, Vol. 9780199694587 (Oxford University Press, Oxford, 2012)","DOI":"10.1093\/acprof:oso\/9780199694587.003.0017"},{"key":"10402_CR44","doi-asserted-by":"publisher","first-page":"828","DOI":"10.1080\/01621459.2013.869223","volume":"109","author":"V Ro\u010dkov\u00e1","year":"2014","unstructured":"Ro\u010dkov\u00e1, V., George, E.I.: Emvs: the EM approach to Bayesian variable selection. J. Am. Stat. Assoc. 109, 828\u2013846 (2014)","journal-title":"J. Am. Stat. Assoc."},{"key":"10402_CR45","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1080\/01621459.2016.1260469","volume":"113","author":"V Ro\u010dkov\u00e1","year":"2018","unstructured":"Ro\u010dkov\u00e1, V., George, E.I.: The spike-and-slab lasso. J. Am. Stat. Assoc. 113, 431\u2013444 (2018)","journal-title":"J. Am. Stat. Assoc."},{"key":"10402_CR46","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1214\/20-BA1199","volume":"16","author":"V Rockova","year":"2021","unstructured":"Rockova, V., McAlinn, K.: Dynamic variable selection with spike-and-slab process priors. Bayesian Anal. 16, 233\u2013269 (2021)","journal-title":"Bayesian Anal."},{"key":"10402_CR47","doi-asserted-by":"publisher","first-page":"947","DOI":"10.1198\/jcgs.2010.09188","volume":"19","author":"AJ Rothman","year":"2010","unstructured":"Rothman, A.J., Levina, E., Zhu, J.: Sparse multivariate regression with covariance estimation. J. Comput. Graph. Stat. 19, 947\u2013962 (2010). https:\/\/doi.org\/10.1198\/jcgs.2010.09188","journal-title":"J. Comput. Graph. Stat."},{"key":"10402_CR48","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s11222-022-10102-5","volume":"32","author":"S Samanta","year":"2022","unstructured":"Samanta, S., Khare, K., Michailidis, G.: A generalized likelihood-based Bayesian approach for scalable joint regression and covariance selection in high dimensions. Stat. Comput. 32, 47 (2022)","journal-title":"Stat. Comput."},{"key":"10402_CR49","unstructured":"Song, S., Bickel, P.: Large vector auto regressions. Papers, arxiv.\u00a0org (2011)"},{"key":"10402_CR50","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/BF02289464","volume":"51","author":"LR Tucker","year":"1966","unstructured":"Tucker, L.R.: Some mathematical notes on three-mode factor analysis. Psychometrika 51, 279\u2013311 (1966). https:\/\/doi.org\/10.1007\/BF02289464","journal-title":"Psychometrika"},{"key":"10402_CR51","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/S0377-0427(00)00393-9","volume":"123","author":"C Van Loan","year":"2000","unstructured":"Van Loan, C.: The ubiquitous Kronecker product. J Comput. Appl. Math. 123, 85\u2013100 (2000)","journal-title":"J Comput. Appl. Math."},{"key":"10402_CR52","doi-asserted-by":"publisher","unstructured":"Van Loan, C.F., Pitsianis, N.: Approximation with Kronecker Products, pp. 293\u2013314 (Springer, Dordrecht, 1993). https:\/\/doi.org\/10.1007\/978-94-015-8196-7_17","DOI":"10.1007\/978-94-015-8196-7_17"},{"key":"10402_CR53","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1093\/biomet\/asz002","volume":"106","author":"D Vats","year":"2019","unstructured":"Vats, D., Flegal, J.M., Jones, G.L.: Multivariate output analysis for Markov chain Monte Carlo. Biometrika 106, 321\u2013337 (2019). https:\/\/doi.org\/10.1093\/biomet\/asz002","journal-title":"Biometrika"},{"key":"10402_CR54","doi-asserted-by":"publisher","unstructured":"Vats, D., Flegal, J.M. & Jones, G.L.: Monte Carlo Simulation: Are we there yet?, pp. 1\u201315. Wiley, New York (2021). https:\/\/doi.org\/10.1002\/9781118445112.stat08283","DOI":"10.1002\/9781118445112.stat08283"},{"key":"10402_CR55","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s11222-016-9714-6","volume":"28","author":"T Wang","year":"2018","unstructured":"Wang, T., Chen, M., Zhao, H., Zhu, L.: Estimating a sparse reduction for general regression in high dimensions. Stat. Comput. 28, 33\u201346 (2018)","journal-title":"Stat. Comput."},{"key":"10402_CR56","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/j.jeconom.2018.09.013","volume":"208","author":"D Wang","year":"2019","unstructured":"Wang, D., Liu, X., Chen, R.: Factor models for matrix-valued high-dimensional time series. J. Econom. 208, 231\u2013248 (2019). (https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0304407618301787)","journal-title":"J. Econom."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-024-10402-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-024-10402-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-024-10402-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,23]],"date-time":"2024-03-23T04:12:53Z","timestamp":1711167173000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-024-10402-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,11]]},"references-count":56,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["10402"],"URL":"https:\/\/doi.org\/10.1007\/s11222-024-10402-y","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"type":"print","value":"0960-3174"},{"type":"electronic","value":"1573-1375"}],"subject":[],"published":{"date-parts":[[2024,3,11]]},"assertion":[{"value":"10 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"91"}}