{"id":2914,"date":"2025-04-18T08:00:33","date_gmt":"2025-04-18T00:00:33","guid":{"rendered":"https:\/\/changjinyuan.com\/?p=2914"},"modified":"2025-07-07T16:57:41","modified_gmt":"2025-07-07T08:57:41","slug":"%e5%b8%b8%e6%99%8b%e6%ba%90-fang-q-qiao-x-yao-q-2024-on-the-modeling-and-prediction-of-high-dimensional-functional-time-series-journal-of-the-american-statistical-association-1-15","status":"publish","type":"post","link":"https:\/\/changjinyuan.com\/index.php\/publications\/publications-all\/2914\/","title":{"rendered":"\u5e38\u664b\u6e90, Tang, C. Y., &amp; \u6731\u5143\u6b63 (2025+). Bayesian penalized empirical likelihood and Markov Chain Monte Carlo sampling. Journal of the Royal Statistical Society Series B, in press."},"content":{"rendered":"<p>We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series p is large in relation to the length of time series n. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from any two different groups are uncorrelated both contemporaneously and serially. Consequently in our second step those groups are handled separately without the information loss on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for all the transformed functional time series within each group. Furthermore the finite-dimensional structure is represented by that of a vector time series. Modeling and forecasting for the original high-dimensional functional time series are realized via those for the vector time series in all the groups. We investigate the theoretical properties of our proposed methods, and illustrate the finite-sample performance through both extensive simulation and two real datasets. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.<\/p>\r\n\r\n\r\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2025\/04\/JRSSB_online.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"\u5d4c\u5165 Bayesian penalized empirical likelihood and Markov Chain Monte Carlo sampling\"><\/object><a id=\"wp-block-file--media-fe754d1e-2844-47ff-8fc6-dcbabe2ebe58\" href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2025\/04\/JRSSB_online.pdf\">Bayesian penalized empirical likelihood and Markov Chain Monte Carlo sampling<\/a><a href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2025\/04\/JRSSB_online.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-fe754d1e-2844-47ff-8fc6-dcbabe2ebe58\">\u4e0b\u8f7d<\/a><\/div>\r\n","protected":false},"excerpt":{"rendered":"<p>In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two primary objectives: (i) to enhance the inherent flexibility of EL in accommodating diverse model conditions, and (ii) to facilitate the use of well-established Markov Chain Monte Carlo (MCMC) sampling schemes as a convenient alternative to the complex optimization typically required for statistical inference using EL. To achieve the first objective, we propose a penalized approach that regularizes the Lagrange multipliers, significantly reducing the dimensionality of the problem while accommodating a comprehensive set of model conditions. For the second objective, our study designs and thoroughly investigates two popular sampling schemes within the BPEL context. We demonstrate that the BPEL framework is highly flexible and efficient, enhancing the adaptability and practicality of EL methods. Our study highlights the practical advantages of using sampling techniques over traditional optimization methods for EL problems, showing rapid convergence to the global optima of posterior distributions and ensuring the effective resolution of complex statistical inference challenges.<\/p>\n","protected":false},"author":1,"featured_media":4613,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[15],"tags":[],"class_list":["post-2914","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-publications-all"],"acf":[],"lang":"cn","translations":{"cn":2914,"en":2922},"pll_sync_post":[],"_links":{"self":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2914","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/comments?post=2914"}],"version-history":[{"count":16,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2914\/revisions"}],"predecessor-version":[{"id":5048,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2914\/revisions\/5048"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media\/4613"}],"wp:attachment":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media?parent=2914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/categories?post=2914"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/tags?post=2914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}