{"paper":{"title":"Order Determination of Large Dimensional Dynamic Factor Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Chen Wang, Matthew Harding, Ya Xue, Z. D. Bai","submitted_at":"2015-11-08T21:55:08Z","abstract_excerpt":"Consider the following dynamic factor model: $\\mathbf{R}_t=\\sum_{i=0}^q \\mathbf{\\Lambda}_i \\mathbf{f}_{t-i}+\\mathbf{e}_t,t=1,...,T$, where $\\mathbf{\\Lambda}_i$ is an $n\\times k$ loading matrix of full rank, $\\{\\mathbf{f}_t\\}$ are i.i.d. $k\\times1$-factors, and $\\mathbf{e}_t$ are independent $n\\times1$ white noises. Now, assuming that $n/T\\to c>0$, we want to estimate the orders $k$ and $q$ respectively. Define a random matrix $$\\mathbf{\\Phi}_n(\\tau)=\\frac{1}{2T}\\sum_{j=1}^T (\\mathbf{R}_j \\mathbf{R}_{j+\\tau}^* + \\mathbf{R}_{j+\\tau} \\mathbf{R}_j^*),$$ where $\\tau\\ge 0$ is an integer. When there "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02534","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}