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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. 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