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Bai","submitted_at":"2013-12-08T22:55:01Z","abstract_excerpt":"The auto-cross covariance matrix is defined as \\[\\mathbf{M}_n=\\frac{1} {2T}\\sum_{j=1}^T\\bigl(\\mathbf{e}_j\\mathbf{e}_{j+\\tau}^*+\\mathbf{e}_{j+ \\tau}\\mathbf{e}_j^*\\bigr),\\] where $\\mathbf{e}_j$'s are $n$-dimensional vectors of independent standard complex components with a common mean 0, variance $\\sigma^2$, and uniformly bounded $2+\\eta$th moments and $\\tau$ is the lag. Jin et al. [Ann. Appl. Probab. 24 (2014) 1199-1225] has proved that the LSD of $\\mathbf{M}_n$ exists uniquely and nonrandomly, and independent of $\\tau$ for all $\\tau\\ge 1$. 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