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• W2000733833 abstract "This paper studies the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix. The auto-cross covariance matrix is defined as $mathbf{M}_{tau}=frac{1}{2T}sum_{j=1}^{T}(mathbf{e} _{j}mathbf{e} _{j+tau}^{*}+mathbf{e} _{j+tau}mathbf{e} _{j}^{*})$, where $mathbf{e} _{j}$ is an $N$ dimensional vectors of independent standard complex components with properties stated in Theorem 1.1, and $tau$ is the lag. $mathbf{M}_{0}$ is well studied in the literature whose LSD is the Marčenko–Pastur (MP) Law. The contribution of this paper is in determining the LSD of $mathbf{M}_{tau}$ where $tauge1$. It should be noted that the LSD of the $mathbf{M}_{tau}$ does not depend on $tau$. This study arose from the investigation of and plays an key role in the model selection of any large dimensional model with a lagged time series structure, which is central to large dimensional factor models and singular spectrum analysis." @default.
• W2000733833 created "2016-06-24" @default.
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• W2000733833 date "2014-06-01" @default.
• W2000733833 modified "2023-09-24" @default.
• W2000733833 title "Limiting spectral distribution of a symmetrized auto-cross covariance matrix" @default.
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• W2000733833 doi "https://doi.org/10.1214/13-aap945" @default.
• W2000733833 hasPublicationYear "2014" @default.
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