Limiting spectral distribution of a symmetrized auto-cross covariance matrix
Limiting spectral distribution of a symmetrized auto-cross covariance matrix
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. …