Joint CLT for top eigenvalues of sample covariance matrices of separable high dimensional long memory processes

Peng Tian

For $N,n\in \mathbb{N}$, consider the sample covariance matrix $$S_N(T)=\frac{1}{N}X{X}^{\ast }$$ from a data set $X=C_N^{1/2}Z{T}_n^{1/2}$, where $Z=(Z_{i,j})$ is a $N\times n$ matrix having…