ABSTRACT
Sample autocovariance matrices are important in high-dimensional linear time series. In addition to just Γˆu and Γˆ
∗ u, we may also be interested in functions
of these. For example, if we wish to study the singular values of Γˆu, we need to consider ΓˆuΓˆ
∗ u. Likewise, as we may recall, in the one-dimensional case,
all tests for white noise are based on quadratic functions of autocovariances. The analogous objects in our model are quadratic polynomials in autocovariances. Thus, we are naturally led to the consideration of matrix polynomials of autocovariances.
