Toeplitz Inverse Eigenvalue Problem (ToIEP) and Random Matrix Theory (RMT) Support for Calculation of the Toeplitz Covariance Matrix Estimate
Yuri I. Abramovich, Tanit Pongsiri · 2023
“Toeplitization” or “redundancy averaging” is the well-known procedure of getting the Toeplitz matrix estimate from the standard sample covariance matrix. Despite the recently proven asymptotic consistency of this estimate (with$N\rightarrow\infty_{2}T\rightarrow \infty,T/N\rightarrow c)$, for the weakly positive definite covariance matrices, redundancy averaging typically leads to the estimates with a number of negative eigenvalues. In this paper, we demonstrate how these estimates may be rectified to meet a sub-optimal condition, using computational tools from ToIEP and RMT methodologies.