Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing

Abstract

In this paper, we combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition to give a parameter estimation method for any perturbed vector autoregressive (VAR) or vector moving average (VMA) process, when we only know a perturbed version of the sequence of correlation matrices of the process. In order to combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition, we first need to generalize a known result on the Cholesky decomposition of Toeplitz matrices to perturbed block Toeplitz matrices.

Keywords

• parameter estimation
• periodogram method for perturbed block Toeplitz matrices
• the Cholesky decomposition
• vector autoregressive (VAR) processes
• vector moving average (VMA) processes