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.
Highlights
The Cholesky decomposition has been widely used in statistical signal processing
It has been used for parameter estimation of vector autoregressive (VAR) processes and for parameter estimation of vector moving average (VMA) processes
The parameters of a VAR process can be directly obtained from the Cholesky decomposition of the inverses of its correlation matrices, and the parameters of a VMA process can be directly obtained from the Cholesky decomposition of its correlation matrices
Summary
The Cholesky decomposition has been widely used in statistical signal processing It has been used for parameter estimation of vector autoregressive (VAR) processes and for parameter estimation of vector moving average (VMA) processes. We use the Cholesky decomposition to give a parameter estimation method for any perturbed VAR or VMA process, whenever the sequence of correlation matrices of the perturbed process is asymptotically equivalent to the sequence of correlation matrices of the original process in the. Our parameter estimation method combines the Cholesky decomposition with the periodogram method for perturbed block Toeplitz matrices presented in [2]. Our parameter estimation method for perturbed VMA processes is there applied in another statistical signal processing problem, namely, in multiple-input multiple-output (MIMO).
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