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

Jesús Gutiérrez-Gutiérrez, Xabier Insausti and Marta Zárraga-Rodríguez
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Jesús Gutiérrez-Gutiérrez: Department of Biomedical Engineering and Sciences, Tecnun, University of Navarra, Paseo Manuel Lardizábal 13, 20018 San Sebastián, Spain
Xabier Insausti: Department of Biomedical Engineering and Sciences, Tecnun, University of Navarra, Paseo Manuel Lardizábal 13, 20018 San Sebastián, Spain
Marta Zárraga-Rodríguez: Department of Biomedical Engineering and Sciences, Tecnun, University of Navarra, Paseo Manuel Lardizábal 13, 20018 San Sebastián, Spain

Mathematics, 2020, vol. 8, issue 4, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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