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Testing hypotheses about the pentadiagonal banded toeplitz covariance structure

John Mateusz

Journal of Applied Mathematics and Computational Mechanics

2025

Vol. 24, nr 2

33--46

In the paper, two tests of pentadiagonal Toeplitz covariance structure are presented. In contrast to standard testing procedures, the likelihood ratio test and the Rao score test, based on maximum likelihood estimation, which in the considered case requires computationally intensive numerical algorithms, the estimators obtained by projection onto the linear space of banded Toeplitz matrices or onto the asymptotic cone of nonnegative definite banded Toeplitz matrices are applied. To investigate the behavior of the test statistics distributions, the simulation study is performed for two particular examples of pentadiagonal Toeplitz structured covariances.