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Pentadiagonal Matrices and an Application to the Centered MA(1) Stationary Gaussian Process

Maicon J. Karling, Artur O. Lopes, Sílvia R. C. Lopes

Abstract



In this work we study the limiting cumulant generating function associated to the bivariate sequence of random vectors, defined by expression (1.2), when the underlying process is the centered stationary moving average of first order with Gaussian innovations. We exhibit the explicit expression of this limiting cumulant generating function. Finally, we present three examples illustrating the theory. To obtain such results, it was first necessary to show some new properties for pentadiagonal symmetric matrices with perturbed corners.

Keywords


pentadiagonal symmetric matrices, non-negative and positive definite matrices, moving average process, limiting cumulant generating function, time series.

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