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Spectral analysis of ARMA processes by Prony’s method. (English) Zbl 0553.62084
In this paper a method based on the ARMA process autocovariance coefficients fitting to the exponential model is presented. It is shown that the parameters of the exponential model can be estimated by the extended Prony’s algorithm which requires solving two systems of linear equations and usual methods for finding polynomial roots.
Furthermore, it is shown that the spectral density ARMA process can be computed directly from the parameters of the exponential model. Two numerical examples demonstrate that the presented method can give good spectral estimations even in the cases where classical methods based on the estimates of the covariance coefficients give no results.
62M15 Inference from stochastic processes and spectral analysis
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