Egozcue, J. J.; Griful, E. Equations of model decomposition of ARMA processes. (Spanish) Zbl 0681.62077 Stochastica 11, No. 2-3, 121-136 (1987). The problem of decomposing a stationary ARMA process Y as the sum of autoregressive processes of order 1, each corresponding to a pole of the transfer function, is considered. By equating the spectral densities, a system of nonlinear equations is obtained, having the covariance C of the forcing white noise as unknown. Since existence is always guaranteed, the multiplicity of solutions is investigated. If C has rank 1, each of these solutions comes from the spectral representation of an ARMA process having the same spectral density as Y. If C has rank \(r>1\), it is firstly needed to decompose (in \(L^ 2)\) the process Y as the sum of r orthogonal ARMA processes with the same poles as Y in order to apply the previous result. So, in this latter case, solutions may only reproduce the second order characteristics of Y. Reviewer: M.Piccioni MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60G10 Stationary stochastic processes 62M15 Inference from stochastic processes and spectral analysis Keywords:decomposition of ARMA processes; stationary ARMA process; sum of autoregressive processes of order 1; spectral densities; nonlinear equations; white noise; multiplicity of solutions; spectral representation; orthogonal ARMA processes; poles; second order characteristics PDFBibTeX XMLCite \textit{J. J. Egozcue} and \textit{E. Griful}, Stochastica 11, No. 2--3, 121--136 (1987; Zbl 0681.62077)