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Equations of model decomposition of ARMA processes. (Spanish) Zbl 0681.62077

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
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