An Autoregressive Representation of ARMA Processes

Jiři Anděl
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Jiři Anděl: Charles University

A chapter in Probability and Statistical Inference, 1982, pp 13-21 from Springer

Abstract: Abstract Let {Xt} be a p-dimensional stationary invertible autoregressive-moving average process given by $$\mathop {\min }\limits_x f(x)/g(x){\text{ subject to }}h(x) \leqslant 0$$ where {Yt} is a p-dimensional white noise and Aj, Bk are p × p matrices. Denote by f(λ) the matrix of spectral densities of the process {Xt}. It is proved that there exists a 2p-dimensional stationary autoregressive process {Vt} such that the matrix of spectral densities of its first p components is equal to f(λ). An example is given for p=1 for a moving average process of the first order Xt=Yt+ ςYt-1.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-7840-9_2

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DOI: 10.1007/978-94-009-7840-9_2

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