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Strictly stationary solutions of spatial ARMA equations

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  • Martin Drapatz

Abstract

The generalization of the ARMA time series model to the multidimensional index set $$\mathbb {Z}^d$$ Z d , $$d\ge 2$$ d ≥ 2 , is called spatial ARMA model. The purpose of the following is to specify necessary conditions and sufficient conditions for the existence of strictly stationary solutions of the ARMA equations when the driving noise is i.i.d. Two different classes of strictly stationary solutions are studied, solutions of causal and noncausal models. For the special case of a first-order model on $$\mathbb {Z}^2$$ Z 2 conditions are obtained, which are simultaneously necessary and sufficient. Copyright The Institute of Statistical Mathematics, Tokyo 2016

Suggested Citation

  • Martin Drapatz, 2016. "Strictly stationary solutions of spatial ARMA equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 385-412, April.
    • Handle: RePEc:spr:aistmt:v:68:y:2016:i:2:p:385-412
    DOI: 10.1007/s10463-014-0500-y
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    References listed on IDEAS

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    1. Roknossadati, S.M. & Zarepour, M., 2010. "M-Estimation For A Spatial Unilateral Autoregressive Model With Infinite Variance Innovations," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1663-1682, December.
    2. Peter J. Brockwell & Alexander Lindner, 2010. "Strictly stationary solutions of autoregressive moving average equations," Biometrika, Biometrika Trust, vol. 97(3), pages 765-772.
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    Cited by:

    1. Pham, Viet Son, 2020. "Lévy-driven causal CARMA random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7547-7574.

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