Strictly stationary solutions of multivariate ARMA equations with i.i.d. noise

Peter Brockwell (), Alexander Lindner () and Bernd Vollenbröker ()

Annals of the Institute of Statistical Mathematics, 2012, vol. 64, issue 6, 1089-1119

Abstract: We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of multivariate ARMA equations with independent and identically distributed driving noise. For general ARMA(p, q) equations these conditions are expressed in terms of the coefficient polynomials of the defining equations and moments of the driving noise sequence, while for p = 1 an additional characterization is obtained in terms of the Jordan canonical decomposition of the autoregressive matrix, the moving average coefficient matrices and the noise sequence. No a priori assumptions are made on either the driving noise sequence or the coefficient matrices. Copyright The Institute of Statistical Mathematics, Tokyo 2012

Keywords: VARMA process; Multivariate ARMA; Heavy tails; Infinite variance; Strict stationarity (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10463-012-0357-x

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