THE REAL PART OF A COMPLEX ARMA PROCESS

Ralph Bailey ()

Econometric Theory, 2007, vol. 23, issue 3, 537-545

Abstract: In what follows all processes referred to are weakly stationary. Let us call the real part of a complex ARMA(p,q) process a Re CARMA(p,q) process. Every real ARMA(p,q) process can trivially be written as a Re CARMA(p,q) process. Provided the moment properties of complex linear processes are appropriately specified, the following inverse result is available: every Re CARMA(p,q) process is spectrally equivalent to a real ARMA(2p,p + q) process or some simpler process. Thus the ARMA and Re CARMA classes are spectrally equivalent. The question of whether an ARMA or a Re CARMA parametrization is better in a given context then arises. If cyclicality is present, and especially if we wish to treat cycles, growth, and decay together, in a model whose parameters are easy to interpret, then a Re CARMA approach may be helpful.The author thanks Paolo Paruolo, A.M. Robert Taylor, and an anonymous referee for helpful suggestions.

Date: 2007
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