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The Real Part Of A Complex Arma Process

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  • Bailey, Ralph W.

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.

Suggested Citation

  • Bailey, Ralph W., 2007. "The Real Part Of A Complex Arma Process," Econometric Theory, Cambridge University Press, vol. 23(3), pages 537-545, June.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:03:p:537-545_07
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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