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The Real Part of a Complex ARMA Process


  • Ralph Bailey


Every real ARMA(p,q) process can trivially be written as the real part of a complex ARMA(p,q) process, which we abbreviate as ReCARMA(p,q). Less trivially, every ReCARMA(p,q) process can be represented as a real ARMA(2p,p + q) process or some simpler process. This provides an alternative, ReCARMA, parametrization for real ARMA processes. The choice of which parametrization is preferable in a given context then arises. When cycles are present, the ReCARMA representation is often to be preferred as being more parsimonious, or as having parameters that are easier to interpret.

Suggested Citation

  • Ralph Bailey, 2005. "The Real Part of a Complex ARMA Process," Discussion Papers 05-09, Department of Economics, University of Birmingham.
  • Handle: RePEc:bir:birmec:05-09

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    Complex ARMA processes; cycles; reciprocal polynomials; palindromic polynomials;

    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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