THE REAL PART OF A COMPLEX ARMA PROCESS

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+