Finding an ARMA(p,q) model given its spectral density or its correlogram
  An ARMA model can be fully determined based on either its spectral density, or its correlogram, i.e. a formula for computing the corresponding k th serial correlation for any integer k. In this article we describe how to find, given one of these three ways of specifying the model, the other two. 
Jan Vrbik
math.ST stat.TH