NEW RELATIONSHIPS BETWEEN ARMA AND AR PROCESSES.

The authors show that the autoregressive part of an ARMA(p,q) model can be represented as a linear combination of q higher order AR models, and that the coefficients of this linear combination form an approximation to the moving-average part. These results are used to develop efficient algorithms for ARMA model estimation. The algorithms presented are substantially faster and simpler than others proposed in the literature and do not require complicated operations such as eigenvalue computation or Newton-method iterations. Moreover, the algorithms the estimation of stable models, which is not provided by other methods.