A recursive procedure for ARMA modeling

This paper presents a two-part fast recursive algorithm for ARMA modeling. The algorithm first obtains estimates of the p autoregressive coefficients from a set of p extended Yule-Walker equations. An exact recursive lattice algorithm for this estimator is then derived. The q + 1 numerator spectrum coefficients are then obtained by using one of the output data sequences of this lattice algorithm. The complete recursive algorithm is fast in the sense that O(p + q) computations are required for each update. Moreover, an exponential forgetting factor is incorporated to facilitate tracking of time variations in the time series.