ARMA processes: order estimation

The authors study, for an ARMA (autoregressive moving-average) ( p₀, q₀) process, the joint determination from a finite data sample of its structural parameters p₀ and q₀, its AR and MA components, and its innovation power σ². The order estimation algorithm is based on the minimization of a functional d that measures the mismatch of the assumed model ARMA (p, q) to the data. The functional is evaluated from the estimated reflection coefficient sequence associated with the process. When the orders are decided, the proposed technique simultaneously provides the estimates of the AR and the MA coefficients as well as σ²