Regression Procedures for ARMA Estimation

Abstract

Abstract Regression procedures for parameter estimation in autoregression moving average (ARMA) models are discussed, mainly for providing initial estimates for iterative maximization of a Gaussian likelihood. An iterative procedure of Spliid (1983) is compared to a procedure of Hannan and Rissanen (1982), and a global convergence result is established for an iterative modification of Spliid's procedure. Spliid's iteration does not always converge; when it does, it has the same asymptotic distribution as the second stage of the Hannan-Rissanen procedure. This second-stage iteration gives the same problems as Spliid's procedure, so it is preferable to go immediately to the third stage, which is asymptotically efficient in the Gaussian case. An example is provided by a first-order ARMA model, y(t) + αy(t − 1) = e(t) + βe(t −1), under the usual regularity conditions of stationarity and invertibility. Spliid's procedure fits an autoregression of predetermined order (i.e., 2) to obtain estimates of the e(t), a...