AN INSTRUMENTAL VARIABLE APPROACH TO ARMA MODEL IDENTIFICATION AND ESTIMATION

The paper describes an optimal Instrumental Variable (IV) algorithm for estimating an AutoRegressive Moving Average model of a time series. This IVARMA method is based on a modification of a previous algorithm and utilizes the Simplified Refined Instrumental Variable (SRIV) algorithm to estimate the ARMA model from the results of initial, high order, AutoRegressive (AR) model estimation. Using Monte Carlo simulation, the new algorithm is compared with the maximum likelihood method of ARMA estimation, using the well known PEM algorithm, and shown to produce parameter estimates with similar, statistically efficient properties. It is also incorporated in the Refined Instrumental Variable (RIV) algorithm to produce a new implementation of RIV for the full Box-Jenkins TF model form. Once again, MCS analysis confirms that this performs in a similar, statistically optimal manner to PEM, without the need for gradient-type optimization and with less sensitivity to the choice of initial conditions.