On the numerical implementation of the generalized least squares procedure for arma estimation

Abstract

This paper provides a formal justification for using the generalized least squares procedure to estimate scalar autoregressive moving average models and also suggests an alternative numerical method for evaluating the generalized least squares estimator. The proposed technique makes use of a sequence of recursions supplemented by relatively simple matrix calculations and is at least an order of magnitude faster than the existing methods. Simulation experiments are performed to compare the relative computational efficiency of the suggested method.

Keywords:

• Autoregressive moving average
• Toeplitz band matrix
• Computational method
• Generalized least squares
• Recursive calculation
• Simulation