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An Iterative GLS Approach to Maximum Likelihood Estimation of Regression Models with ARIMA Errors
An Iterative GLS Approach to Maximum Likelihood Estimation of Regression Models with ARIMA Errors
RR87-34
Abstract
We present a method for estimating regression models with autoregressive integrated moving average (ARIMA) time series errors. The method maximizes the likelihood for different groups of parameters (AR, regression, and MA) separately within each iteration. The idea is to gain numerical efficiency by using generalized least squares (GLS) to maximize the likelihood over the regression and the autoregressive parameters, leaving only the moving average parameter estimates to be obtained by a nonlinear optimization routine. The method uses the "exact likelihood" suggested by Hillmer and Tiao (1979) that is the exact likelihood for pure moving average models. Implementing the method amounts to feeding vectors of the regression and lagged dependent variable to routines that calculate exact likelihood residuals for pure MA models, and then doing regression with these residuals to get the regression and AR parameters. In this way the same software used for exact MA likelihood estimation may be easily modified and used to estimate models with AR and regression effects.
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Page Last Revised - October 28, 2021
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