Testing for Autocorrelation in the Autoregressive Moving Average Error Model

Failure to allow for autocorrelation of the disturbances in a regression model can lead to biased and inconsistent parameter estimates, particularly if the model is autoregressive. While consistent estimation methods are available which allow for autocorrelation, estimation is usually much easier when there is some assurance that autocorrelation is absent. In pursuit of such assurance the present paper develops methods of testing for autocorrelation in two common autoregressive linear regression models. The first model considered is the autoregressive moving average error model (ARMA). It occurs when a first order (two period) moving average of structural disturbances generates the error term of an equation which is to be estimated, and this moving average autocorrelation is taken into account in the process of estimation. A test is developed for the presence of additional Markov autocorrelation of the structural disturbances. The second model considered is the standard autoregressive linear regression model, with a disturbance term which for the purposes of estimation is taken to be serially uncorrelated. Estimation is therefore performed by means of ordinary least squares. A test is developed for the presence of moving average autocorrelation in the disturbance term. In keeping with tradition, both tests are performed by examining the serial correlation of the estimated disturbances. The tests derive from a