Testing for AR(p) against IMA(1, q) disturbances in the linear regression model

This paper investigates the Lagrange multiplier (LM) test for AR(p) against IMA(1, q) error processes in the linear regression model. The main finding of the Monte Carlo experiment, conducted to assess this test, is that the LM test has satisfactory small sample size and power properties. The sizes and powers of this test are found to be invariant to the set of regressors. The test proposed in this paper can be used for testing cointegration against no cointegration of variables in the linear regression model. The LM test was applied to the Australian real Gross Domestic Product (GDP)/capita series.