This paper investigates the Lagrange multiplier (LM) test for AR(p) ag
ainst IMA(1, q) error processes in the linear regression model. The ma
in finding of the Monte Carlo experiment, conducted to assess this tes
t, is that the LM test has satisfactory small sample size and power pr
operties. 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 re
al Gross Domestic Product (GDP)/capita series.