Testing for ar(1) against ima(1,1) disturbances in the linear regression model

This paper examines the testing of stationary AR(1) against non-stationary IMA(1,1) error processes in the linear regression model. The tests investigated include a pure significance test (PS), the Lagrange multiplier (LM) test and the point optimal invariant (POI) tests. A Monte Carlo experiment compares their small sample properties. The main finding of this experiment is that the LM test generally has the most satisfactory size and power properties, particularly in large samples. The asymptotic tests can also be used for testing cointegration against no cointegration of I(1) variables. The PS and LM tests are applied to test for a unit root in Australian 3-month real interest rates and for cointegration of 3- and 6-month Australian Treasury bill rates.