Testing moving average against autoregressive disturbances in the linear-regression model

This article considers testing for first-order moving average against first-order autoregressive disturbances in the linear-regression model. Tests investigated include approximate point-optimal invariant (POI) tests, an asymptotic test of the second-order residual autocorrelation coefficient, and a Lagrange multiplier-(LM) test. A Monte Carlo experiment compares their small- sample performances. Of the asymptotic tests, the LM test has the most satisfactory sizes, but its rival has the better overall power. We find that the approximate POI tests have superior size and power properties in comparison to the asymptotic tests. An approximate POI test is applied to a random-walk model for Australian real interest rates.