NONNESTED TESTING FOR AUTOCORRELATION IN THE LINEAR-REGRESSION MODEL

This paper investigates the construction and application of point-opti mal invariant (POI) tests of joint AR(1)-AR(4) disturbances against jo int MA(1)-MA(4) disturbances in the linear regression model. A Monte C arlo experiment is conducted to assess and compare the small sample pe rformances of two asymptotic tests and two POI tests. Of the asymptoti c tests, the Lagrange multiplier test is found to have distinctly bett er small sample properties than the prediction test. We also find that the extra computation required to perform a POI test is rewarded by a clear improvement in size and power properties in comparison to the a symptotic tests. The use of a POI test is illustrated with an applicat ion to a quarterly model of price inflation in the United Kingdom duri ng 1947-1970. The paper concludes with some discussion of the problem of testing general AR(p) disturbances against MA(q) disturbances.