Abstract: The power of a score or Lagrange multiplier test to discriminate between a linear time series model and some simple bilinear alternatives is examined. It is assumed that the exact form of the bilinear model is unknown so that, instead of the true linear part of the model, the best fitting linear approximation is used as a null model in the test. Theoretical results based on Pitman's asymptotic relative efficiency suggest that selecting the null model in this way may have an adverse effect on the power of the test. According to the simulation results of the paper the problem may have practical significance if the model has a non-zero intercept and the sample size is not large.
Key words and phrases: Asymptotic relative efficiency, bilinear model, Lagrange multiplier test, linear time series, non-linear time series, score test.