Testing for Unit Roots with Prediction Errors

This paper analyzes the relationship between the properties of the prediction errors of a predictor that assumes an autoregressive unit root and its optimal detection. According with this relationship, new autoregressive unit root tests are proposed based on multi-step prediction errors. It is shown that the proposed tests have optimal properties. In the simple AR(1) case, they have similar power to existing tests and very close to the Gaussian power envelope. However, in the general ARMA case, the competing tests have a high size distortion whereas the size distortion of the proposed tests is very small.