Improving Size and Power in Unit Root Testing

A frequent criticism of unit root tests concerns the poor power and size properties that many of such tests exhibit. However, the past decade or so intensive research has been conducted to alleviate these problems and great advances have been made. The present paper provides a selective survey of recent contributions to improve upon both size and power of unit root tests and in so doing the approach of using rigorous statistical optimality criteria in the development of such tests is stressed. In addition to presenting tests where improved size can be achieved by modifying the standard Dickey-Fuller class of tests, the paper presents theory of optimal testing and the construction of power envelopes for unit root tests under different conditions allowing for serial correlation, deterministic components, assumptions regarding the initial condition, non-Gaussian errors, and the use of covariates.