Abstract This work develops M-estimator–based unit root tests within a broad class of nonlinear dynamic models. These tests are derived using Taylor-series approximations of nonlinearities to any order, allowing them to be viewed as M-estimator–based extensions of Ramsey’s RESET test with unit root regressors. The theory presented is general and encompasses much of the existing framework for both M-estimator–based unit root tests in the linear AR(1) model and LS-based unit root tests in linear and nonlinear models. The finite sample properties of the test are examined in Monte Carlo simulations. Under a unit root null hypothesis with innovation (additive) outliers, results show that the tests can be slightly (grossly) under (over)-sized. To partially address these issues, a bootstrap version of the tests is proposed in the case for innovation outliers. Regarding power, the M-estimator–based tests outperform LS-estimator–based tests in nonlinear time series models with innovation outliers. The practical application of these M-estimator–based unit root tests is illustrated using eight major exchange rate series. Outlier robust tests, based on ESTAR nonlinearities, provide support for the purchasing power parity hypothesis in all but two series.
Rickard Sandberg (Thu,) studied this question.