Determining seasonal unit roots with bridge estimator: Monte Carlo evidence and an application to convergence hypothesis

Abstract

HEGY test is a commonly used procedure to test seasonal unit roots. However, the HEGY test is highly sensitive to the deterministic components of the model and the selected lag structure. Therefore, the test may give wrong results if the correct model is not used in terms of the lag structure and deterministic components. Moreover, there is a requirement in the HEGY test that unit roots at different frequencies should be tested separately. Lasso and Bridge estimators, which have been proposed recently with the arise of big data and artificial intelligence studies, are frequently used for model selection and parameter estimation for cross-sectional data. This study proposes a novel approach by adapting the Bridge estimator to the HEGY model and automatically selecting the correct model. Monte Carlo simulations have shown that this approach gives good results in terms of both choosing the correct model and automatically determining the frequencies with a seasonal unit root, with the help of the oracle feature of the Bridge estimator. Moreover, a real data example is provided to demonstrate the usage of our method and to provide a numerical comparison between the Bridge estimator and HEGY test to test the seasonal convergence hypothesis.