This paper considers a class of parametric models with nonparametric autoregressive errors. A new test is established and studied to deal with the parametric specification of the nonparametric autoregressive errors with either stationarity or nonstationarity. Such a test procedure can initially avoid misspecification through the need to parametrically specify the form of the errors. In other words, we estimate the form of the errors and test for stationarity or nonstationarity simultaneously. We establish asymptotic distributions of the proposed test. Both the setting and the results differ from earlier work on testing for unit roots in parametric time series regression. We provide both simulated and real-data examples to show that the proposed nonparametric unit root test works in practice.
The authors thank the editor, Professor Tom Fomby, and a referee for their constructive comments. The first author also acknowledges useful comments from the participants of the the Advances in Econometrics conference held at Southern Methodist University on November 1–3, 2013. Thanks also go to Dr. Jiying Yin for his excellent computing assistance and the Australian Research Council Discovery Grants under Grant Numbers DP0558602 and DP0879088 for the financial support.
Gao, J. and King, M. (2014), "Specification Testing in Parametric Trending Models with Unknown Errors", Essays in Honor of Peter C. B. Phillips (Advances in Econometrics, Vol. 33), Emerald Group Publishing Limited, Bingley, pp. 151-202. https://doi.org/10.1108/S0731-905320140000033006
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