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SPECIFICATION TESTING DRIVEN BY ORTHOGONAL SERIES FOR NONLINEAR COINTEGRATION WITH ENDOGENEITY
Published online by Cambridge University Press: 09 June 2017
Abstract
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This paper proposes two simple and new specification tests based on the use of an orthogonal series for a considerable class of bivariate nonlinearly cointegrated time series models with endogeneity and nonstationarity. The first test is proposed for the case where the regression function is integrable, which fills a gap in the literature, and the second test, which nests the first one, deals with regression functions in a quite large function space that is sufficient for both theoretical and practical use. As a starting point of our asymptotic theory, the first test is studied initially and then the theory is extended to the second test. Endogeneity in two general forms is allowed in the models to be tested. The finite sample performance of the tests is examined through several simulated examples. Our experience generally shows that the proposed tests are easily implementable and also have stable sizes and good power properties even when the ‘distance’ between the null hypothesis and a sequence of local alternatives is asymptotically negligible.
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Footnotes
The authors acknowledge the constructive comments from Professor Peter Phillips, the Co–Editor and three referees on the earlier versions. The authors would also like to thank Professor Maxwell King for the proofreading and useful comments on a final version. Thanks also go to Dr Qiying Wang for making an earlier version of Wang and Phillips (2016) available to us while we were writing this paper as well as his constructive comments on an earlier version. The authors would like to acknowledge constructive comments and suggestions from Professor Oliver Linton and Professor Peter Robinson on earlier versions. Thanks from the authors also go to the seminar participants at various seminars for their comments and suggestions. The first author acknowledges financial support from the National Natural Science Foundation of China under Grant No. 71671143 and the second author thanks the Australian Research Council Discovery Grants Program for its support under Grant numbers: DP150101012 & DP170104421.
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