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  • Jiti Gao (a1), Oliver Linton (a2) and Bin Peng (a3)


We consider a model with both a parametric global trend and a nonparametric local trend. This model may be of interest in a number of applications in economics, finance, ecology, and geology. We first propose two hypothesis tests to detect whether two nested special cases are appropriate. For the case where both null hypotheses are rejected, we propose an estimation method to capture certain aspects of the time trend. We establish consistency and some distribution theory in the presence of a large sample. Moreover, we examine the proposed hypothesis tests and estimation methods through both simulated and real data examples. Finally, we discuss some potential extensions and issues when modelling time effects.


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*Address correspondence to Oliver Linton, Faculty of Economics, University of Cambridge, Cambridge CB3 9DD, UK; e-mail:


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The authors would like to thank Professor Peter C.B. Phillips, Professor Liangjun Su, and the three referees for their constructive suggestions and comments on earlier versions of this article. The first author would like to acknowledge the Australian Research Council Discovery Grants Program for its support under Grant numbers: DP150101012 & DP170104421.



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  • Jiti Gao (a1), Oliver Linton (a2) and Bin Peng (a3)


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