In this paper, we consider a semiparametric time series regression model and establish a set of identification conditions such that the model under discussion is both identifiable and estimable. We estimate the parameters in the model by using the method of moment and the nonlinear function by using the local linear method, and establish the asymptotic distributions for the proposed estimators. We then discuss how to estimate a sequence of local departure functions nonparametrically when the null hypothesis is rejected and establish some related asymptotic theory. Both the simulation study and the empirical application are also provided to illustrate the finite sample behavior of the proposed models and methods.
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