This paper studies a general class of nonlinear varying coeﬀicient time series models with possible nonstationarity in both the regressors and the varying coﬀiecient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coeﬀicient drivers, and the residuals. This framework allows for a mixture of stationary and non-stationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coeﬀicient functions. The analytical ﬁndings reveal some important diﬀerences, including convergence rates, that can arise in the conduct of semiparametric regression with nonstationary data. The results include some new asymptotic theory for nonlinear functionals of nonstationary and stationary time series that are of wider interest and applicability and subsume much earlier research on such systems. The ﬁnite sample properties of the proposed econometric methods are analyzed in simulations. An empirical illustration examines nonlinear dependencies in aggregate consumption function behavior in the US over the period 1960-2009.
Gao, Jiti and Phillips, Peter C.B., "Functional Coefficient Nonstationary Regression" (2013). Cowles Foundation Discussion Papers. 2299.