Partial parametric estimation for nonstationary nonlinear regressions

This paper proposes an estimation method for a partial parametric model with multiple integrated time series. Our estimation procedure is based on the decomposition of the nonparametric part of the regression function into homogeneous and integrable components. It consists of two steps: In the first step we parameterize and fit the homogeneous component of the nonparametric part by the nonlinear least squares with other parametric terms in the model, and use in the second step the standard kernel method to nonparametrically estimate the integrable component of the nonparametric part from the residuals in the first step. We establish consistency and obtain the asymptotic distribution of our estimator. A simulation shows that our estimator performs well in finite samples. For the empirical illustration, we estimate the money demand functions for the US and Japan using our model and methodology.