COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1657 Structural Nonparametric Cointegrating Regression Qiying Wang and Peter C.B. Phillips May 2008 Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill-posed inverse problems. In functional cointegrating regressions where the regressor is an integrated time series, it is shown here that inverse and ill-posed inverse problems do not arise. Remarkably, nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution theory is mixed normal, giving simple useable asymptotics in practical work. The results provide a convenient basis for inference in structural nonparametric regression with nonstationary time series. The methods may be applied to a wide range of empirical models where functional estimation of cointegrating relations is required. Keywords: Brownian Local time, Cointegration, Functional regression, Gaussian process, Integrated process, Kernel estimate, Nonlinear functional, Nonparametric regression, Structural estimation, Unit root JEL Classification: C14, C22 |
