Structural Nonparametric Cointegrating Regression

26 Pages Posted: 21 May 2008

See all articles by Qiying Wang

Qiying Wang

University of Sydney

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Date Written: May 2008

Abstract

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 usable 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

Suggested Citation

Wang, Qiying and Phillips, Peter C. B., Structural Nonparametric Cointegrating Regression (May 2008). Cowles Foundation Discussion Paper No. 1657, Available at SSRN: https://ssrn.com/abstract=1135588

Qiying Wang

University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

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