Publication Type

Journal Article

Publication Date

4-2016

Abstract

This paper explores nonparametric estimation, inference, and specification testing in a nonlinear cointegrating regression model where the structural equation errors are serially dependent and where the regressor is endogenous and may be driven by long memory innovations. Generalizing earlier results of Wang and Phillips (2009a, b, Econometric Theory 25, 710-738, Econometrica 77, 1901-1948), the conventional nonparametric local level kernel estimator is shown to be consistent and asymptotically (mixed) normal in these cases, thereby opening up inference by conventional nonparametric methods to a wide class of potentially nonlinear cointegrated relations. New results on the consistency of parametric estimates in nonlinear cointegrating regressions are provided, extending earlier research on parametric nonlinear regression and providing primitive conditions for parametric model testing. A model specification test is studied and confirmed to provide a valid mechanism for testing parametric specifications that is robust to endogeneity. But under long memory innovations the test is not pivotal, its convergence rate is parameter dependent, and its limit theory involves the local time of fractional Brownian motion. Simulation results show good performance for the nonparametric kernel estimates in cases of strong endogeneity and long memory, whereas the specification test is shown to be sensitive to the presence of long memory innovations, as predicted by asymptotic theory.

Keywords

integrated time-series, asymptotic theory, whittle estimation, inference, models, heteroskedasticity, convergence, functionals, tests

Discipline

Econometrics | Economics

Research Areas

Econometrics

Publication

Econometric Theory

Volume

32

Issue

2

First Page

359

Last Page

401

ISSN

0266-4666

Identifier

10.1017/S0266466614000917

Publisher

Cambridge University Press (CUP): HSS Journals

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://dx.doi.org/10.1017/S0266466614000917

Included in

Econometrics Commons

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