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NONPARAMETRIC COINTEGRATING REGRESSION WITH ENDOGENEITY AND LONG MEMORY

  • Qiying Wang (a1) and Peter C. B. Phillips (a2)
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.

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Copyright
Corresponding author
*Address correspondence to Qiying Wang, School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia; e-mail: qiying@maths.usyd.edu.au.
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D.W.K. Andrews & Y. Sun (2004) Adaptive local polynomial Whittle estimation of long-range dependence. Econometrica 72, 569614.

I. Berkes & L Horváth . (2006) Convergence of integral functionals of stochastic processes. Econometric Theory 22, 304322.

Z. Cai , Q. Li , & J.Y. Park (2009) Functional-coefficient models for nonstationary time series data. Journal of Econometrics 148, 101113.

Y. Chang , J.Y. Park , & P.C.B. Phillips (2001) Nonlinear econometric models with cointegrated and deterministically trending regressors. Econometrics Journal 4, 136.

X. Chen , Z. Liao , & Y. Sun (2014) Sieve inference on possibly misspecified semi-nonparametric time series models. Journal of Econometrics 178, 639658.

J. Gao , K., Maxwell, Z. Lu , & D Tjøstheim . (2009) Speci.cation testing in nonlinear and nonstationary time series autoregression. Annals of Statistics 37, 38933928.

D. Geman & J. Horowitz (1980) Occupation densities. Annals of Probability 8, 167.

W. Härdle & E. Mammen (1993) Comparing nonparametric versus parametric regression fits. Annals of Statistics 21, 19261947.

J.L. Horowitz & V.G. Spokoiny (2001) An adaptive rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599631.

H.A. Karlsen , T. Myklebust , & D. Tjostheim (2007) Nonparametric estimation in a nonlinear cointegration model. Annals of Statistics 35, 252299.

N.M. Kiefer & N.J Vogelsang . (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21, 11301164.

J.Y. Park & P.C.B. Phillips (1999) Asymptotics for nonlinear transformation of integrated time series, Econometric Theory 15, 269298.

J.Y. Park & P.C.B. Phillips (2001) Nonlinear regressions with integrated time series. Econometrica 69, 117161.

P.C.B Phillips . (2005) HAC estimation by automated regression. Econometric Theory 21, 116142.

K. Shimotsu & P.C.B. Phillips (2005) Exact local Whittle estimation of fractional integration. Annals of Statistics 33(4), 18901933.

Y Sun . (2011) Robust trend inference with series variance estimator and testing-optimal smoothing parameter. Journal of Econometrics 164, 345366.

Y Sun . (2014) Let’s fix it: Fixed-b asymptotics versus small-b asymptotics in heteroskedasticity and autocorrelation robust inference. Journal of Econometrics 178, 659677.

Q. Wang , Y.X. Lin , & C.M. Gulati (2003) Asymptotics for general fractionally integrated processes with applications to unit root tests. Econometric Theory 19, 143164.

Q. Wang & P.C.B. Phillips (2012) A specification test for nonlinear nonstationary models. Annals of Statistics 40, 727758.

J.M Wooldridge . (1994) Estimation and inference for dependent processes. Handbook of econometrics 4, 26392738.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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