Open Access
April 2012 A specification test for nonlinear nonstationary models
Qiying Wang, Peter C. B. Phillips
Ann. Statist. 40(2): 727-758 (April 2012). DOI: 10.1214/12-AOS975


We provide a limit theory for a general class of kernel smoothed U-statistics that may be used for specification testing in time series regression with nonstationary data. The test framework allows for linear and nonlinear models with endogenous regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self-intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This result is of independent interest and is useful in other applications. Simulations examine the finite sample performance of the test.


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Qiying Wang. Peter C. B. Phillips. "A specification test for nonlinear nonstationary models." Ann. Statist. 40 (2) 727 - 758, April 2012.


Published: April 2012
First available in Project Euclid: 17 May 2012

zbMATH: 1273.62228
MathSciNet: MR2933664
Digital Object Identifier: 10.1214/12-AOS975

Primary: 62G07 , 62M10
Secondary: 60F05

Keywords: Intersection local time , kernel regression , nonlinear nonparametric model , nonstationary time series , specification tests , weak convergence

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 2 • April 2012
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