A specification test for nonlinear nonstationary models
Qiying Wang and Peter C. B. Phillips
Source: Ann. Statist. Volume 40, Number 2
(2012), 727-758.
Abstract
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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Keywords: Intersection local time; kernel regression; nonlinear nonparametric model; nonstationary time series; specification tests; weak convergence
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1337268210
Digital Object Identifier: doi:10.1214/12-AOS975
Zentralblatt MATH identifier: 06073773
Mathematical Reviews number (MathSciNet): MR2933664
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