A specification test for nonlinear nonstationary models

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.

Published in at http://dx.doi.org/10.1214/12-AOS975 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Nonparametric estimation in a nonlinear cointegration type model
• Specification testing in nonlinear and nonstationary time series autoregression
• Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence
• Convergence of functionals of sums of r.v.s to local times of fractional stable motions

Cited by in corpus (4)

• Estimation for single-index and partially linear single-index integrated models
• Uniform convergence rates for a class of martingales with application in non-linear cointegrating regression
• A uniform law for convergence to the local times of linear fractional stable motions
• Cointegration with Occasionally Binding Constraints