The Annals of Statistics
- Ann. Statist.
- Volume 40, Number 2 (2012), 727-758.
A specification test for nonlinear nonstationary models
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.
Ann. Statist., Volume 40, Number 2 (2012), 727-758.
First available in Project Euclid: 17 May 2012
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Wang, Qiying; Phillips, Peter C. B. A specification test for nonlinear nonstationary models. Ann. Statist. 40 (2012), no. 2, 727--758. doi:10.1214/12-AOS975. https://projecteuclid.org/euclid.aos/1337268210
- Supplementary material: Supplement to “A specification test for nonlinear nonstationary models”. Further details on the derivations in the present paper and supporting lemmas and proofs of the main results on convergence to intersection local time are contained in the supplement to the paper, Wang and Phillips (2012).