The Annals of Statistics

A specification test for nonlinear nonstationary models

Qiying Wang and Peter C. B. Phillips

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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.

Article information

Source
Ann. Statist. Volume 40, Number 2 (2012), 727-758.

Dates
First available in Project Euclid: 17 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1337268210

Digital Object Identifier
doi:10.1214/12-AOS975

Mathematical Reviews number (MathSciNet)
MR2933664

Zentralblatt MATH identifier
1273.62228

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62G07: Density estimation
Secondary: 60F05: Central limit and other weak theorems

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

Citation

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.


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Supplemental materials

  • 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).