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A specification test for nonlinear nonstationary models. (English) Zbl 1273.62228
Summary: 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.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G07 Density estimation
62G10 Nonparametric hypothesis testing
60F05 Central limit and other weak theorems
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