A General Limit Theory for Nonlinear Functionals of Nonstationary Time Series

Limit theory is provided for a wide class of covariance functionals of a nonstationary process and stationary time series. The results are relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root or fractional processes and they include both parametric and nonparametric regressions. Self normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals a strong bimodality in the finite sample distributions that persists for very large sample sizes although the limit theory is Gaussian. New self normalized versions are introduced that deliver improved approximations.