Uniform Convergence on Nonlinear Cointegrating Regression

Abstract:

For a nonlinear cointegration model, uniform convergence for the Nadara-Watson estimator and the local linear nonparametric estimator are investigated. Sharp convergence rates and optimal range in which the uniform convergence holds are obtained. Unlike the point-wise situation, it is shown that the performance of the local linear nonparametric estimator is superior to that of the Nadaraya-Watson estimator in uniform asymptotics. Uniform convergence for a class of martingales are developed as a main tool. The main condition imposed is only related to the conditional variance of the martingale, which holds true for a wide range of both stationary and nonstationary data generating processes. Examples include stationary mixing time series, stationary iterated random function, Harris recurrent Markov chains and I(1) processes with innovations being linear processes.