Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series

This paper establishes several results for uniform convergence of nonparametric kernel density and regression estimates for the case where the time series regressors concerned are nonstationary null-recurrent Markov chains. Under suitable conditions, certain rates of convergence are also established for these estimates. Our results can be viewed as an extension of some well-known uniform consistency results for the stationary time series to the nonstationary time series case