Uniform convergence rates over maximal domains in structural nonparametric cointegrating regression

TL;DR

This paper establishes uniform convergence rates for kernel regression estimators in a broad class of nonlinear cointegrating models, accommodating wide domains, serially correlated disturbances, and data-dependent bandwidths.

Contribution

It extends existing uniform convergence results to wider domains, allows for correlated disturbances, and permits data-dependent bandwidths in nonlinear cointegrating regressions.

Findings

Uniform convergence rates over large domains

Handling serially correlated and cross-correlated disturbances

Allowing fractional integration and infinite variance in regressors

Abstract

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these rates apply is much wider than has been previously considered, and can be chosen so as to contain as large a fraction of the sample as desired in the limit. Second, our results allow the regression disturbance to be serially correlated, and cross-correlated with the regressor; previous work on this problem (of obtaining uniform rates) having been confined entirely to the setting of an exogenous regressor. Third, we permit the bandwidth to be data-dependent, requiring only that it satisfy certain weak asymptotic shrinkage conditions. Our assumptions on the regressor process are consistent with a very broad range of departures from the standard unit root autoregressive model, allowing the regressor to be fractionally integrated, and to have an infinite variance (and even infinite lower-order moments).