Nonparametric LAD Cointegrating Regression

We deal with nonparametric estimation in a nonlinear cointegration model whose regressor and dependent variable can be contemporaneously correlated. The asymptotic properties of the Nadaraya-Watson estimator are already examined in the literature. In this paper, we consider nonparametric least absolute deviation (LAD) regression and derive the asymptotic distributions of the local constant and local linear estimators by appealing to the local time approach.Nonlinear Cointegration, Integrated Process, Local Time, Least Absolute Deviation, Local Polynomial Regression, Bias

Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series

This paper establishes a suite of uniform consistency results for nonparametric kernel density and regression estimators when the time series regressors concerned are nonstationary null-recurrent Markov chains. Under suitable conditions, certain rates of convergence are also obtained for the proposed estimators. Our results can be viewed as an extension of some well-known uniform consistency results for the stationary time series case to the nonstationary time series case.β-null recurrent Markov chain, nonparametric estimation, rate of convergence, uniform consistency

Local linear m-estimators in null recurrent time series

In this paper, we study a nonlinear cointegration type model Yκ = m(Xκ) + wκ, where {Yκ} and {Xκ} are observed nonstationary processes and {Wκ} is an unobserved stationary process. The process {Xκ} is assumed to be a null-recurrent Markov chain. We apply a robust version of local linear regression smoothers to estimate m(-). Under mild conditions, the uniform weak consistency and asymptotic normality of the local linear M-estimators are established. Furthermore, a one-step iterated procedure is introduced to obtain the local linear M-estimator and the optimal bandwidth selection is discussed. Meanwhile, some numerical examples are given to show that the proposed theory and methods perform well in practice

Uniform Consistency of Nonstationary Kernel-Weighted Sample Covariances for Nonparametric Regression

We obtain uniform consistency results for kernel-weighted sample covariances in a nonstationary multiple regression framework that allows for both fixed design and random design coefficient variation. In the fixed design case these nonparametric sample covariances have different uniform convergence rates depending on direction, a result that differs fundamentally from the random design and stationary cases. The uniform convergence rates derived are faster than the corresponding rates in the stationary case and confirm the existence of uniform super-consistency. The modelling framework and convergence rates allow for endogeneity and thus broaden the practical econometric import of these results. As a specific application, we establish uniform consistency of nonparametric kernel estimators of the coefficient functions in nonlinear cointegration models with time varying coefficients and provide sharp convergence rates in that case. For the fixed design models, in particular, there are two uniform convergence rates that apply in two different directions, both rates exceeding the usual rate in the stationary case

Robust estimation in a nonlinear cointegration model

Copyright © 2009 Elsevier Inc. All rights reserved.Jia Chen, Degui Li, and Lixin Zhan

Robust estimation in a nonlinear cointegration model

This paper considers the nonparametric M-estimator in a nonlinear cointegration type model. The local time density argument, which was developed by Phillips and Park (1998) [6] and Wang and Phillips (2009) [9], is applied to establish the asymptotic theory for the nonparametric M-estimator. The weak consistency and the asymptotic distribution of the proposed estimator are established under mild conditions. Meanwhile, the asymptotic distribution of the local least squares estimator and the local least absolute distance estimator can be obtained as applications of our main results. Furthermore, an iterated procedure for obtaining the nonparametric M-estimator and a cross-validation bandwidth selection method are discussed, and some numerical examples are provided to show that the proposed methods perform well in the finite sample case.Cointegration model Local time density Nonparametric M-estimator