We provide a limit theory for a general class of kernel smoothed U statistics that may be used for specification testing in time series regression with nonstationary data. The framework allows for linear and nonlinear models of cointegration and regressors that have autoregressive unit roots or...

Some convenient limit properties of usual information criteria are given for cointegrating rank selection. Allowing for a nonparametric short memory component and using a reduced rank regression with only a single lag, standard information criteria are shown to be weakly consistent in the choice...

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is...

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time. These time-varying coefficient functions are well-suited to many practical applications and can be estimated conveniently by nonparametric kernel methods. It is shown that the...

Reduced rank regression (RRR) models with time varying heterogeneity are considered. Standard information criteria for selecting cointegrating rank are shown to be weakly consistent in semiparametric RRR models in which the errors have general nonparametric short memory components and shifting...

This paper studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified...

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time...