In regressions involving integrable functions we examine the limit properties of IV estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or I(1) processes. We show that this kind of nonlinearity in the regression function can...

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...

A unifying framework for inference is developed in predictive regressions where the predictor has unknown integration properties and may be stationary or nonstationary. Two easily implemented nonparametric F-tests are proposed. The test statistics are related to those of Kasparis and Phillips...

We examine the limit properties of the Non-linear Least Squares (NLS) estimator under functional form misspecification in regression models with a unit root. Our theoretical framework is the same as that of Park and Phillips, Econometrica 2001. We show that the limit behaviour of the NLS...

We adapt the Bierens (Econometrica, 1990) test to the I-regular models of Park and Phillips (Econometrica, 2001). Bierens (1990) defines the test hypoth- esis in terms of a conditional moment condition. Under the null hypothesis, the moment condition holds with probability one. The probability...

A simple specification test based on fully modified residuals and the CUSUM test for cointegration of Xiao and Phillips (Journal of Econometrics, 2002) are considered as means of testing for functional form in long-run cointegrating relations. It is shown that both tests are consistent under...