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...

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...