On a measure of lack of fit in nonlinear cointegrating regression with endogeneity

Abstract

This paper proposes a portmanteau test for the adequacy of nonlinear cointegrating regression models. The proposed test is applicable to a wide class of integrable and nonintegrable regression functions, with endogenous regressors driven by either short or long memory innovations. In addition, the limiting distribution of the test is shown to be approximated by a chisquared distribution. Moreover, the scope of the test is generalized to include an additive nonlinear cointegrating regression model, the consistency results of which are investigated as an independent interest. Finally, the effectiveness of the portmanteau test is demonstrated using simulations and real data.