Testing For Two Classes Of Nonlinear Adjustments In Vector Error Correction Models

In 2003, Nobel economic prize is awarded to Clive W.J. Granger and Robet F. Engle for their major contributation in the field of nonlinear time series. Threshold models and smooth transition threshold models as two important classes of the field have extensive background. But the theory has not been developed satisfactoryly. This paper studies the testing for nonlinear adjustment in two classes of nonlinear VECM, proposes some algorithms for estimating the unidentified parameters. We obtain some results as follow:Firstly, we develop a test for the presence of threshold cointegration in a new TVECM with the linear no cointegration null hypothesis. We propose two simple algorithms—grid search algorithm and genetic algorithm—to obtain maximum likelihood estimation of the complete threshold cointegration model for the all non-identifications case, and point out the applicability of two algorithms. We adopt a SupLM type test and, derive its null asymptotic distribution and present bootstrap approximation. Simulation evidence shows that bootstrap inference generates moderate size and power of the test. Our method is illustrated with used U.S. treasury yield curve rates.Secondly, we consider testing for the presence of nonlinear adjustment in a new STVECM. We develop an algorithm to obtain ordinary least square estimation of the unknown coingtegrating parameter and the unidentified associated parameter in STVECM and Seo (2004) STVECM. The direct tests for smooth transition nonlinear adjustment, calculated under linear error correction model, are proposed. The transition parameter(s) is unidentified under null hypothesis, and therefore we develop the optimal tests for smooth transition nonlinearity, the associated asymptotic theory, and bootstrap inference.