Abstract
Since Engle and Granger (1987) first introduced the concept of cointegration, researchers have proposed numerous methods of its estimation. However, there is some evidence that cointegration does not always provide an improvement over an unrestricted vector autoregression (VAR) model. To date, most assessments of cointegration models have been based on in-sample-estimation. In addition, focus has been on linear cointegration modelling. This study evaluates two widely used nonlinear cointegration models using long-run out-of-sample forecasts. Two nonlinear cointegration estimation methods, the maximum likelihood estimation (MLE) and the canonical correlation estimation (CC) are studied. Johansen's derivation of the MLE is shown to be equivalent to the ordinary least squares (OLS) of a function of a set of vector of variables. This demonstration helps us better understand the logic and intuition behind Johansen's derivation of the MLE. Geometric representation of the cointegrating space are discussed. Multi-step ahead forecasts of multivariate data from two previously published studies show that the MLE performs well relative to CC. However, in one set of the data, none of the cointegration methods show an improvement over VAR. Moreover, an analysis of this data set reveals an empirical counter-example to Granger representation theorem. This counter-example is probably the reason that enables us to establish a counter-claim to that of Engle and Granger that cointegration "may not" help improve prediction. The computer programs developed by this study substantially reduce the task of recursive estimation by nonlinear cointegration models. The programs help open an avenue for the analysis of the nonlinear models that need recursive estimation such as the comparison of forecasting performances and the analysis of structural shift in a cointegrated system.
Chaisantikulawat, Thanapat (1995). Essays on forecasting cointegrated data. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -1574339.