Nonlinear Cointegration using Lyapunov Stability Theory

This paper extends the nonlinear cointegration approach of Granger and Hallman (1991) and Sephton (1994) using the framework of stochastic Lyapunov stability theory. The extended approach is nonparametric and has the advantage of being general enough to accommodate complicated nonlinear behavior. It is demonstrated that it is possible to construct nonlinear cointegrated systems with error-correction mechanisms that have no predictive ability. An empirical application of the proposed methodology shows that the monthly UK Gilt-Equity ratio implies a significant nonlinear cointegration relationship for the period January 1965 to December 1995. Error-correction models built from this cointegration relationship are found to have superior forecasting performance compared to a simple dynamic regression.