Abstract. Multivariate adaptive regression spline (MARS) models due to Friedman (1991)
I. In~oducfionEngle and Granger (1987) provided a set of residual based tests of whether two or more series that appear to be random walks were in fact tied together by a long-run linear relationship. Since this seminal work there has been an explosion of empirical research on both testing for cointegration and in modelling cointegrated series, a Relatively rudimentary residual based tests have been extended and replaced, in great measure, by those based on systems methods of estimation.The purpose of this paper is to provide yet another extension to the Engle and Granger test to examine the extent to which non-linear cointegrating relationships can be identified and examined. Attempts to model non-linear cointegrating relationships have already begun to appear in the literature. Meese and Rose (1991) used the relatively simple ACE (alternating conditional expectations) algorithm of Breiman and Friedman (1985) to compare models of exchange rate determination, while Chinn (1991) used ACE to estimate a monetary model of the exchange rate. The ACE algorithm searches for data transformations that maximize the R -~ between the transformed series. Granger and Hallman (1991) and Hallman (1991) employed ACE in an attempt to identify non-linear cointegration, and suggested that ACE may be capable of capturing time-varying cointegration. Granger and Hallman (1991) provided some experimental evidence on the behaviour of the Dickey-Fuller and Augmented Dickey-Fuller cointegration tests based on ACE residuals, but their Monte Carlo simulations used only 100 replications on 100 data points, after which they applied ACE to a dataset of over 400 observations.The primary aim of this paper is to use the more sophisticated MARS algorithm to examine non-linear cointegration, since there may be stable long-run equilibrium relationships that escape additive analysis. MARS allows for both additive