The Problem of Co-integration

This paper is concerned with the problem of multiple time series modelling under the condition of nonstationarity in means. It is well known that the economic time series are characteristic by nonstationary development. In the univariate case this problem is solved very simply, just by differencing. But in the multivariate case the differencing is not an effective way how to get rid of nonstationarity in means because of co-integration which can occure. If the co-integration between some time series does exists and is not respected it usually leads to the incorrect model of the multivariate time series. This model has to be transformed into a restricted form which is called the error correction model. The problem of co-integration and error correction model is relatively new. The relationship between co-integration and error correction models was first suggested by C.W.J. Granger (1981). A theorem showing precisely that co-integration series can be represented by error correction models was originally stated and proved in Granger (1983). This theorem was than presented in Engle, Granger (1987) under the name 'Granger Representation Theorem'. These articles were than followed by many other papers, especially concerning the testing of co-integration and the estimating of error correction models.