Abstract: This monograph is concerned with the statistical analysis of multivariate systems of non-stationary time series of type I(1). It applies the concepts of cointegration and common trends in the framework of the Gaussian vector autoregressive model. The main result on the structure of cointegrated processes as defined by the error correction model is Grangers representation theorem. The statistical results include derivation of the trace test for cointegrating rank, test on cointegrating relations, and test on adjustment coefficients and their asymptotic distributions.

Keywords: adjustment coefficients, cointegrating relations, cointegration, common trends, error correction model, Granger representation theorem, non-stationary time series, trace test, vector autoregressive model