Cointegration: an overview

An overview is given of cointegration analysis in the framework of the vec- tor autoregressive model for processes integrated of order one. We …nd the representation of the solution under dierent assumptions on the coe¢ cients and discuss brie‡y the role of the deterministic terms. We discuss the inter- pretation of cointegrating vectors and adjustment coe¢ cients and show by example for integrated processes of order one how many hypotheses can be formulated in terms of cointegrating vectors. The reduced rank approach to inference is discussed, and we show that many hypotheses on cointegrating vectors and adjustments vectors can be estimated and tested using Gaussian likelihood methods. The asymptotic analysis is outlined and a small sample correction is discussed. The mixed Gaussian distribution is used to for infer- ence on the cointegrating vectors. We treat brie‡y some further topics like testing for rational expectations, analysis of explosive roots and outline some results for the I(2) model. We conclude with a few results related to nonlinear cointegration and panel data cointegration.

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