Cointegration

The concept of cointegration in the context of time series analysis and econometrics goes back to the British Clive WJ Granger and the American Robert F. Engle . A cointegration relationship exists when there is a long-term equilibrium between two or more unsteady ( integrated ) variables. In the short term, there may be deviations from the equilibrium . But at least one of the variables adjusts over time in such a way that long-term equilibrium is restored.

A relationship between the concept of cointegration of variables and an error correction model can be established using the Engle-Granger representation theorem . This means that for every cointegration model there is an error correction model that describes the short-term dynamics of the system.

The cointegration is used for trend-affected time series ( unsteady time series). It represents an alternative to trend adjustment, for example by forming differences. Trend adjustment is often suggested in order to avoid sham regressions . The disadvantage of this handling of unsteadiness, however, is that information is lost as a result of the purging. This is where the advantage of working with level variables or cointegration lies. Long-term equilibrium relationships can be recognized and analyzed.

In 2003, Clive WJ Granger and Robert F. Engle were awarded the Swedish Reichsbank's Economics Prize in memory of Alfred Nobel for their work on cointegration .

literature

The fundamental contribution of Robert F. Engle and Granger is:

• Robert F. Engle, Clive WJ Granger: Co-integration and error correction: Representation, estimation and testing . In: Econometrica . tape 55 , 1987, pp. 251-276 , JSTOR : 1913236 (English, registration required).

German-language textbooks with introductory presentations are:

• Peter Hackl : Introduction to Econometrics. Pearson Studium, Munich 2005, ISBN 3-8273-7118-X .
• Michael Schröder : Financial Markets Econometrics. Schaeffer-Poeschel Verlag, Stuttgart 2002, ISBN 3-7910-1836-1 .
• Gebhard Kirchgässner , Jürgen Wolters: Introduction to modern time series analysis. Vahlen, Munich 2006, ISBN 3-8006-3268-3 .

Standard textbooks for advanced learners are:

• James D. Hamilton : Time series analysis. Princeton University Press, Princeton 1994, ISBN 0-691-04289-6 .
• Helmut Lütkepohl : New introduction to multiple time series analysis. Springer, Berlin 2007, ISBN 978-3-540-26239-8 .