Lesson plan
Cointegration
In econometrics, cointegration is a statistical property that describes a long-run equilibrium relationship among two or more time series variables, even if the individual series are non-stationary (i.e., they contain stochastic trends). In such cases, the variables may drift in the short run, but their linear combination is stationary, implying that they move together over time and remain bound by a stable equilibrium. More formally, if several time series are individually integrated of order d (meaning they require d differences to become stationary) but a linear combination of them is integrated of a lower order, then those time series are said to be cointegrated. That is, if (X,Y,Z) are each integrated of order d, and there exist coefficients a,b,c such that is integrated of order less than d, then X, Y, and Z are cointegrated. Cointegration is a crucial concept in time series analysis, particularly when dealing with variables that exhibit trends, such as macroeconomic data. In an influential paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends.
Article summary
In econometrics, cointegration is a statistical property that describes a long-run equilibrium relationship among two or more time series variables, even if the individual series are non-stationary (i.e., they contain stochastic trends). In such cases, the variables may drift in the short run, but their linear combination is stationary, implying that they move together over time and remain bound by a stable equilibrium. More formally, if several time series are individually integrated of order d (meaning they require d differences to become stationary) but a linear combination of them is integrated of a lower order, then those time series are said to be cointegrated. That is, if (X,Y,Z) are each integrated of order d, and there exist coefficients a,b,c such that is integrated of order less than d, then X, Y, and Z are cointegrated. Cointegration is a crucial concept in time series analysis, particularly when dealing with variables that exhibit trends, such as macroeconomic data. In an influential paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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