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In one of my econometrics classes. I'm nearly finished a problem set and assigned readings on an introduction to cointegration. I've essentially finished the assignment, run dickey fuller tests on some data, estimated cointegration relationships, and estimated an error correction model. But I'm often surprised at how textbooks in econometrics tend to drive right away into the details without first explaining the big picture and how various concepts are applied in practice. I was wondering:

Could anyone offer an intuitive explanation on how cointegration is important in practice. For example, if you are building models for policy analysis, or finance, or macroeconomic analysis, could you talk about some practical instances where cointegration comes into play and why it is important in these instances?

Thanks very much everyone for the help!

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I think it is a very classical economic teaching problem - showing how something is relevant in the real world.

First, it solved a problem where linear regressions could lead to spurious results: https://en.wikipedia.org/wiki/Cointegration

...Before the 1980s many economists used linear regressions on (de-trended[citation needed]) non-stationary time series data, which Nobel laureate Clive Granger and Paul Newbold showed to be a dangerous approach that could produce spurious correlation, since standard detrending techniques can result in data that are still non-stationary. Granger's 1987 paper with Robert Engle formalized the cointegrating vector approach, and coined the term.

For integrated I(1) processes, Granger and Newbold showed that de-trending does not work to eliminate the problem of spurious correlation, and that the superior alternative is to check for co-integration. Two series with I(1) trends can be co-integrated only if there is a genuine relationship between the two. Thus the standard current methodology for time series regressions is to check all-time series involved for integration. If there are I(1) series on both sides of the regression relationship, then it's possible for regressions to give misleading results...

Second, our "Sister site" actually does a nice job explaning the intuition behind, which can explain why it is important in the real world - are two different time series related? And can we test for this?:

https://quant.stackexchange.com/questions/219/what-is-the-intuition-behind-cointegration

I really like this one:

"Think of a man walking his dog. He will go along and his dog will stroll along running back and forth. Man and dog are mathematically "cointegrated".

As an investor you bet that the dog is coming back to his master or that the leash has only a certain length.

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A good example from finance is the CAY variable. Lettau-Ludvigson. They claim that consumption and aggregate wealth are cointegrated, and that deviations of these from their long run relationship are good predictors of asset returns. The econometrics are somewhat tricky in the sense that the tests that prove that there is or is not a cointegration relationship are not very powerful.

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