"Spurious regression" (in the context of time series) and associated terms like unit root tests are something I've heard a lot about, but never understood.

Why/when, intuitively, does it occur? (I believe it's when your two time series are cointegrated, i.e., some linear combination of the two is stationary, but I don't see why cointegration should lead to spuriousness.) What do you do to avoid it?

I'm looking for a high-level understanding of what cointegration/unit root tests/Granger causality have to do with Spurious regression (those three are terms I remember being associated with spurious regression somehow, but I don't remember what exactly), so either a custom response or a link to references where I can learn more would be great.

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#### Best Answer

These concepts have been created to deal with **regressions (for instance correlation) between non stationary series.**

Clive Granger is the key author you should read.

Cointegration has been introduced in 2 steps:

*1/ Granger, C., and P. Newbold (1974): "Spurious Regression in Econometrics,"*

In this article, the authors point out that regression among non stationary variables should be conducted as regressions among **changes** (or log changes) of the variables. Otherwise you might find high correlation without any real significance. (= spurious regression)

*2/ Engle, Robert F., Granger, Clive W. J. (1987) "Co-integration and error correction: Representation, estimation and testing", Econometrica, 55(2), 251-276.*

In this article (for which Granger has been rewarded by the Nobel jury in 2003), the authors go further, and introduce cointegration as a way to study the error correction model that can exist between two non stationary variables.

Basically the 1974 advice to regress the change in the time series may lead to unspecified regression models. You can indeed have variables whose changes are uncorrelated, but which are connected through an "error correction model".

Hence, you can have correlation without cointegration, and cointegration without correlation. The two are complementary.

If there was only one paper to read, I suggest you start with this one, which is a very good and nice introduction:

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