Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The condition of two nonstationary time series whose linear combination is stationary
Etymologies
Examples

Today, cointegration is a central aspect in time series analysis in economics.
The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 19692006

He minted the term cointegration to describe such systems and demonstrated that cointegration provides a key to reliable statistical inference.

Granger minted the term cointegration for a stationary combination of nonstationary variables.

Granger has instead developed and applied new statistical methods, based on socalled "cointegration", to differentiate between, and combine the analysis of, shortterm fluctuations and longterm trends.
The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 19692006

The idea is called "cointegration" and provides ways to discover that two large boats are drifting with the same current or that two macroeconomies are moving together.

The NY Times piece does an absolute hatchet job to the concept of nonstationarity and cointegration and incorrectly asserts that Robert Engle was awarded the nobel prize for his work on cointegration.

For methods of analyzing economic time series with common trends (cointegration)

It links to another article “Econometrics vs Climate Science” Note 3 saying QUOTE: What physical mechanism is responsible for the dominant 65 year trend is not known, but the cointegration analysis paper we previously examined says that is not greenhouse gas levels—CO2 is not driving Earth's temperature change UNQUOTE.

In terms of cointegration, if the second difference had a unit root, then it would be I3 or higher and it would be even worse.

But I'm not an expert on cointegration so it's just my opinion.
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