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