Cointegration vs Spurious Correlation: Perceive the Distinction for Correct Evaluation | by Egor Howell | Jul, 2023

Why correlation doesn’t equal causation for time sequence

In time sequence evaluation, it’s priceless to grasp if one sequence influences one other. For instance, it’s helpful for commodity merchants to know if a rise in commodity A results in a rise in commodity B. Initially, this relationship was measured utilizing linear regression, nevertheless, within the Nineteen Eighties Clive Granger and Paul Newbold confirmed this method yields incorrect outcomes, significantly for non-stationary time sequence. Because of this, they conceived the idea of cointegration, which gained Granger a Nobel prize. On this submit, I wish to focus on the necessity and utility of cointegration and why it is a crucial idea Information Scientists ought to perceive.

Overview

Earlier than we focus on cointegration, let’s focus on the necessity for it. Traditionally, statisticians and economists used linear regression to find out the connection between totally different time sequence. Nevertheless, Granger and Newbold confirmed that this method is wrong and results in one thing referred to as spurious correlation.

A spurious correlation is the place two time sequence might look correlated however actually they lack a causal relationship. It’s the basic ‘correlation doesn’t imply causation’ assertion. It’s harmful as even statistical assessments might effectively say that there’s a casual relationship.

Instance

An instance of a spurious relationship is proven within the plots under:

Right here we’ve two time sequence A(t) and B(t) plotted as a perform of time (left) and plotted in opposition to one another (proper). Discover from the plot on the best, that there’s some correlation between the sequence as proven by the regression line. Nevertheless, by wanting on the left plot, we see this correlation is spurious as a result of B(t) constantly will increase whereas A(t) fluctuates erratically. Moreover, the typical distance between the 2 time sequence can also be rising…