Why correlation doesn’t equal causation for time sequence
In time sequence evaluation, it’s precious to know 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 strategy yields incorrect outcomes, significantly for non-stationary time sequence. In consequence, they conceived the idea of cointegration, which received Granger a Nobel prize. On this submit, I wish to focus on the necessity and utility of cointegration and why it is a vital idea Knowledge 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. Nonetheless, Granger and Newbold confirmed that this strategy is inaccurate and results in one thing referred to as spurious correlation.
A spurious correlation is the place two time sequence might look correlated however really they lack a causal relationship. It’s the basic ‘correlation doesn’t imply causation’ assertion. It’s harmful as even statistical checks might nicely say that there’s a informal relationship.
Instance
An instance of a spurious relationship is proven within the plots beneath:
Right here now we have two time sequence A(t) and B(t) plotted as a operate of time (left) and plotted towards one another (proper). Discover from the plot on the best, that there’s some correlation between the sequence as proven by the regression line. Nonetheless, by trying on the left plot, we see this correlation is spurious as a result of B(t) persistently will increase whereas A(t) fluctuates erratically. Moreover, the common distance between the 2 time sequence can be rising…
