Phenomenon of Spurious Regression (Co Integration - Applied Econometrics)

■ Spurious Co relation

Viewing this concept in the cross section concept.

Spurious correlation in this context is used to describe the situation when two variables are related even though they are not correlated but they are correlated through a third way.

In the cross section, variables above way occurs, but in the context of the time series it can occur with I(0) variable.

Also we find the spurious relation in time series if they are increasing or decreasing trends.

Say, that the trend is deterministic, then the problem can be solved easily by introducing trend as an additional variable in the regression model.

The problem of Spurious correlation was first discovered by Yule in 1926.

But if we have two series Y and X but not trending even in that case we get a significant relation in the case of spurious regression;

Say that, Xt = Xt-1 + at

                 Yt = Yt-1 + bt

These are the examples of pure Random Walk.

Xt and Yt are independent with at and bt satisfying the classical assumption.

If we let Xo = 0 and Yo = 0, then we consider a regression;

Yt = beta t + beta 2 Xt

Ho: beta 2 = 0 

Ha: beta 2 is not equal to 0

(Xt and Yt are independent random walk process, they are not related).

If null hypothesis is accepted, then there's no any problem, X and Yt are independent random walk processes (they aren't related).

However, Granger and Newbond in 1974 had shown that even of Xt and Yt are independent if we regress Yt on Xt, the level of significance is much larger than conventional level of significance  (1% or 5%).

This was further confronted in 1993 by Davidson and McKinon.

Granger and Newbonds suggested that whenever R ^ 2 > D.W we must suspect that the regression is spurious.

● Implications of spurious regressions.

¤ Chance of getting non 0 estimates even though there's no any relationship between is very high.

¤ The estimated coefficients are mislead.

Say that we regress Y on X the betahat2 is significant or if we run correlation between X and Y the "r" is significant. Let's take dX and dY, now if the correlation between dY and dX is also significant then its not spurious and vice versa.

The exceptions in making stationary will be considered in upcoming blogs.

Thank you

Aditya Raz Pokhrel

MBA, MA Economics, MPA.