Granger Causality Test

If X(t) and Y(t) are two time series

Xt granger causes Yt if the past values of Xt helps in predicting the future values of Yt

Yt is not just = f(Yt-1,Xt)

Xt granger causes Yt

Condition = cause happens prior to the effect Yt= f(Xt-1)

Cause has unique information about the future values of its effect. Extra effect.


Mathematically ,

Yt = a0 + a1 + Yt-1

Yt = a0 + a1 + Yt-1 + a2 Xt-1

If a2 is significant, then Xt granger causes Yt.


H0: a2 = 0 , H1: a2 not equal to 0

Steps for Granger Causality test

Step 1

Yt = a0+a1Yt-1+a2Yt-2+…….+apYt-p

Step 2

Yt = a0+a1Yt-1+…+apYt-p+b1Xb-1+…+bpXt-p

Step 3

  1. T test for individual coefficients
  2. H0: b1=b2=….=bp=0

H1: At least one of them is non Zero

GC test helps improve prediction.


Not necessarily true causality

If Xt affects Yt, through third variable Zt, then we may not be able to find GC

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