Dear all,
I am struggling to understand the johansen test procedure in the context of
co-integration in time series. Yes I understand that this forum is not directly
statistics related but still I am posting here hoping that I would get som help.
The error correction representation of a VAR[p] model can be written as:
Delta y[t] = A[0]*y[t-1] + A[1]*Delta y[t-1] +..............
where, y[t] is a vector of n variables.
It is said that "if the variables in system are all co-integrated, then Rank
of A[0] will be different from zero"
My understanding is following : suppose, y[t] is of order 3 and p = 1
Then Delta y[t] = A[0]*y[t-1] + epsilon[t]
Hence : Delta y1[t] = a[11]*y1[t-1] + a[12]*y1[t-1] +a[13]*y1[t-1] +
epsilon1[t]
Delta y2[t] = a[12]*y1[t-1] + a[22]*y1[t-1] +a[23]*y1[t-1] +
epsilon2[t]
Delta y3[t] = a[31]*y1[t-1] + a[32]*y1[t-1] +a[33]*y1[t-1] +
epsilon3[t]
But is rank of A[0] is 0 then it is possible to find non-zero coef for all of
above three equations such that : a[11]*y1[t-1] + a[12]*y1[t-1] +a[13]*y1[t-1]
= 0
a[12]*y1[t-1] + a[22]*y1[t-1] +a[23]*y1[t-1] = 0
a[12]*y1[t-1] + a[22]*y1[t-1] +a[23]*y1[t-1] = 0
therefore number of co-integrating relationship is 3 am I correct?
Therefore in my understanding : if variables in a system show some
co-integrating relationship thenrank should be close to zero.
Am I making any mistakes? Can anyone here clarify me?
Regards,
Megh
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