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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