[R] Help with ca.jo and cajools (Johansen's Cointegration)

From: Chilton, Alexander B [MSD] <alexander.b.chilton_at_citigroup.com>
Date: Wed 21 Dec 2005 - 09:30:50 EST


I am trying to run a conintegration analysis. I am a former user of S-Plus and understand the output of the coint and VECM output, but I am having trouble understanding the equivalent output in R.

Here is what I ran

> coint=ca.jo(data,constant=T,K=2,spec="longrun")
> summary(coint)

The first portion of the output that I did not understand

          [,1]      [,2]      [,3]
y1        1.000000  1.000000  1.000000
y2       -1.114734 -2.461872 -2.216456

constant 1.364641 7.473149 7.331977

>From this i think that y1 - 1.143*y2 + 1.36 ~ I(0)

What i don't understand is where columns [,2] and [,3] come into play. Now i run the following:

> cajools(coint)

Call:
lm(formula = z@Z0 ~ z@Z1 + z@ZK - 1)

Coefficients:

           [,1]       [,2]     
z@Z11       0.028114   0.065968
z@Z12       0.371630   0.183797
z@ZKy1     -0.011724  -0.002647
z@ZKy2      0.012282   0.001827
z@ZK       -0.012430   0.001482


My understanding is that the specification of the VECM was as follows (with K=2):

deltay1 = c1 + a1*(y1_t-1-b2*y2_t-1)+ phi11*lag(deltay1_t-1) + phi12*deltay2_t-1+e1

deltay2 = c2 + a2*(y1_t-1-b2*y2_t-1)+ phi21*lag(deltay1_t-1) + phi22*deltay2_t-1+e2

My guess is that Z11 and Z12 correspond to the above phis. That c1 and c1 correspond to ZK. That b2 is -1.11 from the step before? The rest, ZKy1 and ZKy2 I can't place. Please help,

Alex



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