[R] Help with ca.jo and cajools (Johansen's Cointegration)
Chilton, Alexander B [MSD]
alexander.b.chilton at citigroup.com
Tue Dec 20 23:30:50 CET 2005
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 at Z0 ~ z at Z1 + z at ZK - 1)
Coefficients:
[,1] [,2]
z at Z11 0.028114 0.065968
z at Z12 0.371630 0.183797
z at ZKy1 -0.011724 -0.002647
z at ZKy2 0.012282 0.001827
z at 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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