# How to check stability condition of VEC estimates in R?

I am estimating a VEC model and need to check the stability of its parameters. The vars package has a function to do this on an object of class varest generated by var() function. I would appreciate any comment regarding this.

• Have you thought about converting the ca.jo object to a varest object using the function vec2var and applying the function on it? – Richard Hardy Sep 1 '15 at 19:40
• Hi Richard, thanks. Yes I did, but I was using 'VECM()' of 'tsDyn' package at the time of posting this question. – mr.rox Sep 2 '15 at 19:55
• So did you move on to ca.jo from "vars", or are you still using VECM from "tsDyn"? In the latter case, I do not have a good idea how to do what you want in a simple way. – Richard Hardy Sep 2 '15 at 20:08
• Hello Richard, No, i moved back to VECM() after checking for normality and serial correlation. Also, I have just posted another question regarding VARs. Can you please have a look: stats.stackexchange.com/questions/169988/… – mr.rox Sep 3 '15 at 15:10

One way to check for stability is obtaining the roots of the determinant (using eigen) of the companion matrices of lagged endogenous variables that you obtain by applying vec2var on the estimated VECM.

Using the example provided in the vec2var help page:

library(urca)
data(finland)
sjf <- finland
sjf.vecm <- ca.jo(sjf, ecdet = "none", type = "eigen", K = 2,
spec = "longrun", season = 4)
vec2var <- vec2var(sjf.vecm, r = 2)


finally,

> eigen(vec2var$A$A1)
$values [1] 0.9118953 0.7204302 0.2960268 0.2323736$vectors
[,1]        [,2]       [,3]       [,4]
[1,]  0.63464979  0.38485331  0.4915762  0.4176340
[2,]  0.13477567 -0.13850082  0.8302354  0.6888242
[3,] -0.76072394  0.91184746 -0.0499461 -0.2784035
[4,] -0.01882149  0.03520894  0.2580066  0.5230626


Nonetheless, as the manual of the vecstable function from Stata points out:

...there is no general distribution theory that allows you to determine whether an estimated root is too close to one for all the cases that commonly arise in practice.

Another approach, though more laborious, would be to adapt each individual equation (or the whole system as a varest object) from these matrices in order to assess stability using fluctuation processes, implemented in the stability function.