Extract cointegration parameters A, B and PI
Extract parameters in VECM: adjustment coefficients A,
cointegrating coefficients B , or the composite matrix PI
coefB(object, ...) ## S3 method for class 'VECM' coefB(object, ...) ## S3 method for class 'ca.jo' coefB(object, r = 1, normalize = TRUE, ...) coefA(object, ...) ## S3 method for class 'VECM' coefA(object, ...) ## S3 method for class 'ca.jo' coefA(object, r = 1, normalize = TRUE, ...) coefPI(object, ...)
The functions extract the parameters from a VECM with K variables and rank r:
Adjustment coefficients, of dim K \times r
Cointegrating coefficients, of dim K \times r
Matrix Π=A\dot B^{'}, of dim K \times K
Note that by default, the A and B coefficients returned are normalized (see below). This is
the case for results obtained from VECM/lineVar and
cajorls, while for ca.jo, the user has the choice
(but normalize=TRUE by default), in which case the rank r is also to be specified.
The normalization is the Phillips triangular representation, as suggested by Johansen (1995, p. 72),
standardising the first r\times r coefficients to I_r:
B_{norm}=B (c^{'}B)^{-1} with c=(I_r,0_{p-r,r})^{'}
A_{norm}=B^{'}c
Finally, note that the function also apply to objects obtained from tests of class
ca.jo.test (from blrtest etc...). Care should be taken
however, since the normalization might override the restrictions imposed.
A matrix containing the coefficients
Matthieu Stigler
data(barry)
vecm <- VECM(barry, lag=1, estim="ML")
vecm_r2 <- VECM(barry, lag=1, estim="ML", r=2)
## extract coefficients:
coefA(vecm)
coefB(vecm)
coefPI(vecm)
coefB(vecm_r2)
coefPI(vecm_r2)
## Beta-Restricted VECM:
beta_vecm2 <- coefB(vecm_r2)
beta_vecm2[3,2] <- 0.02
vecm_r2_rest <- VECM(barry, lag=1, estim="ML", r=2, beta=beta_vecm2)
round(coefB(vecm_r2_rest),5)
## Package vars/urca
if(require(urca)){
vecm_ur <- ca.jo(barry, K=2)
coefB(vecm_ur)
coefB(vecm_ur,r=2)
coefB(cajorls(vecm_ur, r=2))
all.equal(coefB(vecm), coefB(vecm_ur), check.attributes=FALSE)
all.equal(coefB(vecm_r2), coefB(vecm_ur, r=2), check.attributes=FALSE)
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