This class contains the relevant information by applying the Johansen procedure to a matrix of time series data.
x:Object of class "ANY": A data matrix, or an
object that can be coerced to it.
Z0:Object of class "matrix": The matrix of the
differenced series.
Z1:Object of class "matrix": The regressor
matrix, except for the lagged variables in levels.
ZK:Object of class "matrix": The matrix of the
lagged variables in levels.
type:Object of class "character": The type of the
test, either "trace" or "eigen".
model:Object of class "character": The model
description in prose, with respect to the inclusion of a linear
trend.
ecdet:Object of class "character": Specifies
the deterministic term to be included in the cointegration
relation. This can be either "none", "const", or "trend".
lag:Object of class "integer": The lag order
for the variables in levels.
P:Object of class "integer": The count of
variables.
season:Object of class "ANY": The frequency of
the data, if seasonal dummies should be included, otherwise NULL.
dumvar:Object of class "ANY": A matrix
containing dummy variables. The row dimension must be equal to
x, otherwise NULL.
cval:Object of class "ANY": The critical
values of the test at the 1%, 5% and 10% level of significance.
teststat:Object of class "ANY": The values
of the test statistics.
lambda:Object of class "vector": The eigenvalues.
Vorg:Object of class "matrix": The matrix of
eigenvectors, such that \(\hat V'S_{kk}\hat V = I\).
V:Object of class "matrix": The matrix of
eigenvectors, normalised with respect to the first variable.
W:Object of class "matrix": The matrix of
loading weights.
PI:Object of class "matrix": The coeffcient
matrix of the lagged variables in levels.
DELTA:Object of class "matrix": The
variance/covarinace matrix of V.
GAMMA:Object of class "matrix": The
coeffecient matrix of Z1.
R0:Object of class "matrix": The matrix of
residuals from the regressions in differences.
RK:Object of class "matrix": The matrix of
residuals from the regression in lagged levels.
bp:Object of class "ANY": Potential break
point, only set if function cajolst is called, otherwise
NA.
test.name:Object of class "character": The
name of the test, i.e. `Johansen-Procedure'.
spec:Object of class "character": The
specification of the VECM.
call:Object of class "call": The
call of function ca.jo.
Class urca, directly.
Type showMethods(classes="ca.jo") at the R prompt for a
complete list of methods which are available for this class.
Useful methods include
show:test statistic.
summary:like show, but critical values, eigenvectors and loading matrix added.
plot:The series of the VAR and their potential cointegration relations.
Bernhard Pfaff
Johansen, S. (1988), Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control, 12, 231--254.
Johansen, S. and Juselius, K. (1990), Maximum Likelihood Estimation and Inference on Cointegration -- with Applications to the Demand for Money, Oxford Bulletin of Economics and Statistics, 52, 2, 169--210.
Johansen, S. (1991), Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models, Econometrica, Vol. 59, No. 6, 1551--1580.
ca.jo, plotres and urca-class.