This class contains the relevant information by estimating and testing a VAR under linear restrictions on \(\bold{\alpha}\) and \(\bold{\beta}\).
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.
ecdet:Object of class "character": Specifies
the deterministic term to be included in the cointegration
relation. This can be either "none", "const", or "trend".
H:Object of class "ANY": The matrix
containing the restrictions placed upon \(\bold{\beta}\).
A:Object of class "ANY": The matrix
containing the restrictions placed upon \(\bold{\alpha}\).
B:Object of class "ANY": The matrix
orthogonal to matrix \(\bold{A}\).
type:Object of class "character": The test type.
teststat:Object of class "numeric": The value
of the test statistic.
pval:Object of class "vector": The p-value and
the degrees of freedom.
lambda:Object of class "vector": The
eigenvalues of the restricted model.
Vorg:Object of class "matrix": The matrix of
eigenvectors, such that \(\hat V_{\dots}'(H'S_{\dots}H)\hat
V_{\dots} = I\).
V:Object of class "matrix": The matrix of the
restricted eigenvectors, normalised with respect to the first variable.
W:Object of class "matrix": The matrix of the
corresponding loading weights.
PI:Object of class "matrix": The coefficient
matrix of the lagged variables in levels.
DELTA:Object of class "ANY": The
variance/covarinace matrix of \(\bold{V}\).
DELTA.bb:Object of class "ANY": The
variance/covarinace matrix of the marginal factor
\(\bold{B}'\bold{R}_{0t}\).
DELTA.ab:Object of class "ANY": The
variance/covarinace matrix of the conditional distribution of
\(\bold{A}'\bold{R}_{0t}\) and \(\bold{R}_{kt}\).
DELTA.aa.b:Object of class "ANY": The
variance/covarinace matrix of the restricted loading matrix.
GAMMA:Object of class "matrix": The
coefficient matrix of \(\bold{Z1}\).
test.name:Object of class "character": The
name of the test, i.e. `Johansen-Procedure'.
Class urca, directly.
Type showMethods(classes="cajo.test") 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 p-value of test statistic, restricted eigenvectors, loading matrix and restriction matrices \(\bold{H}\) and \(\bold{A}\), where applicable, added.
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.
ablrtest, alrtest, blrtest,
ca.jo, ca.jo-class and urca-class.