Description

This class contains the relevant information by estimating and testing a VAR under linear restrictions on \bold{α} and \bold{β}.

Slots

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{β}.

A:

Object of class "ANY": The matrix containing the restrictions placed upon \bold{α}.

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_{…}'(H'S_{…}H)\hat V_{…} = 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’.

Extends

Class urca, directly.

Methods

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.

Author(s)

Bernhard Pfaff

References

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.

See Also

ablrtest, alrtest, blrtest, ca.jo, ca.jo-class and urca-class.