urca (version 1.3-4)

alrtest: Likelihood ratio test for restrictions on alpha

Description

This function estimates a restricted VAR, where the restrictions are base upon \(\bold{\alpha}\), i.e. the loading vectors. The test statistic is distributed as \(\chi^2\) with \(r(p-m)\) degrees of freedom, with \(m\) equal to the columns of the restricting matrix \(\bold{A}\).

Usage

alrtest(z, A, r)

Value

An object of class cajo.test.

Arguments

z

An object of class ca.jo.

A

The \((p \times m)\) matrix containing the restrictions on \(\bold{\alpha}\).

r

The count of cointegration relationships;
inferred from summary(ca.jo-object).

Author

Bernhard Pfaff

Details

The orthogonal matrix to \(\bold{A}\) can be accessed as object@B. The restricted \(\bold{\alpha}\) matrix is normalised with respect to the first variable.

References

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

ca.jo, blrtest, ablrtest, cajo.test-class, ca.jo-class and urca-class.

Examples

data(denmark)
sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
sjd.vecm <- ca.jo(sjd, ecdet = "const", type="eigen", K=2, spec="longrun",
season=4)
DA <- matrix(c(1,0,0,0), c(4,1))
summary(alrtest(sjd.vecm, A=DA, r=1))