urca (version 1.3-3)

ablrtest: Likelihood ratio test for restrictions on alpha and beta

Description

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

Usage

ablrtest(z, H, A, r)

Value

An object of class cajo.test.

Arguments

z

An object of class ca.jo.

H

The $(p\times s)$ matrix containing the restrictions on $\text{bold}\beta$.

A

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

r

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

Author

Bernhard Pfaff

Details

The restricted $\text{bold}\alpha$ matrix, as well as $\text{bold}\beta$ 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, alrtest, blrtest, 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)
HD1 <- matrix(c(1, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1), c(5,3))
DA <- matrix(c(1,0,0,0, 0, 1, 0, 0, 0, 0, 0, 1), c(4,3))
summary(ablrtest(sjd.vecm, H=HD1, A=DA, r=1))