R: Likelihood ratio test for restrictions on alpha and beta

ablrtest {urca} | R Documentation

## Likelihood ratio test for restrictions on alpha and beta

### Description

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

### Usage

    ablrtest(z, H, A, r)

### Arguments

`z` | An object of class `ca.jo`.
`H` | The (p \times s) matrix containing the restrictions on \bold{β}.
`A` | The (p \times m) matrix containing the restrictions on \bold{α}.
`r` | The count of cointegrating relationships; inferred from `summary(ca.jo-object)`.

### Details

The restricted \bold{α} matrix, as well as \bold{β} is normalised with respect to the first variable.

### Value

An object of class `cajo.test`.

### Author(s)

Bernhard Pfaff

### 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))

[Package urca version 1.3-0 Index]