R: Likelihood ratio test for restrictions on alpha

alrtest {urca} | R Documentation

## Likelihood ratio test for restrictions on alpha

### Description

This function estimates a restricted VAR, where the restrictions are base upon \bold{α}, i.e. the loading vectors. The test statistic is distributed as χ^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)

### Arguments

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

### Details

The orthogonal matrix to \bold{A} can be accessed as `object@B`. The restricted \bold{α} matrix 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`, `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))

[Package urca version 1.3-0 Index]