# 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

1 | ```
alrtest(z, A, r)
``` |

### Arguments

`z` |
An object of class |

`A` |
The |

`r` |
The count of cointegration relationships; |

### 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

1 2 3 4 5 6 |