Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 | ```
ablrtest(z, H, A, r)
``` |

`z` |
An object of class |

`H` |
The |

`A` |
The |

`r` |
The count of cointegrating relationships; |

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

An object of class `cajo.test`

.

Bernhard Pfaff

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.

`ca.jo`

, `alrtest`

, `blrtest`

,
`cajo.test-class`

, `ca.jo-class`

and
`urca-class`

.

1 2 3 4 5 6 7 | ```
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))
``` |

```
######################
# Johansen-Procedure #
######################
Estimation and testing under linear restrictions on alpha and beta
The VECM has been estimated subject to:
beta=H*phi and/or alpha=A*psi
[,1] [,2] [,3]
[1,] 1 0 0
[2,] -1 0 0
[3,] 0 1 0
[4,] 0 -1 0
[5,] 0 0 1
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 0 1 0
[3,] 0 0 0
[4,] 0 0 1
Eigenvalues of restricted VAR (lambda):
[1] 0.4100 0.0090 0.0053
The value of the likelihood ratio test statistic:
2.13 distributed as chi square with 2 df.
The p-value of the test statistic is: 0.35
Eigenvectors, normalised to first column
of the restricted VAR:
[,1]
[1,] 1.0000
[2,] -1.0000
[3,] 5.9508
[4,] -5.9508
[5,] -6.2162
Weights W of the restricted VAR:
[,1]
[1,] -0.1519
[2,] 0.0992
[3,] 0.0000
[4,] 0.0288
```

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