# ablrtest: Likelihood ratio test for restrictions on alpha and beta In urca: Unit Root and Cointegration Tests for Time Series Data

## 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

 1 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.

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.

ca.jo, alrtest, blrtest, cajo.test-class, ca.jo-class and urca-class.

## Examples

 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)) 

### Example output

######################
# 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


urca documentation built on May 2, 2019, 2:08 a.m.