# bh6lrtest: Likelihood ratio test for restrictions under partly known... In urca: Unit Root and Cointegration Tests for Time Series Data

## Description

This function estimates a restricted VAR, where some restrictions are placed on r1 cointegrating relations which are chosen in the space of the matrix H. The test statistic is distributed as χ^2 with (p-s-r2)r1 degrees of freedom, with s equal to the number of columns of \bold{H}, r1 the number of cointegrating relations in the first partition and r2 the number of cointegrating relations in the second partition which will be estimated without any restrictions.

## Usage

 1 bh6lrtest(z, H, r, r1, conv.val = 0.0001, max.iter = 50) 

## Arguments

 z An object of class ca.jo. H The (p \times s) matrix containing the known cointegration relations. r The count of cointegrating relationships; inferred from summary(ca.jo-object). r1 The count of cointegrating relationships in the first partition of the cointegration space; conv.val The convergence value of the algorithm. (see details); max.iter The maximal number of iterations.

## Details

Please note, that the following ordering of the dimensions should be obeyed: r1 ≤q s ≤q p - r2. A two-step algorithm is used to determine the eigen values of the restricted model. Convergence is achieved if the quadratic norm of the eigen values is smaller than conv.val.

## Value

An object of class cajo.test.

Bernhard Pfaff

## References

Johansen, S. (1995), Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press, Oxford.

Johansen, S. and Juselius, K. (1992), Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK, Journal of Econometrics, 53, 211–244.

ca.jo, alrtest, ablrtest, blrtest, bh5lrtest, cajo.test-class, ca.jo-class and urca-class.

## Examples

 1 2 3 4 5 6 7 data(UKpppuip) attach(UKpppuip) dat1 <- cbind(p1, p2, e12, i1, i2) dat2 <- cbind(doilp0, doilp1) H1 <- ca.jo(dat1, type='trace', K=2, season=4, dumvar=dat2) H6 <- matrix(c(1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0), c(5,3)) bh6lrtest(z=H1, H=H6, r=2, r1=1, conv.val=0.0001, max.iter=50) 

### Example output

#####################################################
# Johansen-Procedure Unit Root / Cointegration Test #
#####################################################

The value of the test statistic is: 4.9312


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