Likelihood ratio test for restrictions under partly known beta in a subspace

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 \(\chi^2\) 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

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: \(r1 \leq s \leq p - r2\). 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.

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.

Author

Bernhard Pfaff

Examples

data(UKpppuip)
attach(UKpppuip)
#> The following objects are masked from UKpppuip (pos = 3):
#> 
#>     doilp0, doilp1, e12, i1, i2, p1, p2
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)
#> 
#> ##################################################### 
#> # Johansen-Procedure Unit Root / Cointegration Test # 
#> ##################################################### 
#> 
#> The value of the test statistic is: 4.9312 
#>