Likelihood ratio test for restrictions under partly known beta

This function estimates a restricted VAR, where some of the cointegration vectors are known. The known cointegration relationships have to be provided in an \(p x r1\) matrix \(\bold{H}\). The test statistic is distributed as \(\chi^2\) with \((p-r)r1\) degrees of freedom, with \(r\) equal to total number of cointegration relations.

Usage

bh5lrtest(z, H, r)

Arguments

z: An object of class ca.jo.
H: The \((p \times r1)\) matrix containing the known cointegration relations.
r: The count of cointegrating relationships;
inferred from summary(ca.jo-object).

Details

Please note, that the number of columns of \(\bold{H}\) must be smaller than the count of cointegration relations \(r\).

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)
dat1 <- cbind(p1, p2, e12, i1, i2)
dat2 <- cbind(doilp0, doilp1)
H1 <- ca.jo(dat1, type='trace', K=2, season=4, dumvar=dat2)
H51 <- c(1, -1, -1, 0, 0)
H52 <- c(0, 0, 0, 1, -1)
summary(bh5lrtest(H1, H=H51, r=2))
#> 
#> ###################### 
#> # Johansen-Procedure # 
#> ###################### 
#> 
#> Estimation and testing under partly known beta 
#> 
#> The VECM has been estimated subject to: 
#> beta=H*phi and/or alpha=A*psi
#> 
#>      [,1]
#> [1,]    1
#> [2,]   -1
#> [3,]   -1
#> [4,]    0
#> [5,]    0
#> 
#> Eigenvalues of restricted VAR (lambda):
#> [1] 0.3956 0.2812 0.2541 0.1008
#> 
#> The value of the likelihood ratio test statistic:
#> 14.52 distributed as chi square with 3 df.
#> The p-value of the test statistic is: 0 
#> 
#> Eigenvectors, normalised to first column
#> of the restricted VAR:
#> 
#>      [,1]     [,2]
#> [1,]    1   1.0000
#> [2,]   -1   0.7845
#> [3,]   -1   0.2155
#> [4,]    0 -64.9725
#> [5,]    0 -40.7031
#> 
#> Weights W of the restricted VAR:
#> 
#>          [,1]    [,2]
#> p1.d  -0.0744 -0.0031
#> p2.d  -0.0147 -0.0009
#> e12.d  0.0724  0.0057
#> i1.d   0.0164  0.0020
#> i2.d   0.0416  0.0035
#> 
summary(bh5lrtest(H1, H=H52, r=2))
#> 
#> ###################### 
#> # Johansen-Procedure # 
#> ###################### 
#> 
#> Estimation and testing under partly known beta 
#> 
#> The VECM has been estimated subject to: 
#> beta=H*phi and/or alpha=A*psi
#> 
#>      [,1]
#> [1,]    0
#> [2,]    0
#> [3,]    0
#> [4,]    1
#> [5,]   -1
#> 
#> Eigenvalues of restricted VAR (lambda):
#> [1] 0.4064 0.2607 0.1052 0.1007
#> 
#> The value of the likelihood ratio test statistic:
#> 1.89 distributed as chi square with 3 df.
#> The p-value of the test statistic is: 0.59 
#> 
#> Eigenvectors, normalised to first column
#> of the restricted VAR:
#> 
#>      [,1]    [,2]
#> [1,]    0  1.0000
#> [2,]    0 -0.9102
#> [3,]    0 -0.9334
#> [4,]    1 -2.6163
#> [5,]   -1 -2.6163
#> 
#> Weights W of the restricted VAR:
#> 
#>          [,1]    [,2]
#> p1.d   0.0881 -0.0678
#> p2.d  -0.0597 -0.0189
#> e12.d -0.2731  0.0975
#> i1.d  -0.1450  0.0320
#> i2.d   0.2197  0.0625
#>