Likelihood ratio test for restrictions on beta

This function estimates a restricted VAR, where the restrictions are base upon \(\bold{\beta}\), i.e. the cointegration vectors. The test statistic is distributed as \(\chi^2\) with \(r(p-s)\) degrees of freedom, with \(s\) equal to the columns of the restricting matrix \(\bold{H}\).

Usage

blrtest(z, H, r)

Arguments

z: An object of class ca.jo.
H: The \((p \times s)\) matrix containing the restrictions on \(\bold{\beta}\).
r: The count of cointegrating relationships;
inferred from summary(ca.jo-object).

Details

Please note, that in the case of nested hypothesis, the reported p-value should be adjusted to \(r(s1-s2)\) (see Johansen, S. and K. Juselius (1990)).

Value

An object of class cajo.test.

References

Johansen, S. (1988), Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control, 12, 231–254.

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.

Author

Bernhard Pfaff

Examples

data(denmark)
sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
sjd.vecm <- ca.jo(sjd, ecdet="const", type="eigen", K=2, spec="longrun",
season=4)
HD0 <- matrix(c(-1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1), c(5,4))
summary(blrtest(sjd.vecm, H=HD0, r=1))
#> 
#> ###################### 
#> # Johansen-Procedure # 
#> ###################### 
#> 
#> Estimation and testing under linear restrictions on beta 
#> 
#> The VECM has been estimated subject to: 
#> beta=H*phi and/or alpha=A*psi
#> 
#>      [,1] [,2] [,3] [,4]
#> [1,]   -1    0    0    0
#> [2,]    1    0    0    0
#> [3,]    0    1    0    0
#> [4,]    0    0    1    0
#> [5,]    0    0    0    1
#> 
#> Eigenvalues of restricted VAR (lambda):
#> [1] 0.4327 0.1722 0.0436 0.0056
#> 
#> The value of the likelihood ratio test statistic:
#> 0.04 distributed as chi square with 1 df.
#> The p-value of the test statistic is: 0.84 
#> 
#> Eigenvectors, normalised to first column
#> of the restricted VAR:
#> 
#>         [,1]    [,2]     [,3]    [,4]
#> [1,]  1.0000  1.0000   1.0000  1.0000
#> [2,] -1.0000 -1.0000  -1.0000 -1.0000
#> [3,]  5.3004  0.2293  99.7012  1.5513
#> [4,] -4.2904  8.9614 -51.8139 -2.0206
#> [5,] -6.2645 -6.6551 -13.4082 -5.8223
#> 
#> Weights W of the restricted VAR:
#> 
#>          [,1]    [,2]   [,3]    [,4]
#> LRM.d -0.2120 -0.0195  4e-04  0.0131
#> LRY.d  0.1075 -0.0061  2e-04  0.0196
#> IBO.d  0.0226 -0.0097 -4e-04  0.0003
#> IDE.d  0.0297 -0.0226  0e+00 -0.0021
#>