R: Likelihood ratio test for restrictions under partly known...

bh6lrtest {urca} | R Documentation

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

### 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

    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`.

### Author(s)

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.

### See Also

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

### 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)
    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)

[Package urca version 1.3-0 Index]