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\name{bh6lrtest}
\alias{bh6lrtest}
\encoding{latin1}
\title{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 \eqn{r1} cointegrating relations which are chosen in the
space of the matrix H. The test statistic is distributed as
\eqn{\chi^2} with \eqn{(p-s-r2)r1} degrees of freedom, with \eqn{s}
equal to the number of columns of \eqn{\bold{H}}, \eqn{r1} the number
of cointegrating relations in the first partition and \eqn{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{
\item{z}{An object of class \code{ca.jo}.}
\item{H}{The \eqn{(p \times s)} matrix containing the known
cointegration relations.}
\item{r}{The count of cointegrating relationships; \cr
inferred from \code{summary(ca.jo-object)}.\cr}
\item{r1}{The count of cointegrating relationships in the first
partition of the cointegration space; \cr}
\item{conv.val}{The convergence value of the algorithm. (see details); \cr}
\item{max.iter}{The maximal number of iterations.}
}
\details{
Please note, that the following ordering of the dimensions should be
obeyed: \eqn{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
\code{conv.val}.
}
\value{
An object of class \code{cajo.test}.
}
\references{
Johansen, S. (1995), \emph{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,
\emph{Journal of Econometrics}, \bold{53}, 211--244.
}
\seealso{
\code{\link{ca.jo}}, \code{\link{alrtest}}, \code{\link{ablrtest}},
\code{\link{blrtest}}, \code{\link{bh5lrtest}}, \code{\link{cajo.test-class}},
\code{\link{ca.jo-class}} and \code{\link{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)
}
\author{Bernhard Pfaff}
\keyword{regression}
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