\name{roots}
\alias{roots}
\alias{roots.SS}
\alias{roots.ARMA}
\alias{roots.TSestModel}
\title{Calculate Model Roots}
\description{Calculate roots of a TSmodel.}
\usage{
roots(obj, ...)
\method{roots}{SS}(obj, fuzz=0, randomize=FALSE, ...)
\method{roots}{ARMA}(obj, fuzz=0, randomize=FALSE, warn=TRUE, by.poly=FALSE, ...)
\method{roots}{TSestModel}(obj, ...)
}
\arguments{
\item{obj}{An object of class TSmodel.}
\item{fuzz}{If non-zero then roots within fuzz
distance are considered equal.}
\item{randomize}{
Randomly arrange complex pairs of roots so the one with the positive imaginary
part is not always first (so random experiments are not biased).}
\item{warn}{If FALSE then warnings about unit roots added for TREND are not printed.}
\item{by.poly}{
If TRUE then roots are calculated by expanding the determinant of the A
polynomial. Otherwise, they are calculated by converting to a state
space representation and calculating the eigenvalues of F. This second
method is preferable for speed, accuracy, and because of a limitation
in the degree of a polynomial which can be handled by polyroot.}
\item{...}{arguments passed to other methods.}
}
\value{
The eigenvalues of the state transition matrix or the inverse of the roots of the
determinant of the AR polynomial are returned.
}
\details{
The equality of roots for equivalent state space and ARMA models is
illustrated in \cite{Gilbert (1993)}. The calculation of ARMA model roots is
more stable if the model is converted to state space and the roots
calculated from the state transition matrix (see \cite{Gilbert,2000}). The
calculation is done this way by default. If \code{by.poly=TRUE} then
the determinant of the AR polynomial is expanded to get the roots.
}
\seealso{
\code{\link{stability}},
\code{\link{McMillanDegree}}
}
\examples{
data("eg1.DSE.data.diff", package="dse")
model <- estVARXls(eg1.DSE.data.diff)
roots(model)
}
\references{
Gilbert, P. D. (1993) State space and ARMA models: An overview of
the equivalence. Working paper 93-4, Bank of Canada. Available at
\url{www.bank-banque-canada.ca/pgilbert}
Gilbert, P.D. (2000) A note on the computation of time series model roots.
\emph{Applied Economics Letters}, \bold{7}, 423--424
}
\concept{DSE}
\keyword{ts}