InvertibleQ.Rd

\name{InvertibleQ}
\alias{InvertibleQ}
\title{ Test if Invertible or Stationary-casual }
\description{
Tests if the polynomial 
\deqn{1 -\phi(1) B  \ldots - \phi(p) B^p,}
where p=length[phi] has all roots 
outside the unit circle.
This is the invertibility condition for the polynomial.
}
\usage{
InvertibleQ(phi)
}
\arguments{
  \item{phi}{ a vector of AR coefficients }
}
\details{
The PACF is computed for lags 1, \dots, p using eqn. (1) in
McLeod and Zhang (2006). 
The invertibility condition is satisfied if and only if
all PACF values are less than 1 in absolute value.
}
\value{
  TRUE, if invertibility condition is satisfied.
  FALSE, if not invertible.
}
\references{ 
McLeod, A.I. and Zhang, Y. (2006).  
Partial autocorrelation parameterization for subset autoregression.  
Journal of Time Series Analysis, 27, 599-612.
}
\author{ A.I. McLeod and Y. Zhang}

\seealso{ \code{\link{ARToPacf}} }
\examples{
#simple examples
InvertibleQ(0.5)
#find the area of the invertible region for AR(2). 
#We assume that the parameters must be less than 2 in absolute value.
#From the well-known diagram in the book of Box and Jenkins (1970), 
#this area is exactly 4.
NSIM<-10^4
phi1<-runif(NSIM, min=-2, max=2)
phi2<-runif(NSIM, min=-2, max=2)
k<-sum(apply(matrix(c(phi1,phi2),ncol=2), MARGIN=1, FUN=InvertibleQ))
area<-16*k/NSIM
area
}
\keyword{ ts }