FitAR (version 1.94)

InvertibleQ: Test if Invertible or Stationary-casual

Description

Tests if the polynomial $$1 -\phi(1) B \ldots - \phi(p) B^p,$$ where p=length[phi] has all roots outside the unit circle. This is the invertibility condition for the polynomial.

Usage

InvertibleQ(phi)

Arguments

phi

a vector of AR coefficients

Value

• TRUE, if invertibility condition is satisfied. FALSE, if not invertible.

Details

The PACF is computed for lags 1, ..., 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.

References

McLeod, A.I. and Zhang, Y. (2006). Partial autocorrelation parameterization for subset autoregression. Journal of Time Series Analysis, 27, 599-612.

See Also

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