InvertibleQ: Test if Invertible or Stationary-casual
In FitAR: Subset AR Model Fitting

Description Usage Arguments Details Value Author(s) References See Also Examples

Tests if the polynomial

1 -φ(1) B … - φ(p) B^p,

where p=length[phi] has all roots outside the unit circle. This is the invertibility condition for the polynomial.

1	InvertibleQ(phi)

phi

a vector of AR coefficients

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.

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

A.I. McLeod and Y. Zhang

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

ARToPacf

#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