InvertibleQ(FitAR) | R Documentation |
Tests if the polynomial
1 -phi(1) B ... - phi(p) B^p,
where p=Length[phi] has all roots outside the unit circle. This is the invertibility condition for the polynomial.
InvertibleQ(phi)
phi |
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
McLeod, A.I. and Zhang, Y. (2006). Partial autocorrelation parameterization for subset autoregression. Journal of Time Series Analysis, 27, 599-612.
#simple examples InvertibleQ(0.5) 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