InvertibleQ: Test if Invertible or Stationary-casual

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

Description

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.

Usage

1

Arguments

phi

a vector of AR coefficients

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.

Value

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

Author(s)

A.I. McLeod and Y. Zhang

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

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#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

FitAR documentation built on May 2, 2019, 3:22 a.m.