portes (version 6.0)

InvertQ: Check Stationary and Invertibility of ARMA or VARMA Models

Description

Utility function checks whether ARMA or VARMA model satisfies the stationary or/and the invertibility conditions.

Usage

InvertQ(coef)

Value

A warning message only if the model is not stationary or/and not invertible.

Arguments

coef

a numeric, matrix, or array.

Author

Esam Mahdi and A.I. McLeod.

Details

It should be noted that, the AR(\(p\)) or VAR(\(p\)) model can always be expressed as a \(kp\)-dimensional AR(\(1\)) or VAR(\(1\)), and the MA(\(q\)) or VMA(\(q\)) model can always be expressed as a \(kq\)-dimensional MA(\(1\)) or VMA(\(1\)). For this reason, we can use this fact when we need to find the explicit solutions of AR(\(p\)) or VAR(\(p\)) models or MA(\(q\)) or VMA(\(q\)) models as the AR(\(1\)) or VAR(\(1\)) or the MA(\(1\)) or VMA(\(1\)) models can be characterized with simple intuitive formulas.

References

Lutkepohl, H. (2005). "New introduction to multiple time series analysis". Springer-Verlag, New York.

Reinsel, G. C. (1997). "Elements of Multivariate Time Series Analysis". Springer-Verlag, 2nd edition.

See Also

varima.sim, vma.sim, ImpulseVMA

Examples

##############################################################
### Check Stationary
phi <- array(c(0.5,0.4,0.1,0.5,0,0.3,0,0),dim=c(2,2,2))
InvertQ(phi)
### Check Invertibility
theta <- array(c(0.5,0.4,0.1,0.5,0,0.3,0,0),dim=c(2,2,2))
InvertQ(theta)