portes (version 1.08)

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)

Arguments

coef

a numeric, matrix, or array.

Value

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

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)