portes (version 1.08)

ImpulseVMA: The Impulse Response Function in the Infinite MA or VMA Representation

Description

The impulse coefficients are computed.

Usage

ImpulseVMA(phi=NULL,theta=NULL,Trunc.Series=NA)

Arguments

phi

a numeric or an array of AR or an array of VAR parameters with order $p$.

theta

a numeric or an array of MA or an array of VMA parameters with order $q$.

Trunc.Series

truncation lag is used to truncate the infinite MA or VMA Process. IF it is NA, then by default Trunc.Series=$p+q$.

Value

• The impulse response coefficients of order Trunc.Series+1 obtained by converting the ARMA$(p,q)$ or VARMA$(p,q)$ process to infinite MA or VMA process, respectively.

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

ARMAtoMA, varima.sim, vma.sim, InvertQ, InvertibleQ

Examples

#####################################################################
### Impulse response coefficients from AR(1,1) to infinite MA process. 
### The infinite process is truncated at lag 20
###
k <- 1
Trunc.Series <- 20
phi <- 0.7
theta <- array(-0.9,dim=c(k,k,1))
ImpulseVMA(phi,theta,Trunc.Series)
#####################################################################
### Impulse response coefficients from VAR(2) to infinite VMA process
### The infinite process is truncated at default lag value = p+q
###
k <- 2
phi <- array(c(0.5,0.4,0.1,0.5,0,0.3,0,0),dim=c(k,k,2))
theta <- NULL
ImpulseVMA(phi,theta)
#####################################################################
### Impulse response coefficients from VARMA(2,1) to infinite VMA process
### The infinite process is truncated at lag 50
###
k <- 2
phi <- array(c(0.5,0.4,0.1,0.5,0,0.25,0,0),dim=c(k,k,2))
theta <- array(c(0.6,0,0.2,0.3),dim=c(k,k,1))
ImpulseVMA(phi,theta,Trunc.Series=50)