portes (version 6.0)

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

Description

The impulse coefficients are computed.

Usage

ImpulseVMA(ar=NULL,ma=NULL,trunc.lag=NULL)

Value

The impulse response coefficients of order trunc.lag+1 obtained by converting the ARMA\((p,q)\) or VARMA\((p,q)\)

process to infinite MA or VMA process, respectively.

Arguments

ar

a numeric or an array of AR or an array of VAR parameters with order \(p\).

ma

a numeric or an array of MA or an array of VMA parameters with order \(q\).

trunc.lag

truncation lag is used to truncate the infinite MA or VMA Process. IF it is NULL, then the default trunc.lag = \(p+q\).

Author

Esam Mahdi and A.I. McLeod.

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

Examples

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