1d:T79e,# The Impulse Response Function in the Infinite MA or VMA Representation The impulse coefficients are computed. ```r ImpulseVMA(ar=NULL,ma=NULL,trunc.lag=NULL) ``` ## 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` = $p+q$. ## Returns 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. ## Author(s) 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 ```r ##################################################################### ### 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) ```

ImpulseVMA function