# Fitting a VARMAX model using MTS library in R

I am trying to fit a VARMAX (vector autoregressive moving-average with exogenous variables) model to some synthetically generated data using the MTS library available in R. I found that there is only one function for fitting models with exogenous variables, it is designed for only VAR models and is called VARX. Reading in the literature, I found that there is a method for finding the VARX representation of the VARMAX model (not that straightforward), thus, finding the VARX representation of the VARMAX model, the VARX function could be used. My question is: Is there any method already implemented in R that transforms VARMAX, VARMA, VMAX into their corresponding VAR representation or how the VARX function must be used for fitting models of this type?

In the following reproducible example is generated an VARMAX model intending to estimate their parameters with VARX function:

library(MTS)
set.seed(2015)
Phi<-matrix(c(0.5,0.2,0.2,0.3),ncol=2)
Theta<-matrix(c(0.4,0.3,0.2,0.5),ncol=2)
Sigma <- matrix(c(1,0.2,0.2,1),ncol=2)
serie_varmax<-VARMAsim(60,arlags=c(1),malags=c(1),phi=Phi,theta=Theta,sigma=Sigma)\$series
exoge1<-serie_varmax[,1]+(0.3*seq(1,60)) #Exogenous variable influencing only the first variable
serie1<-cbind(exoge1,serie_varmax[,2])


As aforementioned, I am wondering how to estimate the VARMAX coefficients using VARX function.

• What is the actual question? How to turn a VARMAX model into a VARX model? Or, given an estimated VARX model, how to turn it back into a VARMAX model? Or yet something else? – Richard Hardy Aug 18 '15 at 16:21
• Richard, my main question is how to turn a VARMAX model into a VARX model in order to use the VARX function. – Hector Aug 18 '15 at 16:37
• You could perhaps refine your original post to highlight that. Also, could you post the source where you found the method for representing VARMAX as VARX? Have you tried it? If so, how far did you get? Is there a particular problem you are stuck at? – Richard Hardy Aug 18 '15 at 16:39