Generate correlated IMA(1,1) using R

Question

I'd like to use R to generate two correlated series that follow IMA(1,1) process. rho is a correlation between the error terms, but when I changed the rho the plot does not change. Is it wrong if I use d[i,] <- d[i-1,] - theta*(e[i-1,]+e[i,]) ?

rho < 0.1
mu <- c(400,400)
theta <- c(0.1,0.1)
d <- ts(matrix(0,ncol=2,nrow=1001))
e <- ts(rmvnorm(1001,sigma=cbind(c(400,rho*400),c(rho*400,400))))
for(i in 2:1001)
  d[i,] <- mu + d[i-1,] - theta*(e[i-1,]+e[i,])

plot(d)

Answer 1

Change your mean to something smaller than 400 like 0.01 to see the time series more clearly. Then try the following code with rho <- 0.1 and rho <- 0.9 to see the effect of rho.

rho <- 0.1
#rho <- 0.9
mu <- c(0.01,0.01)
theta <- c(0.1,0.1)
d <- ts(matrix(0,ncol=2,nrow=1001))
e <- ts(rmvnorm(1001,sigma=cbind(c(400,rho*400),c(rho*400,400))))
for(i in 2:1001)
 d[i,] <- mu + d[i-1,] - theta*(e[i-1,]+e[i,])

par(mfrow=c(1,2))
plot(d[,1]);plot(d[,2])

Here are some plots: