AR(1) process with non gaussian innovations

Question

i want to simulate an AR(1) process with non gaussian innovations. i tried it on the following way, but i`m not sure:

n<-25
e=rpareto(n,2,1) #can i take any distribution i want for my innovations

phi=0.2
PAR=rep(0,n)
for(t in 2:n) 
{
PAR[1]<-1
PAR[t]<-phi*PAR[t-1]+e[t]
}

and another way: in the R-function arima.sim the innovations are N(0,sigma) distributed, but i want to generate N(m,sigma) innovations.

sigma<-2
mu<-10
arima.sim(n=25,model=list(order=c(1,0,0),ar=0.2), sd=sqrt(sigma))+mu

thanks for your help

Answer 1

Just supply the innovations as the argument innov :

# The first problem:
e1<-rpareto(25,2,1)
arima.sim(n=25,model=list(order=c(1,0,0),ar=0.2), innov=e1)

# And the socond:
sigma<-2
mu<-10
e2<-rnorm(25,mean=mu,sd=sqrt(sigma))
arima.sim(n=25,model=list(order=c(1,0,0),ar=0.2), innov=e2)