[R] arima.sim: innov querry

[Andy Bunn]

Apologies for thickness - I'm sure that this operates as documented and with good reason. However...

My understanding of arima.sim() is obviously imperfect. In the example below I assume that x1 and x2 are similar white noise processes with a mean of 5 and a standard deviation of 1. I thought x3 should be an AR1 process but still have a mean of 5 and a sd of 1. Why does x3 have a mean of ~7? Obviously I'm missing something fundamental about the burn in or the innovations.

x1 <- rnorm(1e3,mean=5,sd=1)
summary(x1)
x2 <- arima.sim(list(order=c(0,0,0)),n=1e3,mean=5,sd=1)
summary(x2)
x3 <- arima.sim(list(order=c(1,0,0),ar=0.3),n=1e3,mean=5,sd=1)
summary(x3) # why does x3 have a mean of ~7?