How to simulate an AR(1) model in R with rho equals to 1

Question

I want to simulate an AR(1) model x_t = rho * x_(t-1) + e_t, where rho=1, n=1050, so I tried the following code in R.

 y <- arima.sim(list(order = c(1,0,0), ar = 1), n = 1050)

But R returns the following message: Error: 'ar' part of model is not stationary. How can I simulate this AR(a) model in this case?

Answer 1

An easy way to do this is

y <- cumsum(rnorm(1050, 0, 1))

(assuming your e_t terms are normal with mean 0 and variance 1)

Answer 2

Your AR coefficient of one is essentially just adding a differencing term, so your model is an ARIMA(0,1,0) model. (Since this is non-stationary, R does not like you trying to put it into the AR part.) The code to simulate from this model is:

y <- arima.sim(list(order = c(0,1,0)), n = 1050)