Can a Non-Stationary ARIMA Series Be Simulated Using arima.sim in R? I am performing an experiment using classes of ARIMA models which I have to simulate for instance AR, MA, ARMA and possibly ARIMA using arima.sim() function in R. I am able to AR, MA, ARMA but ARIMA seems impossible as the coefficient of AR must be greater than 1 ($|\phi| > 1$) for the series to be non-stationary.
When $|\varphi| < 1$
Simulate AR(1) of 10 sample size with a coefficient of 0.8
# simulate ARIMA(1, 0, 0)
n <- 10
phi <- 0.8
set.seed(837530)
wn <- rnorm(n, mean = 0, sd = 1)
ar1 <- sqrt((wn[1])^2/(1-phi^2))
for(i in 2:n){
  ar1[i] <- ar1[i - 1] * phi + wn[I]
}

Here the arithmetic of this expression $\varphi = \sqrt((\varepsilon _{1})^2/(1-\varphi^2))$ is valid in the sense that $\varphi = \sqrt(0.1309045/0.36)$ which is $\sqrt0.3636236$
When $|\varphi| > 1$
Simulate AR(1) of 10 sample size with a coefficient of 0.8
# simulate ARIMA(1, 0, 0)
n <- 10
phi <- 1.2
set.seed(837530)
wn <- rnorm(n, mean = 0, sd = 1)
ar1 <- sqrt((wn[1])^2/(1-phi^2))

# Warning message:
#In sqrt((wn[1])^2/(1 - phi^2)) : NaNs produced

for(i in 2:n){
  ar1[i] <- ar1[i - 1] * phi + wn[I]
}
ar1
 #[1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

Here the arithmetic of this expression $\varphi = \sqrt((\varepsilon _{1})^2/(1-\varphi^2))$ is not valid in the sense that $\varphi = \sqrt(0.1309045/-0.44)$ which is $\sqrt-0.2975102$
Similar experiment is performed using arima.sim() function
When $|\varphi| < 1$
set.seed(837530)
ma1 <- arima.sim(n = 10, model = list(ar = c(0.8), order = c(1, 0, 0)), sd = 1)

No error message
When $|\varphi| > 1$
set.seed(837530)
ma1 <- arima.sim(n = 10, model = list(ar = c(1.2), order = c(1, 0, 0)), sd = 1)
#Error in arima.sim(n = 10, model = list(ar = c(1.2), order = c(1, 0, 0)),  : 
  #'ar' part of model is not stationary

What I want to know
Can it be said that a non-stationary series can not be simulated using arima.sim?

You can simulate stationary ARMA models using the rGARMA function in the ts.extend package.  If you want to extend this to ARIMA models then all you have to do is to simulate the ARMA model and then add the required number of differencing steps.  Extensions to non-stationary time-series processes with explosive roots can be done, but it requires specification of starting points for the series.
