Confused about stationarity and ARIMA processes So I am quite confused about stationarity in ARIMA processes. For example, a Random Walk is an ARIMA process with order (1,0,0). Does this mean that a Random walk is stationary?
Stationarity implies that the covariance matrix is constant, is this the case for a random walk? Are all ARIMA processes stationary (I believe so)?
Thank you!
EDIT: I am just going to leave this link here, because it clarified a wrong assumption I made in the question above regarding the formulation of an random walk.
 A: First of all random walk is a (0,1,0) ARIMA series.
Random walk is a non stationary process. That is why we need this one differentiation. Try it in R plot(cumsum(rnorm(100))) although this plot(diff(cumsum(rnorm(100)))) is a stationary process.
I think that you think about white noise as a stationary process (0,0,0).
I am predicting that you thought about Box_Jenkins transformation:
https://en.wikipedia.org/wiki/Box%E2%80%93Jenkins_method
where is always a step od differencing (,d,) to achieve stationarity. Remember that sometimes one differentiation is not satisfactory to brings it.
Summing up if you have some time series it might be non stationary although by differentiation you could bring it to world of stationary processes. If you want to stay with original time series you could use exponential smoothing theory which not demanding such step.
https://en.wikipedia.org/wiki/Exponential_smoothing
for example Holt-Winters.
However ARIMA covers all space of exponential smooting models.
A: The I in ARIMA is for Integrated. The difference between ARMA and ARIMA is specifically that an ARIMA process does not have to initially be stationary (although you have to difference it to be stationary).
