I was wondering if a nonstationary ARMA can always be made stationary after differencing? The question arises from Metrics' comment on my previous question:
... you need to use ARIMA (which means you need to take the difference if ARMA is non-stationary). – Metrics yesterday
A non-stationary ARMA (2,3) means ARMA is say I(1), then it becomes ARIMA(2,1,3) which means if you difference y one time, then it becomes stationary ARMA. – Metrics yesterday
In the example he gave, why can a nonstationary ARMA(2.3) become ARIMA(2,1,3)? ARIMA is defined to be able to become stationary ARMA after differencing. How do we know a nonstationary ARMA(2.3) can become stationary ARMA after differencing?
Thanks and regards!