Is my understanding correct that any stochastic process that is iid, is a stationary process, since the variables are identically distributed? Please guide me if I'm wrong.
A stationary process is one where the joint distribution doesn't change through time. An i.i.d. stochastic process has the same joint distribution regardless of time. So yes, it must be stationary.
The way the word 'stationary' is used usually means 'strictly stationary' in my experience. Do bear in mind stationary is not the same thing as i.i.d. though. Stationarity says nothing about whether the variables are independent of one another.
