I have been thinking about the following question recently. As an econometrics major I'm not sure how to answer this properly.
When trying to predict a time series data, one of the first things you look into is mean stationarity, the data shouldn't have any trend in order to make accurate predictions. However, in my new job I have noticed that they use OLS regression in order to analyse and predict a certain variable y. Among the different explanatory variables they use, they have the lagged values of y. What is strange to me is that they don't check for stationarity and the predictions they make are accurate.
The thing is, I have never though about it this way and was wondering; why there is no need to check check for stationarity in OLS while when we use time series we must do it? Does it have to do with the fitting algorithm we use(OLS against ML)?