Can simple exponential forecasting be used for a non stationary series? I have a non stationary series with trend and seasonal components. I want to use simple exponential smoothing ONLY for forecasting. Does the series need to converted to stationary before using SES? If so, what do you make of the fact that the optimal smoothing parameter value SES selects for my data is very small (less than 0.1)?
 A: SES is not meant for data with trend/seasonal patterns. Why not just make it stationary or pick another method?
Close to 0 alpha means that weighting the most recent values higher is not improving the model. alpha=0 would be a mean of the training data (all data weighted equally in terms of importance) and would predict that mean as the forecast.
For more information see: https://www.otexts.org/fpp/7/1
A: SES basically assumes non-stationarity in the mean. The idea is that the mean level is shifting slowly over time and you want your forecasts to reflect the shift. If you try to use SES where there the rate of change is high, the best alpha will be close to 1, and your forecasts will become very "local", as the SES forecaster struggles to keep up with all the changes. This could be true of either a trend or periodic component that you did not model. 
That said, if the seasonality has a long period (say annual on data measured daily) and the trend is slow moving, SES will cope. 
A: 
Hi: If it was trend only, then one approach would  be double exponential smoothing. But,  the existence of seasonality means that you'll need what is called the Holt-Winters exponential smoothing method. It's pretty well known so you can google for it and many things will come up but here is one pretty detailed explanation.
