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It appears that the first half of the series has much lower variance than 2013-on. Have you tried to only use 2013-on with the same stl decomposition? You could also try a classic decomposition & X-12 …

I'd review the chapter here: https://www.otexts.org/fpp/9/1 Neural networks require extreme amounts of data and many more features than you have for them to typically outperform other time series met …

https://www.otexts.org/fpp2/arima-ets.html Ultimately, one would need to perform time series cross-validation to determine which will perform better in any individual case.

Yes you can, since standard CV doesn't work for time series data. See: https://www.otexts.org/fpp2/accuracy.html

Generally speaking, as others have said, the further out your forecast the more likely your prediction errors will increase. With 2 years of data, I would not trust either. As far as your approach, …

I recommend the books below (no affiliation) for learning more about forecasting and you can review the ARIMA diagnositics sections as well. …

If you optimized parameters to the test data, you'd be partially fitting your data to test data instead of training data. You want to know which method is best over withheld data not, for example, wha …

There is no way to know what will have the highest predictive accuracy, thus the typical solution is to try both on multiple test sets and see which performs best. Using regression only will leave ope …

While I think the comment to your post covers the 'why', what you mention is generally called a 'rolling forecast origin', which is alright for one-step forecasts. Instead, try using a similar conce …

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 th …

Depends how much you value the accuracy of the forecasts as to whether or not they're satisfactory. They don't look strikingly bad, but since you're likely leaving valuable information unaccounted for …

Yes, it generally is a decent idea and likely will improve forecast accuracy. To get a better idea for your specific time-series, you should perform time-series cross-validation on the models and comb …

The value of this method is monthly forecasting is typically more accurate than daily due to the noise to signal level at the daily resolution. … Reading a good practical forecasting book will likely be the best place to start. EDIT: Free online practical forecasting book link: https://www.otexts.org/fpp …

One alternative is using Temporal Hierarchical forecasting via: http://robjhyndman.com/papers/temporalhierarchies.pdf - (implented in the R thief package). …

I'd suggest temporial hierarchical forecasting in this case. …