I can't tell whether my data are seasonal or just affected by calendar effects I used to think my time-serie was seasonal, but then I realized it simply needed some calendar-effect adjustment. I tried that and I'm now in doubt there might still be some seasonality left. I tried adding a 12 month differencing, and it seemed to work, but then I thought: why not just try 12 month differencing in the first place? Shouldn't this account for calendar-effects as well, all in one "bundle"?
There you go, runplot + monthly subseries plot + ACF plot of 


*

*raw (top), 

*adjusted (top middle), 

*12mths differenced (bottom middle) and 

*adjusted+differenced (bottom) 


data.
NOTE: the order of the images does not follow the order of my reasoning, I put seasonal differencing before calendar adjustment + seasonal differencing:






How do I know which method gave the correct results (if any)? Is this "science" or just "messing with numbers"?
Would some further cross-validation help (e.g. stl decomposition, seasonal dummies)?
Thank you, as always, for whatever help you can grant me!
 A: "but then I thought: why not just try 12 month differencing in the first place? Shouldn't this account for calendar-effects as well" There are two distinctly different forms of seasonality .The first type is "deterministic seasonality" often explicable with events and/or trading days and/or number of weekend days in the month and/or particular months of the year that exhibit a fixed effect/ These fixed effects may or may not be uniform through time as for example a June effect may have only been present for the first k periods of a time series ( or the last n-k periods. The second type of seasonality is "stochastic seasonality" often explicable by ARIMA structure ( which includes any needed differencing operators. Note that a willy-nilly approach of assuming differencing or any particular ARIMA model may inject structure much like you trying to see using my reading glasses. Good time series analyis requires considering both of these kinds of seasonaity as one goes about the business of building an equation which can be used for forecasting and/or exceptional data identification.In summary you are trying to use graphical procedures , which often are useful but purely "descriptive in form" while you should be using "statistical procedures" which are inferential to sort out "things". BUT that is just my opinion. Other readers love graphs ! 
