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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:

enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here 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!

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"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 !

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  • $\begingroup$ Ok now play along with my reasoning: in a sense, calendar-adjustment + seasonal differencing is more of a correct approach, as it "describes" both type of seasonality (i.e. deterministic and stochastic), right? That being said, both approaches are wrong as they are just "post-hoc" explanations, while I should instead try to work on actually modelling the characteristics of my time-serie "a priori". I guess that also answers the "science VS messing with numbers" dilemma. How would you suggest I proceed instead? Same as here? $\endgroup$ – Bruder Feb 22 '12 at 13:31
  • $\begingroup$ P.S: I'm currently going through Tsay's paper for the second time. I will get in touch with you, as per your kind offer, as soon as I'm finished studying it. $\endgroup$ – Bruder Feb 22 '12 at 13:34
  • $\begingroup$ :BruderThe explanationI can give is thatone doesn't "kitchen-sink"the model i.e. overpopulate it.What we have found to be useful is to carefully add structure. If you assume (initially) that the ARIMA component, remember the ARIMA component encompasses differencing and ARMA structure. Incorporate day-of-the-week variables and Holiday Events , including any lead and lag structures around these events.incorporate Monthly indicators notweekly as they collide with the holidays.Detect any pulses,shifts,seasonal pulses,time trends that evidence themselves.As an alternativestart with ARIMA structure $\endgroup$ – IrishStat Feb 22 '12 at 14:20
  • $\begingroup$ :Bruder I should have written "If you assume (initially) that the ARIMA component, remember the ARIMA component encompasses differencing and ARMA structure DOESN'T DOMINATE. $\endgroup$ – IrishStat Feb 22 '12 at 15:56

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