Multiplicative Vs. Log-Additive Seasonal Adjustment

[rmendez]

Hi,

When I seasonal adjust a particular time series (the Euro-Area 15 real public investmente expressed in households consumption) stumbled upon
a systematic difference (a shift) between the seasonal adjusted series produced using X11 with the multiplicative option Versus usin the log-additive
option (preceded or not by a boxjenk step).

Questions:

(1) Why the difference? (May be it is related to outliers?)
(2) What method is more reliable?
(3) Shouldn't be exactly equivalent the result from seasonal adjust X with MULTIPLICATIVE and LOGADD and seasonal adjust LOG(X) with ADDITIVE????? What explain the differences?
What method is more reliable (in short samples)?
I have read the User's Guide, Reference Manual and X11 Suplement not founding any light about it.

I attach my example (code and data).

Best Regards,
Rodolfo

[TomDoan]

At least in the U.S., it appears that most series which were multiplicatively adjusted in X11 are now log additively adjusted in X12.

The log additive decomposition has log X = log C + log S + log I, while the multiplicative has X=C x S x I. The first step is to estimate C. In the log additive model, that is done by taking a moving average of log C, which is subtracted from log X to get the preliminary estimate of log S + log I. In the multiplicative model, that is done by taking a moving average of C itself, which is then divided into X to get the preliminary estimation of S x I. The mean of the log is systematically different than the log of the mean which will carry through to the rest of the analysis.

[rmendez]

crystal clear !! thank you very much !