At work, I just started dealing with seasonal adjustment of monthly time series on credit data, so being new to the topic it is quite possible that my question is pretty trivial.
From what I've read so far, procedures like TRAMO-SEATS and X13-ARIMA-SEATS never mention the need to split the data into train/validation/test sets, which is instead a common practice in the context of machine learnign algorithms.
Indeed it seems to me that the seasonal adjustment algorithms use the entire time series and, every time a new observation comes in, it gets added to the input dataset as well, often leading to significant change in the seasonal adjustment factor and in the parameters of the underlying ARIMA model (automatically estimated by the seasonal adjustament procedures).
I am a bit perplexed from a methodological point of view. Is it correct that every time new data is added, the seasonally adjusted series changes in its entirety? How are these variations conceptually justified? Wouldn't it be more correct to use the train/test split to define a single model so that adding a new observation does not lead to changes in the past of the seasonally adjusted series?
Thanks and any insight would be appreciated.
