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How do you know when deseasonalization is not necessary? That is, from what I understand, if you want to just look at the trend and irregular components of a time series, then you just need to remove the seasonal component. However, let's say we're working with an irregular time series that is not affected by seasonality at all (for the sake of this example) and we want to see a trend of specific section of the remaining components.

Would it be beneficial to remove the seasonal component anyways? Or would it skewer the remaining components?

Any help is appreciated, thanks.

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What you are driving at here is unclear to me, but there is a simple answer to your postulate. If there is no seasonal variation, there is nothing to "remove" and methods designed to identify seasonal components should find nothing (or, in practice, produce additive estimates near zero or multiplicative estimates near one). That's pretty much a tautology. Benignly put, fitting some decomposition with a seasonal component should do no harm if that component is negligible.

As you are asking about seasonality in general, I'd warn against the disciplinary myopia that often affects discussions in this field. In particular, many economists are focused on the idea that seasonality is irrelevant or a nuisance and so must be removed. That may well be true depending on their goal. More positively, environmental scientists and epidemiologists of various kinds often regard seasonality as interesting or important. (These named communities are naturally not the only groups concerned with seasonality.)

In terms of your initial question -- How do you know when deseasonalization is not necessary? -- I'd say that if seasonality is important, you can spot it on a graph, but plot against time of year as well as time. In practice, with strongly trending series, detrending first, even crudely, can help. As always, there are many statistical people who prefer a formal test.

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