I've been reading up on seasonal adjustment (removing "seasonal" periodic components from a time series) recently and although I see a lot of fancy work around ARIMA models and fancy ways to detect the seasonality, I see comparatively little work on moving to the frequency domain and looking at series with Fourier transforms or wavelets or anything along those lines. There are some older papers on the topic but it looks like the mainstream approaches don't do anything directly in that space.
Does anyone know why? Does naively applying the Fourier transform, removing undesired periodic components, and inverting it lead to bad results? Is there a survey of seasonal adjustment from the perspective of "you might think to use XYZ, but this is why that doesn't work and how these mainstream techniques improve on that"?