I would like to share a new article on some of the methods and pitfalls of time series forecasting: “A Time Series Apologia”.
Will there be a follow up using actual, non seasonal data?I feel as if the same result could have been derived more simply with FFT. With the qualification that I could be wrong, as with so much else.
ARIMA is a lot like a sparse FFT or Laplace style transform. Essentially you are picking the roots of a transfer operator by fitting the coefficients- so you are working with transforms. So my guess is: it should outperform FFT out of sample- unless you have some good sparsifying ideas (ala compressed sensing style) to add to the FFT.
Always bad luck to promise a follow-up article. However, a lot great seasonal effects can also be modeled by supplying seasonal features (such as month as a set of indicator variables). It is sort of the poor-man's spline way of fitting a seasonal shape (though GAM should outperform that sort of trick).