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I'm following hyndman's advice for using fourier terms when fitting a linear regression model to the taylor time-series (with the very long seasonality of 336). My understanding is that we're generating features for the linear regression model, and these features values are fourier terms up to the K order. The linear regression then fits the best coefficient for each of these terms.

How is that different then using a fourier transform? Why shouldn't I do a fourier transform of the time-series and then choose the top K terms, and then offer these terms to the linear regression, possibly allowing it to scale each term by a coefficient?

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