Controlling seasonality with the Fourier order

Seasonality is at the heart of how Prophet works, and Fourier series are used to model seasonality. To understand what a Fourier series is, and how the Fourier order relates to it, I’ll use an analogy from linear regression.

You may know that increasing the order of a polynomial equation in linear regression will always improve your goodness of fit. For example, the simple linear regression equation is , with being the slope of the line and being the -intercept. Increasing the order of your equation to, say, will always improve your fit, at the risk of overfitting and capturing noise. You can always achieve an value of 1 (perfect fit) by arbitrarily increasing the order of your polynomial equation higher and higher. The following figure illustrates how higher-order fits start to become quite unrealistic and overfit, though:

Figure 5.10 – Linear regression with higher-order polynomials

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