yearly_seasonality parameter

[pamant22]

Hi All,

I'm very new to MMMs and PyMC in particular, so apologies if this is obvious.

Regarding the yearly_seasonality parameter of DelayedSaturatedMMM, how should this be interpreted? I see in the docstring that it specifies the "Number of Fourier modes". Does this mean it is the number of 'peaks' we would expect to see over a year?

In relation to this, does it matter whether the data inputted is weekly, daily or otherwise? If the answer to the above is 'yes' then I guess it does not make a difference, but just to clarify.

Thanks

[williambdean]

The fourier transformations happen based on the day of the year derived from the dates so the frequency of the input data will not have an impact.

With yearly_seasonality=3, all the sin and cos shown below will be part of the regression model. Here they are unscaled but the regression scales each by a parameter (highly regularized). The scaled curves will be summed together which provide the seasonality that can be rather flexible but also repeats yearly.

It's not guaranteed that n_order = n will have n peaks when multiplied with the coefficients and summed. That would depend on the coefficients. For a counter example, we can see only 3 local maximums with order = 4 below.
However, the order will determine how granular the yearly seasonality can go.

Hopefully this gives some clarity