How to use Fourier transform in my MMM model

[KatatoniaSh]

I have a national-level model.
Based on the documentations, we can also add Fourier transform into our data. I am wondering how we can add Fourier transform into our model. I think there are three types of seasonality.

1. There is seasonality in spending but not in the intercept. So, the KPI will show seasonality. x_t= f(t), mu_t=a, kpi shows seasonality because of seasonality in x_t.
2. There are seasonalities in spending and the intercept, x_t=f(t), mu_t=g(t). So, the kpi shows seasonality because of seasonality in both spendings and the intercept. This case might be more relevant because spending will be high when we have seasonality.
3. There is no seasonality in spending, x_t is independent of t, intercept shows seasonality mu_t=g(t). Therefore, kpi is seasonal because of the intercept.
4. Cases 1 to 3 may happpen with control or non-media treatment vairbales too

Now, my question is how we can add Fourier transform into our model given all these possible cases? Any procedure to do that? My personal thought is that we may get biased results if we separate model training from finding the Frourier transform but the current version of Google Meridian does handle Fourier transform integratedly in the model.
Another important question is that when we add Fourier transform, should we use just 1 knot (national-level model)?

[gousesb]

Hello @KatatoniaSh ,

Thank you for contacting us again!

In Meridian, Seasonal or periodic patterns (e.g., Fourier-type terms) can be included as Control Variables in the model. Because the framework is built on Bayesian inference, these periodic functions are included directly in the core likelihood equation rather than being processed separately. Meridian estimates the coefficients for control variables jointly with the media effects and other parameters during the MCMC sampling process and prevents biased results you would get from a separated two-step estimation process.

You should prioritize control variables that impact both your target KPIs and media spends. If you believe there is seasonality impacting both spends and KPI, then you can encode these patterns by modeling them as control variables.

Periodic functions and knots can be used together, but be especially mindful of the total number of parameters given the importance of parsimony in a national model. Keep in mind, for a national-level model using weekly data, the recommended starting value in Meridian is knots = 1. You can combine this with Fourier series (periodic controls) to capture the "smooth and cyclical" seasonal patterns.

Feel free to reach out if you have any further queries or feedback regarding Meridian.

Google Meridian Support Team