Modelling time series seasonality (with increasing amplitude) using PYMC

Hello, I would like to ask you a bit of a generals question about time series modelling using Bayesian statistics with PYMC:

“Do you know any “tried and true” methods for modelling seasonality for which the amplitude should increase over time?”

We are building a marketing mix model using PYMC and have been using Fourier modes to model seasonal component in our models (very similar to as it is done in pymc-marketing). This works quite well, but has one huge drawback for us - the amplitude of the seasonality “swings” is always the same across the whole modelled period.

Which is kinda bad for us, we model new user inflow for the markets for 5-6 years, over which the user inflow increases a lot, and what was a 500 users dip in user inflow in summer one year, becomes a 1000 users summer dip next year, and 1500 dip the year after that and so on, as the brand awareness grows and average user inflow increases. So now we are trying to find a good way to model this YoY increase in seasonality amplitude in our markets.

It seems like it should be a fairly common problem a lot of time series modellers would be facing, so we were wondering are there any “common practice” methods that we should try out, that kind people of this community are aware of? Or maybe there is no common solution but we should try some different methodologies? Anyhow, your opinions and expertise would be greatly valued here! Cheers!

Not sure, but are you talking about multiplicative seasonality?

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In additive framework you can also handle this with time-varying coefficients on the seasonal components.

I’d say the most “tried and true” approach though is to just apply a data transformation to try to minimize the change in variance over the time series. Usually taking logs is enough (in that case you were in the multiplicative regime that @drbenvincent pointed out). Sometimes you can do something more exotic like box-cox, or Guerreo correction – see here for discussion.

Last comment – changes in variance shouldn’t be a problem for Fourier seasonality, because saturated Fourier basis can conform to any arbitrary function. Is the problem in your forecasts?

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