Use own trend model

In the paper Forecasting at Scale by Sean J Taylor and Benjamin Letham, it says that prophet decomposes the timeseries using equation:

y(t) = g(t) + s(t) + h(t), where g is the trend model.

Is it possible to plug in our own trend model and use prophet only for s and h?

[rquintino]

@bletham huge thx for the ProphetLastValue snippet, seems really what we were looking for, let us test asap and share feedback. We have been struggling with trend issues for short term forecasts (mostly kind of “lagging” behind), so will be really interesting to give this a try. again, thank you and all the team!

[bletham]

@pjebs I think there are two different types of custom trends that are getting a bit mixed up in the discussion here. One is to have a trend model that replaces the built-in piecewise-linear/piecewise-logistic trend, and is jointly fit along with the seasonalities in the same way the built-in trends are. That is, the trend model has parameters that will be fit by Prophet. In order to do this, things have to be changed inside the Stan model. #1466 provides a good example of how this can be done. This is sort of adjustment I think for the time being would be made in a fork.

What you’ve described is a little different; there is a trend provided by an external model that we wish to use in the place of the built-in trend. The difference is that the trend parameters do not need to be fit by Prophet. This is quite a bit simpler. With additive seasonality, this can actually be done now. Above I had proposed doing this by including the external trend as an external regressor. But, as noted above, this wasn’t entirely satisfactory because there was no way to prevent Prophet from adding extra trend on top of it until #614 was done. Well, as of the last version push (0.7.1), #614 is now done in Python! So what you would want to do is:

• Use the built-in flat trend (https://facebook.github.io/prophet/docs/additional_topics.html#flat-trend-and-custom-trends)
• Add the external trend as a regressor (https://facebook.github.io/prophet/docs/seasonality,_holiday_effects,_and_regressors.html#additional-regressors) . Include future trend values when making the prediction. You might want to turn off standardization in the regressor - I’m not totally sure.

The reason this would work is because with additive seasonality, the Prophet model is

y(t) = trend(t) + seasonality(t) + beta * regressor(t) + noise

so here we would be setting trend(t) to be flat, and then beta * regressor(t) would be taken the place of the trend.

With multiplicative seasonality, the external trend would have to be used as the trend in the Stan model (and not a regressor), so it would require modification there.