Prophet - Additive & Multiplicative Seasonality Effect

There are two types of data. One is additive, which can be considered as the result of adding numbers. This type of data tends to show a linear trend.

Another is multiplicative, which can be considered as the result of the compounding effect with percentage growth. This type of data tends to show an exponential trend.

And if you’ve got a growing business your sales data tends to look more like the latter. And if you want to forecast such data, you want to try ‘Multiplicative’ for the seasonality effect.

We have a sales data that has the multiplicative nature in the trend. Let’s build a forecasting model and try to apply both Additive and Multiplicative seasonality effects and compare.

Additive Seasonality Effect

Here’s how it looks if we build a forecasting model with the ‘Additive’ option for the seasonality effect.

Notice that the difference between the actual values (blue) and the forecasted values (orange) are becoming wider as the time goes by. And this is a good sign that you want to try the ‘Multiplicative’ option.

Multiplicative Seasonality Effect

And here’s how it looks if we switch to ‘Multiplicative’ option.

Notice that the difference between the actual values (blue) and the forecasted values (orange) are equally spread across the years.

And this makes the forecasting model quality better. We can compare the evaluation metrics between the additive and the multiplicative options.

Additive:

Multiplicative:

All the metrics for the multiplicative model are better than the ones for the additive model.