Can you identify additive and multiplicative seasonality?

In business forecasting it is quite common to deal with seasonal time series. Although several methodologies have been developed to identify when to use a seasonal model, less effort has been invested in identifying whether a time series exhibits additive or multiplicative seasonality. Perhaps here it is useful to remember the distinction between the two. Assuming a time series with changes in the level, the seasonal component may interact with the level in an additive or multiplicative way. This essentially means that in the first case the amplitude of the seasonality remains constant, while in the latter it changes as the level does. Figure 1 provides an example of an additively and a multiplicatively seasonal time series.

Fig 1. Additively and multiplicatively seasonal time series.

Obviously, if the level was decreasing, under multiplicative seasonality the seasonal amplitude would get smaller, while in the case of additive it would remain constant. Typically, to distinguish in a statistical manner between the two, we rely on some fitting criterion, such as minimum Mean Squared Error (MSE). On the other hand, one might rely on human experts to visually identify the nature of seasonality. To test the performance of experts and how they compare against statistics, I devised the following small experiment: you are called to select whether the seasonality of a time series shown is additive or multiplicative. Choose your selection and submit it to be evaluated. Your performance against statistics, but also against all participants so far is calculated and displayed. Can you achieve better accuracy than statistics? Better than the average accuracy of previous participants? Give it a try!

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