The additive versus the multiplicative model

Now that we have defined the series components, and before we continue onto our next topic, the decomposition of time series, it is time to introduce the additive and multiplicative models. These terms describe the model structure. As the name implies, a model is defined as additive whenever we add together its components:

Similarly, a model is defined as multiplicative whenever we multiply its components:

Here, as before, Y_t represents the series observation at time t and , , , and represent the value of the trend, seasonal, cycle, and irregular components of the series at time t, respectively.

We classify a series as additive whenever there is a growth in the trend (with respect to the previous period), or if the amplitude of the seasonal component roughly remains the same over time. On the other hand, we classify a series as...