# Time Series Forecasting Seasonal type

As we all know there are two types of seasonal types, additive and multiplicative, but I have trouble telling them apart. To my understanding, in multiplicative seasonality, the magnitude of a seasonality would grow with the trend. For example with an upward trend, the magnitude of a season would grow bigger. But what if the magnitude of a seasonality grows but the trend stays the same. In other words, the minimum value of one season always seem to be on one horizontal line but the maximum value keeps increasing. What kind of seasonality is this? What model can I use to describe this data series?

This is the formula given in Forecasting, Principles and Practice. From what I read it seems that the trend and the level are not multiplied together in the multiplicative seasonality case. Also in the statsmodels library, both the trend and the seasonality can be chosen as either multiplicative or additive. Can anyone clarify more what kind of additive mode we should be talking about here?

Each time series can be decomposed in at least three elements:

• Trend
• Seasonal component
• Noise

An additive model can be explained as:

y = Trend + Seasonal + Noise


while a multiplicative component as:

y = Trend * Seasonal * Noise


The main difference is that in the case of additive models all three components impact your dependent variable independently. In case of multiplicative models instead, the impact of each component is dependent from the others.

The choice of the "right" model depends on the problem at hand. If you assume that the Seasonal effect is independent from the level of the Trend, then use an additive model. If you think the value of the Trend is going to affect the magnitude of the Seasonal effect, then go for the multiplicative one.

Hope this helps, otherwise let me know.

• Thank you for answering my question, but I still have some confusion. I have updated my question so can you take a look at that and give me more insight? Thanks! – Jiayu Jun 5 '19 at 13:39