Multiplicative vs. Additive Model: What’s the difference?

A time series is a collection of data points that appear in a particular order over a certain amount of time. Any variable that changes over time can be the subject of a time series. The employment of a model to forecast future values based on observed values is known as time series forecasting.

Using data points recorded at regular intervals, a time series is used in investing to track the movement of the selected data points, such as a security’s price, over a given period of time. The data can be acquired in a way that gives the investor or analyst looking at the activity the information they need because there is no minimum or maximum period of time that must be included.

A time series typically consists of three parts:

  • Trend: How things change most of the time
  • Seasonality: How things change over a certain amount of time, such as a year, month, week, or day.
  • Error/residual/irregular: Things that don’t fit the trend or the seasonal value.

A multiplicative vs an additive time series is differentiated by the interaction between these three factors.

Additive And Multiplicative Model
Additive And Multiplicative Model

What Is Additive Model?

A time series is an additive model if the size of the seasonal changes doesn’t change from one level of time series to the next. The observed series is made by adding the seasonality, trend, cyclical, and residual components of the data.

The additive model works best when the changes in the time series are about the same over the whole series. When seasonal changes are mostly the same over time, the additive model works well.

What Is Multiplicative Model?

The multiplicative model is a type of time series in which seasonal changes get bigger or smaller as the level of the series goes up or down. The observed series is made up of seasonality, trend, cyclical, and residual components that are multiplied together.

The multiplicative model works best when the time series is more variable as the level goes up. This model is useful when the difference between seasons gets bigger over time.

Key Difference Between Additive And Multiplicative Mode

ADDITIVE MODELMULTIPLICATIVE MODEL
A time series is an additive model if the size of the seasonal changes doesn’t change from one level of time series to the next.The multiplicative model is a type of time series in which seasonal changes get bigger or smaller as the level of the series goes up or down.
The observed series is made by adding the seasonality, trend, cyclical, and residual components of the data.The observed series is made up of seasonality, trend, cyclical, and residual components that are multiplied together.
used in situations where change is quantified absolutely.utilized when a change is expressed as a percentage change (%).
Data is modeled as-is.Data is modeled just as additive but after taking logarithm (with base as natural or base 10).
When the time series exhibits about the same variability over the course of the series, the additive model performs best. That is, the series’ values are all contained inside a band of constant width that is centered on the trend.The multiplicative model functions best when the level was accompanied by an increase in the time series’ variability. In other words, as the trend gets stronger, the value of the series gets bigger.
It is represented as: Yt=Tt+St+EtIt is represented as: Yt=Tt.St.Et  

Should I use an additive model or a multiplicative model?

Choose the multiplicative model when the size of the seasonal pattern in the data depends on the size of the data. In other words, the size of the seasonal pattern gets bigger when the data values get bigger and gets smaller when the data values get smaller.

Choose the additive model when the size of the seasonal pattern in the data does not depend on the size of the data. In other words, whether the series goes up or down, the size of the seasonal pattern doesn’t change.

If there isn’t a clear pattern in the data and you can’t decide between the additive and multiplicative methods, you can try both and choose the one that gives you the best accuracy.