6 Difference Between Additive And Multiplicative Model

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A time series is a sequence of data points that occur in successive order over some period of time. A time series can be taken on any variable that change over time. Time series forecasting is the use of a model to predict future values on previously observed values.

In investing, a time series is used to track the movement of the chosen data points, such as a security’s price, over a specified period of time with data points recorded at regular intervals. There is no minimum or maximum amount of time that must be included, allowing the data to be gathered in a way that provides the information being sought by the investor or analyst examining the activity.

There are generally three components to a time series:

  • Trend: How things are typically changing
  • Seasonality: How things change within a given period e.g a year, month, week and day.
  • Error/residual/irregular: Activity not explained by the trend or the seasonal value.

How these three components interact determines the difference between a multiplicative and an additive time series.

What Is Additive Model?

An additive model is a time series in which the magnitude of the seasonal fluctuations does not vary with level of time series. Data is represented in terms of addition of seasonality, trend, cyclical and residual components to give the observed series.

The additive model works best when the time series has roughly the same variability through the length of the series. The additive model is useful when the seasonal variation is relatively constant over time.

What Is Multiplicative Model?

The multiplicative model is a time series in which seasonal fluctuations increase or decrease proportionally with increase and decrease in the level of the series. Data is represented in terms of multiplication of seasonality, trend, cyclical and residual component to give the observed series.

The multiplicative model works best when the variability of the time series increased with the level. These model is useful when the seasonal variation increases over time.

Difference Between Additive And Multiplicative Model In Tabular Form

ADDITIVE MODEL MULTIPLICATIVE MODEL
An additive model is a time series in which the magnitude of the seasonal fluctuations does not vary with level of time series. The multiplicative model is a time series in which seasonal fluctuations increase or decrease proportionally with increase and decrease in the level of the series.
Data is represented in terms of addition of seasonality, trend, cyclical and residual components to give the observed series. Data is represented in terms of multiplication of seasonality, trend, cyclical and residual component to give the observed series.
Used where change is measured in absolute quantity. Used where change is measured in percentage (%) change.
Data is modeled as-is. Data is modeled just as additive but after taking logarithm (with base as natural or base 10).
The additive model works best when the time series has roughly the same variability through the length of the series. That is, all the values of the series fall within a band with constant width centered on the trend.   The multiplicative model works best when the variability of the time series increased with the level. That is, the value of the series becomes larger as the trend increases.  
It is represented as: Yt=Tt+St+Et It is represented as: Yt=Tt.St.Et  

Which Model Is The Best Between Additive Model And Multiplicative Model?

Choose the multiplicative model when the magnitude of the seasonal pattern in the data depends on the magnitude of the data. In other words, the magnitude of the seasonal pattern increases as thedata values increase and decreases as the data values decrease.

Choose the additive model when the magnitude of the seasonal pattern in the data does not depend on the magnitude of the data. In other words, the magnitude of the seasonal pattern does not change as the series goes up or down.

If the pattern in the data is not very obvious and you have trouble choosing between the additive and multiplicative procedures, you can try both and choose the one with smaller accuracy measures.