Additive or Multiplicative?
It is important to know the difference between an additive model and a multiplicative model. There are three parts in a time series:
- Trends how things are changing
- Seasonality how things change in a given period
- Residual/error activity not explained by the seasonal or the trend value
The way these three components interact decides the difference between an additive and a multiplicative model. The differences are discussed in the Additive and Multiplicative Models homework assignment help online.
In an additive model, the components are added together and they make a time series. If there is an increasing trend you can see the same peak sizes in the entire time series. This is noticed in the indexed time series where an absolute value is increasing however, changes remain relative.
In multiplicative models, the components multiply in a combined manner to make a time series. When you have an increasing trend the seasonal activity’s amplitude increases. Everything becomes highly exaggerated. This is very common in web traffic.
In an additive model, the time series components are added unlike multiplicative models when they are multiplied. Additive models are useful when the variations of a seasonal nature stay the same with time, while in the multiplicative model the variations in a seasonal nature enhance with time. You should know the situation when you should choose an additive model and where it is better to choose a multiplicative model.
Understanding Time Series Forecasting
In additive models, there is an assumption that various components impact a time series additive.
Data=Trend+Seasonal effect+Residual+cyclical
For instance, in monthly data, additive models assume that the differences between January and June values are almost the same every year. The amplitude of a seasonal effect is the same every year.
This model also assumes that the residuals are almost of the same size in the entire series. They are random components that add other components in the same way as the other parts of a series.
Multiplicative Models
Several times in time series that involve quantities the absolute value differences are of less importance and interest compared to the changes in the percentage.
For instance, in seasonal data, it is more useful to model that the value of June is higher in the same proportion than January every year instead of assuming that the difference is constant. By assuming that the effects including the seasonal effects act in a proportioned manner on a time series are equal to the multiplicative models’.
Data=Trend*Seasonal effect*residual*cyclical