What is the difference between multiplicative and additive

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. 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. Viva Differences. Please enter your comment! Please enter your name here. There are three components to a time series: — trend how things are overall changing — seasonality how things change within a given period e.

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

In a multiplicative time series, the components multiply together to make the time series. If you have an increasing trend, the amplitude of seasonal activity increases.

Everything becomes more exaggerated. In an additive time series, the components add together to make the time series. If you have an increasing trend, you still see roughly the same size peaks and troughs throughout the time series.

This is often seen in indexed time series where the absolute value is growing but changes stay relative. When I first started doing time series analysis, the only way to visualise how a time series splits into different components was to use base R.

About the time I was feeling the pain, someone released a ggplot2 time series extension! You can get the whole script in a GIST. To be able to determine if the time series is additive or multiplicative, the time series has to be split into its components.

Existing functions to decompose the time series include decompose , which allows you pass whether the series is multiplicative or not, and stl , which is only for additive series without transforming the data. I could use stl with a multiplicative series if I transform the time series by taking the log. The first component to extract is the trend.

There are a number of ways you can do this, and some of the simplest ways involve calculating a moving average or median. A moving median is less sensitive to outliers than a moving mean. Lots of 0s can result in very weird trends. Seasonality will be cyclical patterns that occur in our time series once the data has had trend removed. Of course, the way to de-trend the data needs to additive or multiplicative depending on what type your time series is.

To work out the seasonality we need to work out what the typical de-trended values are over a cycle.