Additive and multiplicative seasonality – can you identify them correctly?

By | November 9, 2014

Seasonality is a common characteristic of time series. It can appear in two forms: additive and multiplicative. In the former case the amplitude of the seasonal variation is independent of the level, whereas in the latter it is connected. The following figure highlights this:

mseas.fig1

Note that in the example of multiplicative seasonality the season is becoming “wider”. Obviously if the level was decreasing the seasonal amplitude of the multiplicative case would decrease as well. For selecting the appropriate model to produce our forecasts we need to know the type of seasonality we are dealing with. How do you compare against statistical identification? Select additive or multiplicative in the demonstration below and submit your choice to see if you can do better than statistics and the average accuracy of participants so far.

4 thoughts on “Additive and multiplicative seasonality – can you identify them correctly?

  1. Martin

    Hi Nikolaos,
    Thanks for this interactive tool !

    I can’t find any information about this “KS test”.
    What does it stand for?

    Thanks

    Reply
    1. Nikos Post author

      That is an unpublished test that I have been working on with a colleague of mine, Carlos Diaz. Sometimes it takes quite a bit of time to get an academic publication!
      You can find a prototype of it in TStools for R. The function is called mseastest< \code>.

      Reply
  2. Benjamin

    How did you obtain the plot comparison (additive vs multiplicative) graphs in R that are shown above?

    Reply
    1. Nikos Post author

      It has been a while since I built this plot, so I do not have code any readily, but I think what I did is construct the series, fit a centred moving average through them (red line) and then add or multiply a factor to it to get the dotted blue lines for the two types of seasonality. Hope this helps!

      Reply

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