I'm using R forecast package with a daily time series data, that has complex i.e. Multiple seasonality (weekly, Yearly, monthly). The fit/forecast process also needs to take into account certain day specific effects.

I plan to:

  • Use auto.arima function
  • Set TS frequency to 7, to take care of the weekly seasonality
  • Use Fourier terms for 'xreg' parameter to take care of monthly and yearly seasonality
  • Use a regressor matrix for other effects e.g. Holidays.

    1. Can someone help in providing a concrete example on how to use the fourier function, which can take both monthly and yearly seasonality into account?

    2. Would like to see an example of how to combine a regressor matrix with the fourier result, so that it can be assigned to 'xreg' parameter or together?

On both these questions, I have only found possibilities of the above mentioned by Dr.Hyndman, but concrete examples can really be useful to the community as well.


  • $\begingroup$ Are you ignoring outliers? Yes. Are you ignoring impacts before and after holidays? Yes. Are you ignoring possible changes in the day of the week patterns? Yes. Are you ignoring possible changes in trend (or any trend at all????)? Is there any day of the month importance as has been found with cash data? Take a look here as well...stats.stackexchange.com/questions/58657/… I see that you posted that question I linked to....so you tried TBATS and now you are onto Fourier? Did you try my recommendations? $\endgroup$ – Tom Reilly Jul 23 '13 at 19:39

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