I would like to use Fourier terms to model seasonality in an ARIMA model. The reason for using Fourier terms instead of a seasonal ARIMA model is that the frequency of the time series is very high (672) and that I want to model some special days as if they were different weekdays (e. g. I want to treat Easter Monday as if it was a Sunday). I first wanted to do that by using seasonal dummies but 671 seasonal dummies are probably to much. Thus, I want to use Fourier terms which I would adjust for the special days to get the correct regressors.
Now, I have two questions:
- Does anybody have a good reference for using fourier terms as regressors in ARIMA models? I only find online references like blogs (e. g. http://robjhyndman.com/hyndsight/dailydata/) but no paper or book I could cite.
- Does anybody have comments on whether this approach is useful or not?
Note: I have to use ARIMA models, so I do not need suggestions regarding alternative methods.