How to model seasonal variance in a high frequency time series? I have a time series that exhibits a clear seasonal pattern regarding its variance. Basically at night and morning the variance is low and at midday it is high. The time granularity of the data is 5 minutes. so the length of a season is 288 time periods. As a preprocessing step I want to normalize the data such that the assumptions of ARIMA are roughly satisfied. The method should be fast since I need to process 51840 values every 5 minutes. Alternatively a method that can learn incrementally but takes a long time for initialization would be fine too.
Any Idea which models would be appropriate here?

Perhaps a regression with ARIMA errors (for the conditional mean) combined with a GARCH with external regressors (for the conditional variance) could work. The regressors in both the conditional mean and conditional variance equations would be Fourier terms as in Hyndman "Forecasting with long seasonal periods". I am not sure about the computational speed, though. The method might be slow if a large number of Fourier terms is needed to account for the seasonality.
