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?

  • $\begingroup$ Generally, when you have Seasonal components in your time series, opting SARIMAX/LSTM becomes a more clear approach. Could you give more context towards the problem! $\endgroup$ Mar 31, 2022 at 5:43
  • $\begingroup$ @AtulMishra As I understand SARIMAX assumes constant variance, right?. But the data has an obvious seasonal pattern in variance (not so much in trend). And LSTM is probably too computationally expensive for my usecase. I want to perform online outlier detection. For that I of course need to consider the variance at different time periods. $\endgroup$
    – algebruh
    Mar 31, 2022 at 5:56
  • $\begingroup$ I guess Constant Variance is one of the assumption of timeseries infact. It there is no chronological order/stationarity in the time-series, there is no point in using a TIme-Series Model. Have a look at this: statsmodels.org/dev/examples/notebooks/generated/… $\endgroup$ Mar 31, 2022 at 6:10
  • $\begingroup$ Using SARIMAX you can find the seasonal component as a KPI infact and then decide on using what seasonal factor, you want your model to learn. $\endgroup$ Mar 31, 2022 at 6:11
  • $\begingroup$ @AtulMishra, SARIMAX will not work with such a long seasonal period. See Hyndman "Forecasting with long seasonal periods". $\endgroup$ Apr 1, 2022 at 17:47

1 Answer 1


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.


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