# Efficient forecasting of daily and weekly seasonality in minute data

If I naively apply STL, Holt-Winters or Kalman-Filter approaches to the problem of extracting the seasonality and trend components of a one-minute data stream, I will end up with about 10K cyclic sub-series. Not only does this impose computational problems, it inconsistent with my expectation that the seasonal and trend components of the signal will be smooth on the minute timescale. (Indeed, since I'm trying to decompose the signal into these components, one could say that by definition I want the seasonal and trend components to be smooth on this scale, with any high-frequency variation ending up in the residual.)

In continuous time, I'd want to separate these scales via a multi-scale expansion, but I haven't found references to applying these sort of approaches to analyzing data streams of the sort that I'm interested in.

I've seen mentions of using sub-sampling and non-overlapping averages but have not found concrete papers or examples.

What do folks typically do in cases like this? Papers, examples, pointers, etc. would be greatly appreciated.

There is a tbats() function in the forecast package for R. We also have a tag. Finally, the original publication is De Livera, A. M., Hyndman, R. J. & Snyder, R. D. (2011). Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing. Journal of the American Statistical Association, 106, 1513-1527.