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I'm new to time series analysis, and I am wondering if this is a sound method for generating weekly and monthly predictions.

In my case, I need to generate daily, weekly, and monthly predictions. If I generate daily predictions for a quarter out, could I simply sum those daily predictions to get the weekly and monthly predictions? For example, to generate next week's prediction, could I sum the daily prediction for the 14th-20th? This seems to especially make sense to me when considering weekly seasonality (namely, weekend dropoffs).

Sorry if this a silly question. I gave it a bit of thought, and it seems like a reasonable method. I have been trying to use Facebook Prophet, which seems to work better with daily data out-of-the-box, so I am curious. Thanks!

smxx
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1 Answers1

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Yes, summing daily forecasts to weeks is a common approach.

The alternative would be to base your model on weekly input data and directly forecast weekly totals. (If you have causal factors that change in mid-week, you will need to do some jiggling with the regression.)

Of course, the two forecasts - bottom-up and direct - will usually not give the same result. You have a good chance that combining the two forecasts will improve on both. This is the Multi Aggregation Prediction Algorithm (MAPA) proposed by Kourentzes et al. (2014, IJF).

Stephan Kolassa
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  • I'm big fan of Kourentzes and his team's work, and I really appreciate the elegance of the theory behind the MAPA and MAPAx packages. But I'm still having a hard time wrapping my head around the conceptual difference between considering different time scales as hierarchical levels on one hand, and just using a Fourier series or Fourier transform to decompose your signal into multiple frequency components the way TBATS, STS, and Prophet do - moreover with a Fourier approach, you don't have to worry about how many levels to put into your temporal hierarchy, since it applies across all harmonics – Skander H. Jun 09 '20 at 06:09
  • Am I missing something about temporal hierarchies? – Skander H. Jun 09 '20 at 06:09
  • @SkanderH.: I don't think there is necessarily a meaningful *conceptual* difference. MAPA just happens to work well empirically. One advantage is its simplicity: on the one hand, you don't need to master complicated methods to apply it, and on the other hand, you can apply the basic reconciliation logic to forecasts coming from *any* source. High level forecasts could even be judgmental. I don't think it's very enlightening to dig too deeply into any underlying theory. – Stephan Kolassa Jun 09 '20 at 06:28
  • "I don't think it's very enlightening to dig too deeply into any underlying theory." -- yeah you're right. Box and Jenkins did that back in the day, after being unsatisfied with Holt-Winter's and Croston's lack of theoretical rigor, and the entire forecasting community ended up having to wrestle with Z-transforms and unit roots for almost half a century without any benefit whatsoever to their business stakeholders or to humanity... – Skander H. Jun 09 '20 at 06:51