# Is summing daily forecasts a sound method for generating weekly/monthly forecasts?

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!

## 1 Answer

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).

• 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 Commented Jun 9, 2020 at 6:09
• Am I missing something about temporal hierarchies? Commented Jun 9, 2020 at 6:09
• @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. Commented Jun 9, 2020 at 6:28
• "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... Commented Jun 9, 2020 at 6:51