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A model needs to be fit to a short time series of 3 annual observations of sales (2018 to 2020), e.g. 12, 14 and 13. The next 2 years (annual values) need to be forecasted bsaed on this data.

Is there any theoretical benefit from using the monthly observations instead of the annual data, eg sales in 2018-Jan, 2018-Feb, ..., 2020-Dec?

The number of data point increases, which means that models with more parameters can be fit. However, does this help for the given task? There is for instance no need for seasonal effects because only annual forecasts are relevant anyway.

Would there be a theoretical benefit for increasing the data frequency in this given 3-year period to weeks, days or even minutes? Or is there an argument that for annual forecasts basically filling the gaps by measuring more often within a year cannot increase forecasting accuracy?

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It depends, there definitely can be some positives in going to the monthly level. First off, as you pointed out, you can actually build a model at the monthly freq. With 3 points you will just use some naive forecast for the annual level which can work unless the annual freq is masking an underlying trend which would be evident at the monthly level.

It all really comes down to signal vs. noise ratio. As you go from annual to a frequency like hourly we typically begin to have more noise creeping in which can make it significantly harder to forecast. But going from annual to monthly we gain more data points and may uncover trends which would be beneficial to forecast. So you just need to find the right balance.

If you look at monthly/daily and everything is noise it might just be optimal to average the years.

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  • $\begingroup$ Thank you. I was just wondering whether there is a general mathematical theorem for this. Maybe from signal processing where increasing measurement frequency from seconds to milliseconds is shown to not have an impact on forecasting accuracy. $\endgroup$
    – HOSS_JFL
    Jun 9 at 5:17
  • $\begingroup$ yeah I would just use forecast accuracy aggregated up to the frequency you care about (yearly) as your theory. $\endgroup$
    – Tylerr
    Jun 11 at 19:02

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