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I'm quite new to statistics and forecasting, and I have to build a model to forecast monthly sales of different related products in a bunch of cities.

Seasonal ARIMA seams to be a good model for that, but that implies creating a model for each of the products in each cities (I have about 300 series). I don't think there is anything wrong with that, but I wonder if there is a model that can take all the series into account at the same time to improve the forecast.

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You could use generalized regression model for producing hierarchical forecasts from the individual forecasts.

Here is a link:

https://www.otexts.org/fpp/9/4

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    $\begingroup$ +1. This approach has been found to improve forecast accuracy across the hierarchy, see here and here. $\endgroup$ Jan 14, 2015 at 7:31
  • $\begingroup$ This is not exactly what I was looking for, but it is still pretty neat and it will certainly be useful. Do you know an implementation in Python? $\endgroup$
    – Pafnouti
    Jan 14, 2015 at 10:05
  • $\begingroup$ @Pafnouti No, I do not know but perhaps you can write these equations down by using linear algebra libraries in Python? $\endgroup$
    – Analyst
    Jan 14, 2015 at 13:17
  • $\begingroup$ @StephanKolassa It seems that Prof Hyndman is working quite heavily in this field also... :) $\endgroup$
    – Analyst
    Jan 14, 2015 at 13:19
  • $\begingroup$ He is. He co-authored both the open source textbook you linked to and the hierarchical time series approach, and he created the hts package for R for hierarchical time series - no python implementation, though - and he's editor-in-chief of the IJF and he posts here frequently. Take him seriously. $\endgroup$ Jan 14, 2015 at 14:03
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There is an article on the inside-R website which uses signal decomposition for training and testing and then forecasting with a neural net and which might be a useful alternative to generalized regression models. R code is supplied.

link here

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Try finding the common factors, and model these factors. For instance, you could run PCA, and see if there's a few factors that explain the variance of your 300 series. It is possible that you may find a handful of principal components explain a huge chunk of the variance of all 300 series. In this case you'll model these few factors only. Then you can recover the original series from factors.

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