Hi Alfred,

In demography this is a well-known problem. It is called the problem of (external) consistency. See my paper in Environment and Planning A, vol. 17 (1985), pp. 1473-1498. An improved version of the algorithm proposed there was later implemented in the LIPRO model for multistate forecasts. The program is available for free. See http://nidi.nl/?id=24841&lang=UK.

I guess that the external consistency principles developed by demographers will be useful for your problems.

Best regards,

Nico

Hi Alfred,

Alexandros Tassinopoulos discussed something like this in his PhD-thesis, using external restrictions on the predictions (in accordance to an earlier paper by Walter Oberhofer). Didn't show up to improve the forecasts, when I remember correctly.

If I were sure that a superior aggregate forecast would be available, I would include the series of aggregate forecasts as a leading indicator or factor driving local development. In fact, the predicted factors (e.g. Chamberlain 1983, ECTA; Forni/Hallin/Lippi/Reichlin 2004, JoEconometrics;Bai/Ng 2011, mimeo; Stock/Watson 2011, Oxford Handbook...) are just a sort of predicted aggregates; all you have to do is to determine the factor loading, and to predict the idiosyncratic component. Because of the idiosyncratic components, you doesn't get the aggregate exactly at every point in time, but you shouldn't be too far away.

Best

Norbert

Nico and Norbert, thank you very much for your very helpful hints. I'll let you know once I have further insights into the topic. Best, Alfred

I suggest to look at Rob Hyndman's website, who worked quite a lot on hierarchical forecasts, i.e. forecasting top level time series and disaggregated time series separately and combining these forecasts by various methods..

Thanks, Roland, for the fruitful hint! I am just gathering a few of the articles of Hyndman and coathors...

You may also have a look at this :

https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/6286/forecastingaggregatesdemand.pdf

Thanks Osman. I was not Aware that People are reading this old posts. Meanwhile we got a bit farther in that topic. In Fact, Roland was right and Rob Hyndman has a paper that adresses the question asked above. For example: this paper: Hyndman, R. J., Ahmed, R. A., Athanasopoulos, G. and Shang, H. L. (2011), `Optimal combination forecasts for hierarchical time series', Computational Statistics & Data Analysis 55(9), 2579-2589. Myself, Norbert Schanne and Rüdiger Wapler are working on a Regression based optimal weighting method that combines different time-series models forecasts for the same unit and in addition restricts units to be hierachically consistent.