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Empirical Economics

Erschienen in:

07.04.2017

Forecast combination when outcomes are difficult to predict

verfasst von: Graham Elliott

Erschienen in: Empirical Economics | Ausgabe 1/2017

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Abstract

We show that when outcomes are difficult to forecast in the sense that forecast errors have a large common component that (a) optimal weights are not affected by this common component, and may well be far from equal to each other but (b) the relative mean square error loss from averaging over optimal combination can be small. Hence, researchers could well estimate combining weights that indicate that correlations could be exploited for better forecasts only to find that the difference in terms of loss is negligible. The results then provide an additional explanation for the commonly encountered practical situation of the averaging of forecasts being difficult to improve upon.

Vorheriger Artikel Special issue on forecasting, use of survey data on expectations, and panel data applications: editors’ introduction

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For a book length exposition of these methods as well as the basic forecast combination problem, see Elliott and Timmermann (2016).

Alternatively, we could consider that forecasters do in fact observe the relevant information but have forecasts that differ from each other as they add in an additional random error. This would leave the following mathematical results unchanged, although it is perhaps a less defendable story for the differences amongst forecasts.

This was verified visually. Because forecast errors from this method display large forecast errors before this period, these errors are very influential observations in the regressions used to construct the weights.

Whilst not formally justified here, it is expected that this approximation is likely to be reasonable. First, so long as the optimal weights are not the average weights, the two combined forecast models will not have a degenerate spectral density at frequency zero (so issues of nested models do not arise). Second, we have used the same loss function (squared loss) in the forecast combination as the evaluation.

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Titel: Forecast combination when outcomes are difficult to predict
verfasst von: Graham Elliott
Publikationsdatum: 07.04.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 1/2017
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-017-1253-2

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