Framework. Fix $\alpha\in ]0,1[$. Imagine you have $n$ $\alpha$-quantile forecast methodologies that give you, at time $t$ for look ahead time $t+h$, an estimation of the quantile of wind power. Formally, for $i=1,\dots,n$, you know how to produce $\hat{q}_{t+h|t}^{(i)}$ at time $t$ for look ahead time $t+h$ an estimation. Each methodology is based on a different modeling+estimation and can have performance that depend, for example, on the weather situation.

Question. How do you construct a weighting scheme to combine quantile estimation (say with a linear combination) that can adapt along time $t$? Formally, how to best construct weights $\lambda_1(t,h),\dots,\lambda_n(t,h)$ such that

$$\hat{q}_{t+h|t}=\sum_{i=1}^n \lambda_i(t,h) \hat{q}_{t+h|t}^{(i)}$$

is a very good quantile forecast.

Side Note. For Msc students interested in proposing and elaborating their ideas with the real data, I propose an internship on that subject for summer 2011 (see here, it's in french but I can translate to those interested).


Short answer. The problem you mention is well studied by Granger C.W.J. with co-authors, and known as the forecasts combination (or pooling) problem. The general idea is to choose the loss function criterion and the parameters (may be time dependent) that minimize the latter. Below I put some references that may be useful (only publicly available, look for the original works in references after the text).

  1. K.F.Wallis Combining Density and Interval Forecasts: A Modest Proposal // Oxford bulletin of economics and statistics, 67, supplement (2005) 0305-9049 (provides a general idea of how to combine interval forecasts, though there is no details on how to choose the weights)
  2. Allan Timmermann Forecast combinations. (a survey on different aspects of the forecast combinations by one of the co-editors of Handbook of economic forecasting that I would like to study myself)

Hoping for the longer answer from the community.

  • $\begingroup$ Thanks ! your "short answer" perfectly points out an interesting existing literature. $\endgroup$ Feb 22 '11 at 16:07

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