# How to make a combination (aggregation) of quantile forecast?

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).

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