Prediction Space in Forecasting

In a forecasting problem, we have

  • $\mathcal P$, the priors, e.g., price and demand is negatively correlated,
  • $\mathcal D$, available dataset,
  • $Y$, the observations, and
  • $F$, the forecasts.

Information Set $\mathcal A$

The priors $\mathcal D$ and the available data $\mathcal P$ can be summarized together as the information set $\mathcal A$.

Under a probabilistic view, a forecaster will find out or approximate a CDF $\mathcal F$ such that1

$$ \mathcal F(Y\vert \mathcal D, \mathcal P) \to F. $$

Naively speaking, once the density $\rho(F, Y)$ is determined or estimated, a probabilistic forecaster can be formed. The joint probability of $(F, Y)$ is our prediction space.

  1. Gneiting2014 Gneiting T, Katzfuss M. Probabilistic Forecasting. Annu Rev Stat Appl. 2014;1: 125–151. doi:10.1146/annurev-statistics-062713-085831  ↩︎

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L Ma (2022). 'Prediction Space in Forecasting', Datumorphism, 04 April. Available at: