Combining Predictive Distributions

By Tilmann Gneiting, Roopesh Ranjan. 2011

239 citations recorded by the source corpus.

Predictive distributions need to be aggregated when probabilistic forecasts are merged, or when expert opinions expressed in terms of probability distributions are fused. We take a prediction space approach that applies to discrete, mixed discrete-continuous and continuous predictive distributions alike, and study combination formulas for cumulative distribution functions from the perspectives of coherence, probabilistic and conditional calibration, and dispersion. Both linear and non-linear aggregation methods are investigated, including generalized, spread-adjusted and beta-transformed linear pools. The effects and techniques are demonstrated theoretically, in simulation examples, and in case studies on density forecasts for S&P 500 returns and daily maximum temperature at Seattle-Tacoma Airport.

Subfields: Environmental Engineering, Global and Planetary Change, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/7789a7132f115cf6038c89dfe5dc6744b748c056

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Environmental Engineering

In Global and Planetary Change

In Management Science and Operations Research

Citations in the corpus

Using Entropic Tilting to Combine BVAR Forecasts With External Nowcasts (2014, background): “In particular, merging a multi-step BVAR forecast density with an external nowcast is not a traditional density combination problem in the spirit of Stone (1961), Hall and Mitchell (2007), Geweke and Amisano (2011), and Gneiting and Ranjan (2013).”
Dynamic Prediction Pools: An Investigation of Financial Frictions and Forecasting Performance (2016, unknown): “Most closely related to our work is the literature on density forecast combination, specifically Hall and Mitchell (2007), Geweke and Amisano (2011), Waggoner and Zha (2012), and Billio et al.”
The Evolution of Forecast Density Combinations in Economics (2018, background): “Nonlinear pools, such as the beta-transformed linear pool of Ranjan and Gneit- ing (2010), and the generalized and spread-adjusted pools of Gneiting and Ranjan (2013), can be preferable to linear pools in terms of delivering better calibrated forecast density combinations.”
Forecast combinations: An over 50-year review (2022, background): “, 1998) or discrete (Gneiting and Ranjan, 2013): A uniform histogram indicates a probabilistically calibrated forecast.”
Energy Forecasting: A Review and Outlook (2020, methodology): “To that end, various post-processing techniques, such as ensemble model output statistics [70] or forecast combination [71], are used to calibrate and sharpen the initial forecasts.”
Combining density forecasts using focused scoring rules (2017, unknown): “Gneiting and Ranjan (2013) also develop nonlinear weighting schemes such as spread-adjusted and beta-transformed linear pools.”
Regression diagnostics meets forecast evaluation: conditional calibration, reliability diagrams, and coefficient of determination (2021, methodology): “It is well known that an ideal forecast is both probabilistically calibrated and marginally calibrated (Gneiting and Ranjan, 2013, Theorem 2.8; Song et al., 2019, Theorem 1).”
Bayesian Nonparametric Calibration and Combination of Predictive Distributions (2015, methodology): “We build on the predictive density calibration framework of Ranjan and Gneiting (2010) and Gneiting and Ranjan (2013) and propose finite and infinite beta mixtures as calibration functions.”
Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings (2015, methodology): “To give an example, Table 2 revisits a scenario studied by Gneiting et al. (2007) and Gneiting and Ranjan (2013).”
Generalised Density Forecast Combinations (2015, unknown): “Our approach is also distinct and not subsumed by the combination methods considered in Gneiting & Ranjan (2013) which take nonlinear transformations of a linear pool with ﬁxed weights, rather than nonlinear or what we call generalised pools where the weights themselves induce the nonlinearities.”
Nowcasting GDP in Real Time: A Density Combination Approach (2014, unknown): “However, as shown in Gneiting and Ranjan (2013), if the individual densities are correctly calibrated, the higher variance of the combined density may lead to too dispersed densities.”