Density forecasts describe a probability distribution for future outcomes, not just a point estimate. The lab uses different density paths depending on what the source model can support.
Density Sources
- Bootstrap density uses residual moving-block bootstrap paths around a point forecast.
- Bayesian density uses posterior predictive draws when the model provides posterior samples.
- State-space density uses simulation from the state-space representation when that engine supplies it.
- Approximate Gaussian density uses a point forecast and residual scale. It is labeled approximate.
- External density artifacts can enter as normal, quantile, or kernel-grid inputs when the contract is valid.
Scoring
The lab reports proper scoring and calibration summaries where aligned actuals are available:
- CRPS, where lower is better
- log score, where higher is better
- negative log score, where lower is better
- PIT values and PIT histograms
Recalibration
Where supported, PIT values can feed beta recalibration. Recalibration should be estimated on validation data and judged on a separate test window.
Limits
Normal residual bands are useful as a baseline, but they are not the same as a full model-native predictive distribution. They can understate skew, heavy tails, regime shifts, or parameter uncertainty.
References
- Diebold, Gunther, and Tay, 1998.
- Gneiting and Raftery, 2007.
- Ranjan and Gneiting, 2010.
- Gneiting and Ranjan, 2013.