Time series and forecasting · insight-1218
Check and fix quantile crossing before scoring or serving multi-quantile forecasts
- Evidence type
- documented fact
- Difficulty
- medium
- Roles
- Data scientist, ML engineer
- Industries
- cross-industry
Summary: situation, action, reason, boundary
Situation
A gradient-boosted model fits the 10th, 50th and 90th percentiles with separate runs and the dashboard sometimes shows the 90th below the median.
Action
Count crossings per horizon in the backtest. Fix them by sorting the quantile predictions per row (monotone rearrangement), or by a joint model with monotonic constraints, and then recompute scores.
Reason
Sorting estimated quantile curves yields a monotone curve that is, under the paper's conditions, no further from the true curve than the original estimate.
Boundary
Independently fitted quantile models (boosting, linear quantile regression, neural heads).
Symptom or risk
Crossed quantiles are impossible as a distribution; interval widths turn negative, coverage and interval scores are unreliable, and planners lose trust.
Exceptions
Distributional models that output one parametric distribution cannot cross.
Trade-offs
Rearrangement hides a model-fit problem if crossing is frequent; report the crossing rate.
Pitfalls
Rearranging only for display and scoring the unsorted values.
Lessons and concepts
Claims and their sources
Chernozhukov, Fernandez-Val and Galichon propose monotone rearrangement of estimated quantile curves that cross, and argue the rearranged curve is closer to the true quantile curve in finite samples.