Time series and forecasting · insight-0254
Use count-appropriate intervals for small integer series
- Evidence type
- practitioner heuristic
- Difficulty
- medium
- Roles
- Data scientist
- Industries
- insurance, healthcare, manufacturing
Summary: situation, action, reason, boundary
Situation
Weekly claims at a small branch average three, and a normal-error model produces intervals from minus two to eight.
Action
Use a count distribution such as Poisson or negative binomial for the forecast distribution, or bootstrap residuals on a transformed scale, and report integer quantiles.
Reason
Normal-based intervals assume symmetric continuous errors, which small counts violate; a distribution matched to the data gives sensible bounds.
Boundary
Insurance claims, equipment failures, hospital admissions at small sites, low-volume SKUs.
Symptom or risk
Symmetric normal intervals ignore that counts are non-negative integers with skewed distributions, so lower bounds are meaningless and upper tails are too short.
Exceptions
For counts in the hundreds or more, normal approximations are often adequate.
Trade-offs
Negative binomial adds a dispersion parameter that is hard to estimate on short series; pool across similar series.
Pitfalls
Rounding a continuous forecast and calling it a count forecast.
Lessons and concepts
Claims and their sources
FPP3 states that standard prediction intervals assume normally distributed errors, that bootstrapped intervals drop normality and need not be symmetric, and that its methods assume a continuous sample space, which rarely matters when counts are sufficiently large.