{
 "_comment": "Empirical band-widening factors applied at chart render time. Archived round artifacts under forecasts/rounds/ are never modified; the correction exists only in the published fan charts.",
 "source": {
  "repo": "PolicyEngine/boe-var-model",
  "file": "results/coverage_evaluation.json",
  "code_version": "6fb45d3747fbc6fb71a6ab78f1e17a79b209e8ea741009e239cfdf76e4785c1b",
  "origins": 49,
  "horizons_evaluated": 8,
  "spec": "production_spec: the coverage evaluation re-run with the six Covid dummies (2020Q1-2021Q2) that every published forecast is estimated with"
 },
 "derivation": "Gaussian half-width approximation: k(h, level) = z(nominal) / z(empirical), where z(p) is the standard-normal quantile at (1+p)/2 and empirical is the measured coverage of the nominal band at horizon h. Each band half-width is multiplied by k around the archived median. k below 1 (an over-covering band) narrows it: this is a calibration, not a one-way widening.",
 "extrapolation": "The evaluation covers horizons h1-h8; archived rounds run to 13 quarters. For h > 8 the h8 factor is held constant.",
 "series_mapping": {
  "gdp": "uk_gdp",
  "cpi": "cpisa"
 },
 "caveat": "Coverage was measured on series levels in transformed model units (pseudo-out-of-sample, overlapping origins); the published fans show year-on-year growth, so the factors are an approximation.",
 "unemployment_satellite": "Left raw. The svar-unemployment (Okun) satellite is not among the series in the coverage evaluation, so no measured factor applies to it; borrowing the boe-svar factors would assert a calibration that was never tested. Its fan is labelled as raw model quantiles.",
 "k": {
  "gdp": {
   "68": {
    "h1": 0.8552,
    "h2": 0.9717,
    "h3": 1.1515,
    "h4": 1.1031,
    "h5": 1.2024,
    "h6": 1.2563,
    "h7": 1.4399,
    "h8": 1.4399
   },
   "90": {
    "h1": 1.0648,
    "h2": 1.1227,
    "h3": 1.2372,
    "h4": 1.2952,
    "h5": 1.4145,
    "h6": 1.4145,
    "h7": 1.5407,
    "h8": 1.5407
   }
  },
  "cpi": {
   "68": {
    "h1": 1.2563,
    "h2": 1.4399,
    "h3": 1.5101,
    "h4": 1.8545,
    "h5": 2.0808,
    "h6": 1.9617,
    "h7": 1.8545,
    "h8": 1.9617
   },
   "90": {
    "h1": 1.3542,
    "h2": 1.6072,
    "h3": 1.8245,
    "h4": 1.8245,
    "h5": 1.8245,
    "h6": 1.9888,
    "h7": 1.8245,
    "h8": 1.9046
   }
  }
 },
 "correction": "Superseded factors measured without Covid dummies. The coverage run had always estimated with no dummies while every published fan estimates with them, so the factors were derived from a different model than the one they were applied to \u2014 and in the same direction at every horizon for UK GDP, which was being narrowed by 36% at h1 where the model actually shown wants 14%. Both sets are published in the source artifact.",
 "standard_error": "Binomial standard error sqrt(p(1-p)/n) at the NOMINAL level with n = 49 origins, quoted so a measured coverage is not read as exact. Origins overlap, so the number of independent observations is well below n and this understates the true sampling error. A one-standard-error move in measured coverage shifts k by far more than the fourth decimal these factors are quoted to; the digits are the arithmetic of the run, not the precision of the estimate."
}