# Contract — F3-conf-04

**Question.** Over 40 rolling quarterly origins (2015-10-01 … 2025-07-01), does a chosen time-series model forecast Canadian quarterly CPI inflation (400·Δln of quarterly-average NSA CPI) better than the seasonal-naive forecast at h = 1, 2, 4; and at h = 4 is the mean squared-error loss differential distinguishable from zero using a HAC (long-run variance) SE with truncation lag ≥ 3?

**Estimands.** Out-of-sample RMSE and MAE per horizon for snaive and model; 1 − RMSE_model/RMSE_snaive per h; at h=4, d̄ = mean(e²_snaive − e²_model) over 40 origins, its HAC SE, DM statistic d̄/SE and two-sided p-value. Meaningful under covariance stationarity of the loss differential (DM assumptions); with only 40 overlapping observations, asymptotic normal inference is approximate.

**Outputs.** out/forecasts.csv (240 rows: origin_date, target_date, horizon, forecast, actual, model); out/results.json with all keys in TASK.md table; out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py (regenerates results.json + forecasts.csv deterministically from data/); out/claims.json.

**Information rules.** A forecast at origin t uses only quarters ≤ t (estimation, lag selection, all transformations inside the expanding window). Target = infl_annualised at t+h. Snaive forecast = value at t+h−4. Data as given; no real-time claim.

**Invalidating conditions.** Missing target quarters (last target 2026-07-01 must exist), use of data > t, HAC lag < 3, non-positive SE, row counts ≠ 240.