# Contract — F3-conf-04

Question: Over 40 rolling quarterly origins (2015-10-01 … 2025-07-01), does a chosen time-series model beat the seasonal-naive forecast of Canadian quarterly CPI inflation (400·Δln of quarterly-average NSA CPI) at h=1,2,4; and at h=4 is the mean squared-loss differential nonzero under HAC (DM-type) inference? Estimands: RMSE, MAE per model × horizon (40 errors each); rel. improvement 1−RMSE_m/RMSE_sn; at h=4 d̄ = mean(e²_sn − e²_m), HAC SE (lag ≥3), DM stat, two-sided p. Meaningful assuming covariance-stationary loss differential; small sample (40) makes normal approx rough. Outputs: out/forecasts.csv (240 rows: origin_date,target_date,horizon,forecast,actual,model); out/results.json (keys per TASK.md table); out/report.md (6 sections); out/analysis.py; out/claims.json. Info rules: forecast at origin t uses only quarters ≤ t (expanding window incl. model selection); snaive = y_{t+h−4}; targets y_{t+h}; no real-time claim. Invalidity: use of data after origin; fewer than 40 origins/targets available (last target 2026-07-01 ≤ 2026Q3, OK); HAC lag ❤️.