# 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-error loss differential distinguishable from zero using a HAC (long-run-variance) SE with lag ≥ 3?

Estimands. RMSE and MAE per horizon for snaive and model; 1 − RMSE_model/RMSE_snaive per horizon; at h=4 d̄ = mean(e²_snaive − e²_model), HAC SE, DM stat, two-sided p-value, lag and kernel. Meaningful under covariance stationarity of the loss differential (DM assumption); 40 origins is a small sample, so the asymptotic normal approximation is rough.

Outputs. out/forecasts.csv (240 rows: origin_date, target_date, horizon, forecast, actual, model); out/results.json with all keys of TASK.md table; out/report.md (6 sections); out/analysis.py (deterministic regeneration); out/claims.json.

Information rules. Origin t forecast uses only quarters ≤ t (expanding window, including model selection). Target = infl of t+h. Snaive = infl of t+h−4. Errors on given vintage; no real-time claim.

Invalidity / impossibility. Missing quarters in the 2015Q4–2026Q3 range, any use of data > t at origin t, HAC lag < 3, fewer than 240 forecast rows.