1# Contract — F3-conf-042**Question.** Over 40 rolling quarterly origins (2015-10-01 … 2025-07-01) does a time-series model beat the seasonal-naive forecast of Canadian quarterly CPI inflation (400·Δln of the quarterly-average NSA index) at h = 1, 2, 4, and is the h = 4 squared-error loss differential distinguishable from zero using a HAC standard error (lag ≥ 3)?34**Estimands.** RMSE and MAE per model per horizon over the 40 origins; 1 − RMSE_model/RMSE_snaive per horizon; at h = 4, d̄ = mean(e²_snaive − e²_model), its HAC SE, DM stat = d̄/SE and two-sided p-value. Meaningful under covariance stationarity of d_t (DM assumption) — questionable with COVID / 2021–23 inflation surge in the sample; the 40-origin sample is small.56**Outputs.** out/forecasts.csv (240 rows: origin_date, target_date, horizon, forecast, actual, model); out/results.json (keys listed in TASK.md: task_id, model_name, model_description, n_origins, first_origin, last_origin, rmse/mae snaive & model h1/h2/h4, rel_improvement_rmse_h1/h2/h4, loss_diff_mean_h4, loss_diff_se_h4, hac_lags_h4, hac_kernel_h4, dm_stat_h4, dm_pvalue_h4, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/report.md (6 sections); out/analysis.py; out/claims.json.78**Information rules.** Origin t uses only quarters ≤ t (estimation, lag selection all within the expanding window). Target = infl of t+h. snaive = infl of t+h−4. HAC lag ≥ 3 reported. No real-time claim.910**Invalidity / impossibility.** Missing target quarters (last target 2026-07-01 exists: OK), any use of data after origin, SE ≤ 0 (e.g. rectangular kernel can give negative variance — avoid by Bartlett).11