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The estimands are the out-of-sample RMSE and MAE of the seasonal-naive forecast and of your model at each horizon, the relative improvement 1 − RMSE_model / RMSE_snaive per horizon, and, at h = 4, the mean loss differential d̄ = mean_t (e²_snaive,t − e²_model,t) with a standard error valid under serial correlation of the loss differential (Diebold–Mariano-type test).\n\n## Inputs\n- `data/cpi_quarterly.csv` — observed data derived from the Bank of Canada Valet series V41690973 (Total CPI, Canada, index 2002 = 100, not seasonally adjusted, monthly; Statistics Canada table 18-10-0004-01); retrieved 2026-10-30 UTC; see `data/README.md` for URL, SHA-256 and terms. Columns: `quarter` (first month of the quarter, YYYY-MM-01), `cpi_avg` (mean of the three monthly index values), `infl_annualised` (target series: 400 × Δln cpi_avg, percent at annual rate, 6 decimals; empty for 1995Q1). 127 complete quarters, 1995Q1 to 2026Q3.\n- `data/cpi_monthly.csv` — the monthly index as served (`month`, `cpi`), 381 rows 1995-01 to 2026-09, provided for provenance; the quarterly file is the input of the analysis.\n\n## Information-availability rules\n- Forecast origins: the 40 quarters t = 2015-10-01, 2016-01-01, …, 2025-07-01 (the `quarter` value). Horizons h ∈ {1, 2, 4}; the target of origin t at horizon h is `infl_annualised` of quarter t + h.\n- A forecast made at origin t may use only quarters dated ≤ t (expanding window: estimation, model selection and transformations included); a quarter's value is treated as known at the end of that quarter.\n- Seasonal-naive baseline: the forecast for the target quarter t + h is the value of `infl_annualised` four quarters before the target, i.e. of quarter t + h − 4 (always ≤ t for h ≤ 4).\n- The h = 4 test: with one forecast per origin, consecutive 4-step-ahead errors overlap, so the loss differential d_t is serially correlated; the standard error of d̄ must be computed with a heteroskedasticity-and-autocorrelation-consistent (long-run variance) estimator with a truncation lag of at least h − 1 = 3 quarters; report the lag used.\n- Errors are computed on the data as given; do not claim real-time validity.\n\n## Required outputs\n- `out/forecasts.csv` — one row per (origin, horizon, model), columns `origin_date`, `target_date`, `horizon` (1, 2 or 4), `forecast`, `actual`, `model` (`snaive` or the value of `model_name`). Expected: 40 × 3 × 2 = 240 rows.\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F3-conf-04\" |\n| `model_name` | string | — | short name of your model, used in the `model` column |\n| `model_description` | string | — | one-sentence specification (lags, seasonal terms, direct vs iterated, estimation sample, method) |\n| `n_origins` | integer | — | 40 |\n| `first_origin`, `last_origin` | string | date | first and last origin quarters |\n| `rmse_snaive_h1`, `mae_snaive_h1`, `rmse_snaive_h2`, `mae_snaive_h2`, `rmse_snaive_h4`, `mae_snaive_h4` | number | percentage points (annualised) | seasonal-naive errors per horizon |\n| `rmse_model_h1`, `mae_model_h1`, `rmse_model_h2`, `mae_model_h2`, `rmse_model_h4`, `mae_model_h4` | number | percentage points (annualised) | your model's errors per horizon |\n| `rel_improvement_rmse_h1`, `rel_improvement_rmse_h2`, `rel_improvement_rmse_h4` | number | fraction | 1 − rmse_model / rmse_snaive |\n| `loss_diff_mean_h4` | number | squared percentage points | mean over the 40 origins of e²_snaive − e²_model at h = 4 (positive = model better) |\n| `loss_diff_se_h4` | number | squared percentage points | HAC standard error of `loss_diff_mean_h4` |\n| `hac_lags_h4` | integer | quarters | truncation lag used in the HAC estimator |\n| `hac_kernel_h4` | string | — | kernel used (e.g. \"bartlett\", \"rectangular\") |\n| `dm_stat_h4` | number | — | loss_diff_mean_h4 / loss_diff_se_h4 |\n| `dm_pvalue_h4` | number | — | two-sided p-value of `dm_stat_h4` |\n| `feasibility` | string | — | \"complete\", \"partial\" or \"infeasible\" |\n| `feasibility_reason` | string or null | — | explanation if not complete |\n| `data_issues` | array of {\"issue\",\"handling\"} | — | data problems detected and how handled (empty list if none) |\n| `n_input_rows` | object | — | {\"cpi_quarterly.csv\": rows read excluding header, \"cpi_monthly.csv\": rows read excluding header} |\n| `n_analysed` | integer | — | observations in the last estimation sample |\n| `random_seed` | integer or null | — | seed used, if any |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` and `out/forecasts.csv` from `data/` only, deterministically.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}].\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels available). Do not modify `data/`.\n- This task is designed to be completed in well under 20 minutes of work.\ncpi_monthly.csv\ncpi_quarterly.csv\nREADME.md","is_error":false}]},"uuid":"be48a26d-91b0-47d3-87b7-a4690e458813","timestamp":"2026-10-30T04:24:46.399Z","toolUseResult":{"stdout":"# F3-conf-04 — Multi-horizon forecasts of Canadian quarterly inflation with overlapping targets\n\n## Scientific question\nOver 40 rolling quarterly origins (2015Q4 to 2025Q3), does a time-series model of your choice forecast Canadian quarterly CPI inflation (annualised, not seasonally adjusted) better than the seasonal-naive forecast at horizons of 1, 2 and 4 quarters, and is the difference in squared-error loss at the 4-quarter horizon statistically distinguishable from zero once the dependence created by overlapping multi-step forecast errors is taken into account? The estimands are the out-of-sample RMSE and MAE of the seasonal-naive forecast and of your model at each horizon, the relative improvement 1 − RMSE_model / RMSE_snaive per horizon, and, at h = 4, the mean loss differential d̄ = mean_t (e²_snaive,t − e²_model,t) with a standard error valid under serial correlation of the loss differential (Diebold–Mariano-type test).\n\n## Inputs\n- `data/cpi_quarterly.csv` — observed data derived from the Bank of Canada Valet series V41690973 (Total CPI, Canada, index 2002 = 100, not seasonally adjusted, monthly; Statistics Canada table 18-10-0004-01); retrieved 2026-10-30 UTC; see `data/README.md` for URL, SHA-256 and terms. Columns: `quarter` (first month of the quarter, YYYY-MM-01), `cpi_avg` (mean of the three monthly index values), `infl_annualised` (target series: 400 × Δln cpi_avg, percent at annual rate, 6 decimals; empty for 1995Q1). 127 complete quarters, 1995Q1 to 2026Q3.\n- `data/cpi_monthly.csv` — the monthly index as served (`month`, `cpi`), 381 rows 1995-01 to 2026-09, provided for provenance; the quarterly file is the input of the analysis.\n\n## Information-availability rules\n- Forecast origins: the 40 quarters t = 2015-10-01, 2016-01-01, …, 2025-07-01 (the `quarter` value). Horizons h ∈ {1, 2, 4}; the target of origin t at horizon h is `infl_annualised` of quarter t + h.\n- A forecast made at origin t may use only quarters dated ≤ t (expanding window: estimation, model selection and transformations included); a quarter's value is treated as known at the end of that quarter.\n- Seasonal-naive baseline: the forecast for the target quarter t + h is the value of `infl_annualised` four quarters before the target, i.e. of quarter t + h − 4 (always ≤ t for h ≤ 4).\n- The h = 4 test: with one forecast per origin, consecutive 4-step-ahead errors overlap, so the loss differential d_t is serially correlated; the standard error of d̄ must be computed with a heteroskedasticity-and-autocorrelation-consistent (long-run variance) estimator with a truncation lag of at least h − 1 = 3 quarters; report the lag used.\n- Errors are computed on the data as given; do not claim real-time validity.\n\n## Required outputs\n- `out/forecasts.csv` — one row per (origin, horizon, model), columns `origin_date`, `target_date`, `horizon` (1, 2 or 4), `forecast`, `actual`, `model` (`snaive` or the value of `model_name`). Expected: 40 × 3 × 2 = 240 rows.\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F3-conf-04\" |\n| `model_name` | string | — | short name of your model, used in the `model` column |\n| `model_description` | string | — | one-sentence specification (lags, seasonal terms, direct vs iterated, estimation sample, method) |\n| `n_origins` | integer | — | 40 |\n| `first_origin`, `last_origin` | string | date | first and last origin quarters |\n| `rmse_snaive_h1`, `mae_snaive_h1`, `rmse_snaive_h2`, `mae_snaive_h2`, `rmse_snaive_h4`, `mae_snaive_h4` | number | percentage points (annualised) | seasonal-naive errors per horizon |\n| `rmse_model_h1`, `mae_model_h1`, `rmse_model_h2`, `mae_model_h2`, `rmse_model_h4`, `mae_model_h4` | number | percentage points (annualised) | your model's errors per horizon |\n| `rel_improvement_rmse_h1`, `rel_improvement_rmse_h2`, `rel_improvement_rmse_h4` | number | fraction | 1 − rmse_model / rmse_snaive |\n| `loss_diff_mean_h4` | number | squared percentage points | mean over the 40 origins of e²_snaive − e²_model at h = 4 (positive = model better) |\n| `loss_diff_se_h4` | number | squared percentage points | HAC standard error of `loss_diff_mean_h4` |\n| `hac_lags_h4` | integer | quarters | truncation lag used in the HAC estimator |\n| `hac_kernel_h4` | string | — | kernel used (e.g. \"bartlett\", \"rectangular\") |\n| `dm_stat_h4` | number | — | loss_diff_mean_h4 / loss_diff_se_h4 |\n| `dm_pvalue_h4` | number | — | two-sided p-value of `dm_stat_h4` |\n| `feasibility` | string | — | \"complete\", \"partial\" or \"infeasible\" |\n| `feasibility_reason` | string or null | — | explanation if not complete |\n| `data_issues` | array of {\"issue\",\"handling\"} | — | data problems detected and how handled (empty list if none) |\n| `n_input_rows` | object | — | {\"cpi_quarterly.csv\": rows read excluding header, \"cpi_monthly.csv\": rows read excluding header} |\n| `n_analysed` | integer | — | observations in the last estimation sample |\n| `random_seed` | integer or null | — | seed used, if any |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` and `out/forecasts.csv` from `data/` only, deterministically.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}].\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels available). Do not modify `data/`.\n- This task is designed to be completed in well under 20 minutes of work.\ncpi_monthly.csv\ncpi_quarterly.csv\nREADME.md","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"12b48014-31cd-4dd2-b1d2-3897a7887aa8","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0083","sessionId":"814de002-3f98-485a-bc50-5a0ac58ebbfe","version":"2.1.314","gitBranch":"HEAD"}14{"type":"api-request-blob","sessionId":"814de002-3f98-485a-bc50-5a0ac58ebbfe","hash":"80be5e1194a61bde327a160406ac2f25a1ea7c45e223528c251b6fb643831994","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01NPaxtEzTvw3fNwu2tWAtxF","name":"Bash","input":{"command":"cat TASK.md; ls -R data | head -50"}}]}}15{"type":"api-request","sessionId":"814de002-3f98-485a-bc50-5a0ac58ebbfe","id":"0d588054-ef3b-429f-9e0c-e9181d66a081","timestamp":"2026-10-30T04:24:46.404Z","version":"2.1.314","querySource":"sdk","shapeHash":"fcb65c43e57b0d3d1e5b134153e30f4ebbbb09a7af1c09e04940d71af3d4ecbc","params":{"model":"claude-opus-5-5","betas":["claude-code-20250219","interleaved-thinking-2025-05-14","context-management-2025-06-27","prompt-caching-scope-2026-01-05","per-turn-control-2026-07-01","thinking-token-count-2026-05-13","mid-conversation-system-clear-at-2026-08-21","effort-2025-11-24","thinking-binding-controls-2026-08-01","thinking-display-updates-2026-08-18","cache-diagnosis-2026-04-07"],"max_tokens":128000,"thinking":{"type":"adaptive","display":"updates"},"context_management":{"edits":[{"type":"clear_thinking_20251015","keep":"all"}]},"output_config":{"effort":"medium"}},"base":"c686b3d2-b0fb-4a15-b92f-8bb731189f03","keep":2,"tail":["80be5e1194a61bde327a160406ac2f25a1ea7c45e223528c251b6fb643831994","9f9490dc1b5afdf2af844f502bdf07e005dcc077c39ca6744d1a8bab69e24b4b"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",3,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"d5e76d45439a6701071dcb74f05a9a9f430f82c0084af93dd7896e4bec99e001"}16{"parentUuid":"be48a26d-91b0-47d3-87b7-a4690e458813","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXnXmmqAGkvAHxSbgqzF","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01L3tt9jjfuB3kxLHWnSmLkz","name":"Bash","input":{"command":"cat data/README.md; head -5 data/cpi_quarterly.csv; tail -5 data/cpi_quarterly.csv; wc -l data/*.csv; ~/wp29/venv/bin/python -c \"\nimport pandas as pd;d=pd.read_csv('data/cpi_quarterly.csv');print(d.describe());print(d.isna().sum());print(pd.to_datetime(d.quarter).diff().value_counts())\nm=pd.read_csv('data/cpi_monthly.csv');print(m.isna().sum(), m.month.duplicated().sum())\""},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2500,"cache_read_input_tokens":2234,"output_tokens":242,"output_tokens_details":{"thinking_tokens":0},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":2500},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXnXmVDcbzNKh1UAbQfQ","requestRef":"0d588054-ef3b-429f-9e0c-e9181d66a081","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"d3082c88-871f-4e4c-ad20-d26c1414ca9e","timestamp":"2026-10-30T04:24:48.947Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0083","sessionId":"814de002-3f98-485a-bc50-5a0ac58ebbfe","version":"2.1.314","gitBranch":"HEAD"}17{"parentUuid":"d3082c88-871f-4e4c-ad20-d26c1414ca9e","isSidechain":false,"promptId":"d0ce3eab-219a-43dd-b949-c1a2dd555006","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01L3tt9jjfuB3kxLHWnSmLkz","type":"tool_result","content":"# data/README.md — F3-conf-04\n\n## cpi_monthly.csv\n- **Series**: Bank of Canada Valet series **V41690973** — Total CPI (Consumer Price Index, all-items, Canada, index 2002 = 100, **not seasonally adjusted**, monthly; published by Statistics Canada, table 18-10-0004-01, redistributed by the Bank of Canada).\n- **Retrieval URL**: https://www.bankofcanada.ca/valet/observations/V41690973/json?start_date=1995-01-01\n- **Retrieved (UTC)**: 2026-10-30T03:25:10Z. Terms: https://www.bankofcanada.ca/terms/\n- **Format**: `month` (YYYY-MM-01), `cpi` (index, one decimal, as served). 381 rows, 1995-01 to 2026-09-01. SHA-256 855d069176369d30d02cbbe0cc6456b76d2f3967cdaabc1b362c2461ef9015a2.\n\n## cpi_quarterly.csv\nDerived from the monthly file: `quarter` (first month of the quarter, YYYY-MM-01), `cpi_avg` (arithmetic mean of the three monthly index values, 6 decimals), `infl_annualised` (target series: 400 × (ln cpi_avg_q − ln cpi_avg_{q−1}), percent at annual rate, 6 decimals; empty for 1995Q1). Only complete quarters (three months) are included: 127 rows, 1995Q1 to 2026-07-01. SHA-256 c8652dec1567ec35e3b84ee8fa55545e9bf0ae4990a4d6d05b89a6d22f6801ea. Because the index is not seasonally adjusted, the quarterly inflation series has a pronounced seasonal pattern.\n\n## Vintage caveat\nThe CPI is not revised after publication (except for the periodic basket updates applied to the index chain by Statistics Canada), so the current vintage is essentially the real-time series; nevertheless the exercise treats a quarter's value as known at the end of that quarter (the actual publication occurs about three weeks after the last month), and no claim of historical real-time performance is made.\nquarter,cpi_avg,infl_annualised\n1995-01-01,86.933333,\n1995-04-01,87.633333,3.207961\n1995-07-01,87.800000,0.760023\n1995-10-01,87.833333,0.151831\n2025-07-01,164.866667,2.026963\n2025-10-01,165.233333,0.888620\n2026-01-01,166.100000,2.092560\n2026-04-01,168.866667,6.607773\n2026-07-01,169.900000,2.440232\n 382 data/cpi_monthly.csv\n 128 data/cpi_quarterly.csv\n 510 total\n cpi_avg infl_annualised\ncount 127.000000 126.000000\nmean 119.888451 2.127202\nstd 22.630216 2.385945\nmin 86.933333 -6.037850\n25% 101.866667 0.667988\n50% 117.466667 1.971882\n75% 133.866667 3.503591\nmax 169.900000 12.149214\nquarter 0\ncpi_avg 0\ninfl_annualised 1\ndtype: int64\nquarter\n92 days 62\n91 days 40\n90 days 24\nName: count, dtype: int64\nmonth 0\ncpi 0\ndtype: int64 0","is_error":false}]},"uuid":"bec66225-d1b2-417e-80e1-5f164e463021","timestamp":"2026-10-30T04:24:49.250Z","toolUseResult":{"stdout":"# data/README.md — F3-conf-04\n\n## cpi_monthly.csv\n- **Series**: Bank of Canada Valet series **V41690973** — Total CPI (Consumer Price Index, all-items, Canada, index 2002 = 100, **not seasonally adjusted**, monthly; published by Statistics Canada, table 18-10-0004-01, redistributed by the Bank of Canada).\n- **Retrieval URL**: https://www.bankofcanada.ca/valet/observations/V41690973/json?start_date=1995-01-01\n- **Retrieved (UTC)**: 2026-10-30T03:25:10Z. Terms: https://www.bankofcanada.ca/terms/\n- **Format**: `month` (YYYY-MM-01), `cpi` (index, one decimal, as served). 381 rows, 1995-01 to 2026-09-01. SHA-256 855d069176369d30d02cbbe0cc6456b76d2f3967cdaabc1b362c2461ef9015a2.\n\n## cpi_quarterly.csv\nDerived from the monthly file: `quarter` (first month of the quarter, YYYY-MM-01), `cpi_avg` (arithmetic mean of the three monthly index values, 6 decimals), `infl_annualised` (target series: 400 × (ln cpi_avg_q − ln cpi_avg_{q−1}), percent at annual rate, 6 decimals; empty for 1995Q1). Only complete quarters (three months) are included: 127 rows, 1995Q1 to 2026-07-01. SHA-256 c8652dec1567ec35e3b84ee8fa55545e9bf0ae4990a4d6d05b89a6d22f6801ea. Because the index is not seasonally adjusted, the quarterly inflation series has a pronounced seasonal pattern.\n\n## Vintage caveat\nThe CPI is not revised after publication (except for the periodic basket updates applied to the index chain by Statistics Canada), so the current vintage is essentially the real-time series; nevertheless the exercise treats a quarter's value as known at the end of that quarter (the actual publication occurs about three weeks after the last month), and no claim of historical real-time performance is made.\nquarter,cpi_avg,infl_annualised\n1995-01-01,86.933333,\n1995-04-01,87.633333,3.207961\n1995-07-01,87.800000,0.760023\n1995-10-01,87.833333,0.151831\n2025-07-01,164.866667,2.026963\n2025-10-01,165.233333,0.888620\n2026-01-01,166.100000,2.092560\n2026-04-01,168.866667,6.607773\n2026-07-01,169.900000,2.440232\n 382 data/cpi_monthly.csv\n 128 data/cpi_quarterly.csv\n 510 total\n cpi_avg infl_annualised\ncount 127.000000 126.000000\nmean 119.888451 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-p out; cat > out/analysis.py <<'EOF'\n\"\"\"F3-conf-04: AR(p)+seasonal dummies vs seasonal naive, Canadian quarterly CPI inflation.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\"\"\"\nimport json\nimport numpy as np, pandas as pd\nfrom scipy import stats\n\nD = \"data/\"; O = \"out/\"\nq = pd.read_csv(D + \"cpi_quarterly.csv\", parse_dates=[\"quarter\"])\nm = pd.read_csv(D + \"cpi_monthly.csv\", parse_dates=[\"month\"])\nn_rows = {\"cpi_quarterly.csv\": int(len(q)), \"cpi_monthly.csv\": int(len(m))}\n\n# ---- data checks ----\nissues = []\nassert q[\"quarter\"].is_monotonic_increasing\ngaps = (q[\"quarter\"].dt.to_period(\"Q\").astype(int).diff().dropna() != 1).sum()\nassert gaps == 0, \"non-contiguous quarters\"\n# recompute quarterly series from monthly file to verify derivation\nm[\"q\"] = m[\"month\"].dt.to_period(\"Q\")\nmq = m.groupby(\"q\")[\"cpi\"].agg([\"mean\", \"size\"])\nmq = mq[mq[\"size\"] == 3]\nrec = 400 * np.log(mq[\"mean\"]).diff()\nchk = pd.Series(rec.values, index=mq.index.to_timestamp()).reindex(q[\"quarter\"])\nmaxdiff = float(np.nanmax(np.abs(chk.values - q[\"infl_annualised\"].values)))\nassert maxdiff < 1e-4, maxdiff\nissues.append({\"issue\": \"infl_annualised is empty for 1995Q1 (no previous quarter)\",\n \"handling\": \"first quarter dropped; series starts 1995Q2 (126 obs)\"})\ny = q.set_index(\"quarter\")[\"infl_annualised\"].dropna()\ndates = list(y.index)\nyv = y.values\nqtr = np.array([d.quarter for d in dates])\n\nPMAX = 4\nH = [1, 2, 4]\norigins = pd.date_range(\"2015-10-01\", \"2025-07-01\", freq=\"QS\")\nassert len(origins) == 40\n\ndef design(yv, qtr, p, start):\n \"\"\"rows i=start..end: y_i on const, Q2-Q4 dummies, y_{i-1..i-p}\"\"\"\n idx = np.arange(start, len(yv))\n X = [np.ones(len(idx))] + [(qtr[idx] == s).astype(float) for s in (2, 3, 4)]\n X += [yv[idx - k] for k in range(1, p + 1)]\n return np.column_stack(X), yv[idx]\n\ndef fit_forecast(ys, qs, hmax):\n # AIC lag selection p in 0..PMAX on common sample (first PMAX obs held out)\n best = None\n for p in range(PMAX + 1):\n X, Y = design(ys, qs, p, PMAX)\n b, *_ = np.linalg.lstsq(X, Y, rcond=None)\n rss = float(((Y - X @ b) ** 2).sum()); n = len(Y)\n aic = n * np.log(rss / n) + 2 * X.shape[1]\n if best is None or aic < best[0]:\n best = (aic, p)\n p = best[1]\n X, Y = design(ys, qs, p, p) # re-estimate on all usable obs\n b, *_ = np.linalg.lstsq(X, Y, rcond=None)\n hist = list(ys); qcur = qs[-1]; fc = []\n for h in range(1, hmax + 1): # iterated forecasts\n qn = (qcur + h - 1) % 4 + 1\n x = [1.0] + [float(qn == s) for s in (2, 3, 4)] + [hist[-k] for k in range(1, p + 1)]\n f = float(np.dot(b, x)); fc.append(f); hist.append(f)\n return fc, p, len(Y)\n\nrows = []; lags_used = []\nfor t in origins:\n i = dates.index(t)\n ys, qs = yv[: i + 1], qtr[: i + 1] # only quarters <= t\n fc, p, nobs = fit_forecast(ys, qs, max(H))\n lags_used.append(p)\n for h in H:\n tgt = dates[i + h]\n rows.append(dict(origin_date=t.date(), target_date=tgt.date(), horizon=h,\n forecast=fc[h - 1], actual=yv[i + h], model=\"ar_seas_aic\"))\n rows.append(dict(origin_date=t.date(), target_date=tgt.date(), horizon=h,\n forecast=yv[i + h - 4], actual=yv[i + h], model=\"snaive\"))\nfcst = pd.DataFrame(rows).sort_values([\"model\", \"horizon\", \"origin_date\"])\nfcst.to_csv(O + \"forecasts.csv\", index=False)\nn_analysed = nobs # obs in last (2025Q3 origin) estimation regression\n\ndef err(mod, h):\n s = fcst[(fcst.model == mod) & (fcst.horizon == h)].sort_values(\"origin_date\")\n return (s.actual - s.forecast).values\n\ndef hac_se(d, L, kernel=\"bartlett\"):\n d = d - d.mean(); n = len(d)\n lrv = d @ d / n\n for k in range(1, L + 1):\n w = 1 - k / (L + 1) if kernel == \"bartlett\" else 1.0\n lrv += 2 * w * (d[k:] @ d[:-k]) / n\n return np.sqrt(lrv / n), lrv\n\nres = {\"task_id\": \"F3-conf-04\", \"model_name\": \"ar_seas_aic\",\n \"model_description\": (\"OLS autoregression of quarterly annualised inflation on a constant, \"\n \"three quarterly seasonal dummies and p own lags (p in 0..4 chosen by AIC at each origin on a \"\n \"common sample), estimated on an expanding window from 1995Q2 to the origin, with iterated \"\n \"multi-step forecasts (h=1,2,4) and known future seasonal dummies.\"),\n \"n_origins\": 40, \"first_origin\": str(origins[0].date()), \"last_origin\": str(origins[-1].date())}\nfor h in H:\n es, em = err(\"snaive\", h), err(\"ar_seas_aic\", h)\n res[f\"rmse_snaive_h{h}\"] = float(np.sqrt(np.mean(es ** 2)))\n res[f\"mae_snaive_h{h}\"] = float(np.mean(np.abs(es)))\n res[f\"rmse_model_h{h}\"] = float(np.sqrt(np.mean(em ** 2)))\n res[f\"mae_model_h{h}\"] = float(np.mean(np.abs(em)))\nfor h in H:\n res[f\"rel_improvement_rmse_h{h}\"] = 1 - res[f\"rmse_model_h{h}\"] / res[f\"rmse_snaive_h{h}\"]\n\nd = err(\"snaive\", 4) ** 2 - err(\"ar_seas_aic\", 4) ** 2\nL = 3\nse, _ = hac_se(d, L, \"bartlett\")\ndm = d.mean() / se\nres.update({\"loss_diff_mean_h4\": float(d.mean()), \"loss_diff_se_h4\": float(se),\n \"hac_lags_h4\": L, \"hac_kernel_h4\": \"bartlett\", \"dm_stat_h4\": float(dm),\n \"dm_pvalue_h4\": float(2 * stats.norm.sf(abs(dm))),\n \"feasibility\": \"complete\", \"feasibility_reason\": None, \"data_issues\": issues,\n \"n_input_rows\": n_rows, \"n_analysed\": int(n_analysed), \"random_seed\": None})\n\n# sensitivity (not required keys; stored separately)\nsens = {\"selected_lags_by_origin\": lags_used,\n \"derivation_check_max_abs_diff\": maxdiff}\nn = len(d)\nfor kern, lag in [(\"bartlett\", 4), (\"bartlett\", 6), (\"rectangular\", 3)]:\n s_, lrv = hac_se(d, lag, kern)\n sens[f\"{kern}_L{lag}\"] = {\"se\": float(s_) if lrv > 0 else None,\n \"dm\": float(d.mean() / s_) if lrv > 0 else None,\n \"p_norm\": float(2 * stats.norm.sf(abs(d.mean() / s_))) if lrv > 0 else None}\nhln = np.sqrt((n + 1 - 2 * 4 + 4 * 3 / n) / n)\nsens[\"hln_bartlett_L3\"] = {\"dm\": float(dm * hln), \"p_t39\": float(2 * stats.t.sf(abs(dm * hln), n - 1))}\nfor h in (1, 2):\n dh = err(\"snaive\", h) ** 2 - err(\"ar_seas_aic\", h) ** 2\n s_, _ = hac_se(dh, max(h - 1, 1))\n sens[f\"dm_h{h}_bartlett_L{max(h-1,1)}\"] = {\"mean\": float(dh.mean()), \"se\": float(s_),\n \"dm\": float(dh.mean() / s_), \"p_norm\": float(2 * stats.norm.sf(abs(dh.mean() / s_)))}\n# excluding 2021-2023 inflation surge targets\nfm = fcst[fcst.horizon == 4].copy()\nfm[\"td\"] = pd.to_datetime(fm.target_date)\nkeep = ~fm.td.between(\"2021-01-01\", \"2023-12-31\")\nfor mod in (\"snaive\", \"ar_seas_aic\"):\n s = fm[keep & (fm.model == mod)]\n sens[f\"rmse_h4_excl_2021_2023_{mod}\"] = float(np.sqrt(((s.actual - s.forecast) ** 2).mean()))\nsens[\"n_h4_excl_2021_2023\"] = int((keep & (fm.model == \"snaive\")).sum())\n\njson.dump(res, open(O + \"results.json\", \"w\"), indent=2)\njson.dump(sens, open(O + \"sensitivity.json\", \"w\"), indent=2)\nprint(json.dumps(res, indent=2)); print(json.dumps(sens, indent=2))\nEOF\n~/wp29/venv/bin/python 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\"task_id\": \"F3-conf-04\",\n \"model_name\": \"ar_seas_aic\",\n \"model_description\": \"OLS autoregression of quarterly annualised inflation on a constant, three quarterly seasonal dummies and p own lags (p in 0..4 chosen by AIC at each origin on a common sample), estimated on an expanding window from 1995Q2 to the origin, with iterated multi-step forecasts (h=1,2,4) and known future seasonal dummies.\",\n \"n_origins\": 40,\n \"first_origin\": \"2015-10-01\",\n \"last_origin\": \"2025-07-01\",\n \"rmse_snaive_h1\": 2.849125860156572,\n \"mae_snaive_h1\": 2.1374736750000003,\n \"rmse_model_h1\": 2.1929816943854896,\n \"mae_model_h1\": 1.5194119747378632,\n \"rmse_snaive_h2\": 2.846674080377472,\n \"mae_snaive_h2\": 2.1259446750000004,\n \"rmse_model_h2\": 2.4625629688732484,\n \"mae_model_h2\": 1.5525627877515993,\n \"rmse_snaive_h4\": 2.8823159392575315,\n \"mae_snaive_h4\": 2.181266125,\n \"rmse_model_h4\": 2.3430305749774485,\n \"mae_model_h4\": 1.597327211136124,\n \"rel_improvement_rmse_h1\": 0.23029665868640303,\n \"rel_improvement_rmse_h2\": 0.13493329431421597,\n \"rel_improvement_rmse_h4\": 0.18710140582957746,\n \"loss_diff_mean_h4\": 2.8179528984188726,\n \"loss_diff_se_h4\": 2.0862370066811216,\n \"hac_lags_h4\": 3,\n \"hac_kernel_h4\": \"bartlett\",\n \"dm_stat_h4\": 1.3507347867928952,\n \"dm_pvalue_h4\": 0.17678040465620282,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"infl_annualised is empty for 1995Q1 (no previous quarter)\",\n \"handling\": \"first quarter dropped; series starts 1995Q2 (126 obs)\"\n }\n ],\n \"n_input_rows\": {\n \"cpi_quarterly.csv\": 127,\n \"cpi_monthly.csv\": 381\n },\n \"n_analysed\": 121,\n \"random_seed\": null\n}\n{\n \"selected_lags_by_origin\": [\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1\n ],\n \"derivation_check_max_abs_diff\": 4.928220009858819e-07,\n \"bartlett_L4\": {\n \"se\": 1.8512807864167724,\n \"dm\": 1.5221639629681096,\n \"p_norm\": 0.12796800229110047\n },\n \"bartlett_L6\": {\n \"se\": 1.3784080101108847,\n \"dm\": 2.044353252265405,\n \"p_norm\": 0.04091866197008541\n },\n \"rectangular_L3\": {\n \"se\": 1.6984334664159881,\n \"dm\": 1.6591482410937648,\n \"p_norm\": 0.09708592437817767\n },\n \"hln_bartlett_L3\": {\n \"dm\": 1.2324298424211266,\n \"p_t39\": 0.2251668512290886\n },\n \"dm_h1_bartlett_L1\": {\n \"mean\": 3.308349455103071,\n \"se\": 1.9931443431548812,\n \"dm\": 1.6598644581186708,\n \"p_norm\": 0.09694172293238597\n },\n \"dm_h2_bartlett_L1\": {\n \"mean\": 2.039336944227098,\n \"se\": 2.548462482633978,\n \"dm\": 0.800222470655848,\n \"p_norm\": 0.42358191289791103\n },\n \"rmse_h4_excl_2021_2023_snaive\": 2.032021290160296,\n \"rmse_h4_excl_2021_2023_ar_seas_aic\": 1.5188544884772872,\n \"n_h4_excl_2021_2023\": 28\n}","is_error":false}]},"uuid":"91c81f40-c54d-4fc1-9a73-8013ac9ed1b1","timestamp":"2026-10-30T04:25:23.940Z","toolUseResult":{"stdout":"{\n \"task_id\": \"F3-conf-04\",\n \"model_name\": \"ar_seas_aic\",\n \"model_description\": \"OLS autoregression of quarterly annualised inflation on a constant, three quarterly seasonal dummies and p own lags (p in 0..4 chosen by AIC at each origin on a common sample), estimated on an expanding window from 1995Q2 to the origin, with iterated multi-step forecasts (h=1,2,4) and known future seasonal dummies.\",\n \"n_origins\": 40,\n \"first_origin\": \"2015-10-01\",\n \"last_origin\": \"2025-07-01\",\n \"rmse_snaive_h1\": 2.849125860156572,\n \"mae_snaive_h1\": 2.1374736750000003,\n \"rmse_model_h1\": 2.1929816943854896,\n \"mae_model_h1\": 1.5194119747378632,\n \"rmse_snaive_h2\": 2.846674080377472,\n \"mae_snaive_h2\": 2.1259446750000004,\n \"rmse_model_h2\": 2.4625629688732484,\n \"mae_model_h2\": 1.5525627877515993,\n \"rmse_snaive_h4\": 2.8823159392575315,\n \"mae_snaive_h4\": 2.181266125,\n \"rmse_model_h4\": 2.3430305749774485,\n \"mae_model_h4\": 1.597327211136124,\n \"rel_improvement_rmse_h1\": 0.23029665868640303,\n \"rel_improvement_rmse_h2\": 0.13493329431421597,\n \"rel_improvement_rmse_h4\": 0.18710140582957746,\n \"loss_diff_mean_h4\": 2.8179528984188726,\n \"loss_diff_se_h4\": 2.0862370066811216,\n \"hac_lags_h4\": 3,\n \"hac_kernel_h4\": \"bartlett\",\n \"dm_stat_h4\": 1.3507347867928952,\n \"dm_pvalue_h4\": 0.17678040465620282,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"infl_annualised is empty for 1995Q1 (no previous quarter)\",\n \"handling\": \"first quarter dropped; series starts 1995Q2 (126 obs)\"\n }\n ],\n \"n_input_rows\": {\n \"cpi_quarterly.csv\": 127,\n \"cpi_monthly.csv\": 381\n },\n \"n_analysed\": 121,\n \"random_seed\": null\n}\n{\n \"selected_lags_by_origin\": [\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 2,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1,\n 1\n ],\n \"derivation_check_max_abs_diff\": 4.928220009858819e-07,\n \"bartlett_L4\": {\n \"se\": 1.8512807864167724,\n \"dm\": 1.5221639629681096,\n \"p_norm\": 0.12796800229110047\n },\n \"bartlett_L6\": {\n \"se\": 1.3784080101108847,\n \"dm\": 2.044353252265405,\n \"p_norm\": 0.04091866197008541\n },\n \"rectangular_L3\": {\n \"se\": 1.6984334664159881,\n \"dm\": 1.6591482410937648,\n \"p_norm\": 0.09708592437817767\n },\n \"hln_bartlett_L3\": {\n \"dm\": 1.2324298424211266,\n \"p_t39\": 0.2251668512290886\n },\n \"dm_h1_bartlett_L1\": {\n \"mean\": 3.308349455103071,\n \"se\": 1.9931443431548812,\n \"dm\": 1.6598644581186708,\n \"p_norm\": 0.09694172293238597\n },\n \"dm_h2_bartlett_L1\": {\n \"mean\": 2.039336944227098,\n \"se\": 2.548462482633978,\n \"dm\": 0.800222470655848,\n \"p_norm\": 0.42358191289791103\n },\n \"rmse_h4_excl_2021_2023_snaive\": 2.032021290160296,\n \"rmse_h4_excl_2021_2023_ar_seas_aic\": 1.5188544884772872,\n \"n_h4_excl_2021_2023\": 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-p out; cat > out/analysis.py <<'EOF'\n\"\"\"F3-conf-04: AR(p)+seasonal dummies vs seasonal naive, Canadian quarterly CPI inflation.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\"\"\"\nimport json\nimport numpy as np, pandas as pd\nfrom scipy import stats\n\nD = \"data/\"; O = \"out/\"\nq = pd.read_csv(D + \"cpi_quarterly.csv\", parse_dates=[\"quarter\"])\nm = pd.read_csv(D + \"cpi_monthly.csv\", parse_dates=[\"month\"])\nn_rows = {\"cpi_quarterly.csv\": int(len(q)), \"cpi_monthly.csv\": int(len(m))}\n\n# ---- data checks ----\nissues = []\nassert q[\"quarter\"].is_monotonic_increasing\ngaps = (q[\"quarter\"].dt.to_period(\"Q\").astype(int).diff().dropna() != 1).sum()\nassert gaps == 0, \"non-contiguous quarters\"\n# recompute quarterly series from monthly file to verify derivation\nm[\"q\"] = m[\"month\"].dt.to_period(\"Q\")\nmq = m.groupby(\"q\")[\"cpi\"].agg([\"mean\", \"size\"])\nmq = mq[mq[\"size\"] == 3]\nrec = 400 * np.log(mq[\"mean\"]).diff()\nchk = pd.Series(rec.values, index=mq.index.to_timestamp()).reindex(q[\"quarter\"])\nmaxdiff = float(np.nanmax(np.abs(chk.values - q[\"infl_annualised\"].values)))\nassert maxdiff < 1e-4, maxdiff\nissues.append({\"issue\": \"infl_annualised is empty for 1995Q1 (no previous quarter)\",\n \"handling\": \"first quarter dropped; series starts 1995Q2 (126 obs)\"})\ny = q.set_index(\"quarter\")[\"infl_annualised\"].dropna()\ndates = list(y.index)\nyv = y.values\nqtr = np.array([d.quarter for d in dates])\n\nPMAX = 4\nH = [1, 2, 4]\norigins = pd.date_range(\"2015-10-01\", \"2025-07-01\", freq=\"QS\")\nassert len(origins) == 40\n\ndef design(yv, qtr, p, start):\n \"\"\"rows i=start..end: y_i on const, Q2-Q4 dummies, y_{i-1..i-p}\"\"\"\n idx = np.arange(start, len(yv))\n X = [np.ones(len(idx))] + [(qtr[idx] == s).astype(float) for s in (2, 3, 4)]\n X += [yv[idx - k] for k in range(1, p + 1)]\n return np.column_stack(X), yv[idx]\n\ndef fit_forecast(ys, qs, hmax):\n # AIC lag selection p in 0..PMAX on common sample (first PMAX obs held out)\n best = None\n for p in range(PMAX + 1):\n X, Y = design(ys, qs, p, PMAX)\n b, *_ = np.linalg.lstsq(X, Y, rcond=None)\n rss = float(((Y - X @ b) ** 2).sum()); n = len(Y)\n aic = n * np.log(rss / n) + 2 * X.shape[1]\n if best is None or aic < best[0]:\n best = (aic, p)\n p = best[1]\n X, Y = design(ys, qs, p, p) # re-estimate on all usable obs\n b, *_ = np.linalg.lstsq(X, Y, rcond=None)\n hist = list(ys); qcur = qs[-1]; fc = []\n for h in range(1, hmax + 1): # iterated forecasts\n qn = (qcur + h - 1) % 4 + 1\n x = [1.0] + [float(qn == s) for s in (2, 3, 4)] + [hist[-k] for k in range(1, p + 1)]\n f = float(np.dot(b, x)); fc.append(f); hist.append(f)\n return fc, p, len(Y)\n\nrows = []; lags_used = []\nfor t in origins:\n i = dates.index(t)\n ys, qs = yv[: i + 1], qtr[: i + 1] # only quarters <= t\n fc, p, nobs = fit_forecast(ys, qs, max(H))\n lags_used.append(p)\n for h in H:\n tgt = dates[i + h]\n rows.append(dict(origin_date=t.date(), target_date=tgt.date(), horizon=h,\n forecast=fc[h - 1], actual=yv[i + h], model=\"ar_seas_aic\"))\n rows.append(dict(origin_date=t.date(), target_date=tgt.date(), horizon=h,\n forecast=yv[i + h - 4], actual=yv[i + h], model=\"snaive\"))\nfcst = pd.DataFrame(rows).sort_values([\"model\", \"horizon\", \"origin_date\"])\nfcst.to_csv(O + \"forecasts.csv\", index=False)\nn_analysed = nobs # obs in last (2025Q3 origin) estimation regression\n\ndef err(mod, h):\n s = fcst[(fcst.model == mod) & (fcst.horizon == h)].sort_values(\"origin_date\")\n return (s.actual - s.forecast).values\n\ndef hac_se(d, L, kernel=\"bartlett\"):\n d = d - d.mean(); n = len(d)\n lrv = d @ d / n\n for k in range(1, L + 1):\n w = 1 - k / (L + 1) if kernel == \"bartlett\" else 1.0\n lrv += 2 * w * (d[k:] @ d[:-k]) / n\n return np.sqrt(lrv / n), lrv\n\nres = {\"task_id\": \"F3-conf-04\", \"model_name\": \"ar_seas_aic\",\n \"model_description\": (\"OLS autoregression of quarterly annualised inflation on a constant, \"\n \"three quarterly seasonal dummies and p own lags (p in 0..4 chosen by AIC at each origin on a \"\n \"common sample), estimated on an expanding window from 1995Q2 to the origin, with iterated \"\n \"multi-step forecasts (h=1,2,4) and known future seasonal dummies.\"),\n \"n_origins\": 40, \"first_origin\": str(origins[0].date()), \"last_origin\": str(origins[-1].date())}\nfor h in H:\n es, em = err(\"snaive\", h), err(\"ar_seas_aic\", h)\n res[f\"rmse_snaive_h{h}\"] = float(np.sqrt(np.mean(es ** 2)))\n res[f\"mae_snaive_h{h}\"] = float(np.mean(np.abs(es)))\n res[f\"rmse_model_h{h}\"] = float(np.sqrt(np.mean(em ** 2)))\n res[f\"mae_model_h{h}\"] = float(np.mean(np.abs(em)))\nfor h in H:\n res[f\"rel_improvement_rmse_h{h}\"] = 1 - res[f\"rmse_model_h{h}\"] / res[f\"rmse_snaive_h{h}\"]\n\nd = err(\"snaive\", 4) ** 2 - err(\"ar_seas_aic\", 4) ** 2\nL = 3\nse, _ = hac_se(d, L, \"bartlett\")\ndm = d.mean() / se\nres.update({\"loss_diff_mean_h4\": float(d.mean()), \"loss_diff_se_h4\": float(se),\n \"hac_lags_h4\": L, \"hac_kernel_h4\": \"bartlett\", \"dm_stat_h4\": float(dm),\n \"dm_pvalue_h4\": float(2 * stats.norm.sf(abs(dm))),\n \"feasibility\": \"complete\", \"feasibility_reason\": None, \"data_issues\": issues,\n \"n_input_rows\": n_rows, \"n_analysed\": int(n_analysed), \"random_seed\": None})\n\n# sensitivity (not required keys; stored separately)\nsens = {\"selected_lags_by_origin\": lags_used,\n \"derivation_check_max_abs_diff\": maxdiff}\nn = len(d)\nfor kern, lag in [(\"bartlett\", 4), (\"bartlett\", 6), (\"rectangular\", 3)]:\n s_, lrv = hac_se(d, lag, kern)\n sens[f\"{kern}_L{lag}\"] = {\"se\": float(s_) if lrv > 0 else None,\n \"dm\": float(d.mean() / s_) if lrv > 0 else None,\n \"p_norm\": float(2 * stats.norm.sf(abs(d.mean() / s_))) if lrv > 0 else None}\nhln = np.sqrt((n + 1 - 2 * 4 + 4 * 3 / n) / n)\nsens[\"hln_bartlett_L3\"] = {\"dm\": float(dm * hln), \"p_t39\": float(2 * stats.t.sf(abs(dm * hln), n - 1))}\nfor h in (1, 2):\n dh = err(\"snaive\", h) ** 2 - err(\"ar_seas_aic\", h) ** 2\n s_, _ = hac_se(dh, max(h - 1, 1))\n sens[f\"dm_h{h}_bartlett_L{max(h-1,1)}\"] = {\"mean\": float(dh.mean()), \"se\": float(s_),\n \"dm\": float(dh.mean() / s_), \"p_norm\": float(2 * stats.norm.sf(abs(dh.mean() / s_)))}\n# excluding 2021-2023 inflation surge targets\nfm = fcst[fcst.horizon == 4].copy()\nfm[\"td\"] = pd.to_datetime(fm.target_date)\nkeep = ~fm.td.between(\"2021-01-01\", \"2023-12-31\")\nfor mod in (\"snaive\", \"ar_seas_aic\"):\n s = fm[keep & (fm.model == mod)]\n sens[f\"rmse_h4_excl_2021_2023_{mod}\"] = float(np.sqrt(((s.actual - s.forecast) ** 2).mean()))\nsens[\"n_h4_excl_2021_2023\"] = int((keep & (fm.model == \"snaive\")).sum())\n\njson.dump(res, open(O + \"results.json\", \"w\"), indent=2)\njson.dump(sens, open(O + \"sensitivity.json\", \"w\"), indent=2)\nprint(json.dumps(res, indent=2)); print(json.dumps(sens, indent=2))\nEOF\n~/wp29/venv/bin/python 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> out/report.md <<'EOF'\n# F3-conf-04 — Multi-horizon forecasts of Canadian quarterly CPI inflation\n\n## Question\nOver 40 rolling origins (2015Q4–2025Q3), does a seasonal autoregression forecast Canadian quarterly CPI inflation (annualised, NSA) better than the seasonal-naive forecast at h = 1, 2, 4? And at h = 4, is the mean squared-error loss differential different from zero once we allow for the serial correlation that overlapping 4-step errors create?\n\n## Data and exclusions\n- `data/cpi_quarterly.csv`: 127 rows read (1995Q1–2026Q3). `data/cpi_monthly.csv`: 381 rows read. I used it only to check provenance: rebuilding `infl_annualised` from the monthly file matches the given series to within 5e-7.\n- The quarters run in an unbroken sequence and nothing is missing apart from 1995Q1 inflation, which cannot be computed because there is no earlier quarter. I dropped that row, so the usable series is 1995Q2 onward (126 observations).\n- Targets run from 2016Q1 to 2026Q3. Nothing else was excluded.\n\n## Method\n- **Model (`ar_seas_aic`)**: OLS of y_t on a constant, Q2/Q3/Q4 dummies and p own lags. At each origin p ∈ {0,…,4} is chosen by AIC, comparing all lag lengths on the same sample. The model is then re-estimated on all usable observations from 1995Q2 to the origin (expanding window). Multi-step forecasts are iterated, using the known seasonal dummies of the target quarters. Every estimation and selection step uses only quarters ≤ origin. AIC chose p = 2 for origins up to 2021Q3 and p = 1 after that. The last estimation sample has 121 observations.\n- **Seasonal naive**: the forecast for quarter t+h is y in quarter t+h−4.\n- **Metrics**: RMSE and MAE of the 40 errors per horizon, and relative RMSE improvement 1 − RMSE_model/RMSE_snaive.\n- **DM test at h = 4**: d_t = e²_snaive − e²_model. The standard error of d̄ uses a Newey–West (Bartlett kernel) long-run variance with truncation lag 3 (= h − 1), and the p-value is two-sided from N(0,1). I fixed this specification before seeing any results. Sensitivity checks are in `out/sensitivity.json`, which `analysis.py` also writes.\n\n## Results\n| h | RMSE snaive | RMSE model | MAE snaive | MAE model | rel. RMSE improvement |\n|---|---|---|---|---|---|\n| 1 | 2.849 | 2.193 | 2.137 | 1.519 | 0.230 |\n| 2 | 2.847 | 2.463 | 2.126 | 1.553 | 0.135 |\n| 4 | 2.882 | 2.343 | 2.181 | 1.597 | 0.187 |\n\n(Units: percentage points, annualised.) At all three horizons the model has lower RMSE and lower MAE than the seasonal-naive forecast.\n\nAt h = 4: d̄ = 2.818 squared pp, HAC SE = 2.086 (Bartlett, lag 3), DM = 1.35, two-sided p = 0.177. **The h = 4 improvement is not statistically distinguishable from zero at conventional levels.**\n\n## Uncertainty\n- How strong the h = 4 evidence looks depends on how the long-run variance is estimated:\n - Bartlett lag 4: DM 1.52, p = 0.13.\n - Rectangular lag 3: DM 1.66, p = 0.097.\n - Bartlett lag 6: DM 2.04, p = 0.041.\n - Harvey–Leybourne–Newbold small-sample correction with t(39): p = 0.23.\n- Only the longest lag (6) falls below 5%. That result is a post-hoc sensitivity check and should not replace the pre-specified test. With 40 overlapping errors the long-run variance is imprecisely estimated.\n- Descriptive DM tests at shorter horizons give p ≈ 0.10 at h = 1 and p ≈ 0.42 at h = 2.\n- The 2021–2023 inflation surge dominates the losses. Dropping h = 4 targets in 2021–2023 (28 origins remain) gives RMSE 2.03 for snaive and 1.52 for the model, so the model's ranking stays the same.\n\n## Limitations and open issues\n- I picked one model before looking at the evaluation results; I did not search over specifications. Other models might do better or worse.\n- Errors are computed on the current data vintage, so I make no claim about real-time performance. In reality the data are published about three weeks after quarter-end, and the CPI basket is periodically updated.\n- 40 origins is a small sample. The DM test relies on asymptotic approximations, and the standard error is sensitive to the kernel and lag choice.\n- The DM test treats forecasts as given. It does not adjust for parameter-estimation uncertainty, which is fine for comparing these particular forecasts (in the Giacomini–White sense).\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The seasonal AR model has lower out-of-sample RMSE than the seasonal-naive forecast at h=1, 2 and 4 (relative improvements 0.23, 0.13, 0.19).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_snaive_h1\",\"rmse_model_h2\",\"rmse_snaive_h2\",\"rmse_model_h4\",\"rmse_snaive_h4\",\"rel_improvement_rmse_h1\",\"rel_improvement_rmse_h2\",\"rel_improvement_rmse_h4\"],\"status\":\"supported\",\"caveat\":\"Point estimates over 40 origins; losses dominated by the 2021-2023 surge.\"},\n {\"id\":\"C2\",\"text\":\"The model also has lower MAE than seasonal naive at all three horizons.\",\"results_keys\":[\"mae_model_h1\",\"mae_snaive_h1\",\"mae_model_h2\",\"mae_snaive_h2\",\"mae_model_h4\",\"mae_snaive_h4\"],\"status\":\"supported\",\"caveat\":\"Descriptive only.\"},\n {\"id\":\"C3\",\"text\":\"At h=4 the mean squared-error loss differential (2.82) is not statistically distinguishable from zero using a Bartlett HAC SE with lag 3 (DM=1.35, p=0.18).\",\"results_keys\":[\"loss_diff_mean_h4\",\"loss_diff_se_h4\",\"hac_lags_h4\",\"hac_kernel_h4\",\"dm_stat_h4\",\"dm_pvalue_h4\"],\"status\":\"supported\",\"caveat\":\"Conclusion is sensitive to bandwidth: Bartlett lag 6 gives p=0.04 (post-hoc sensitivity); HLN correction gives p=0.23.\"}\n]\nEOF\n~/wp29/venv/bin/python out/analysis.py >/dev/null && md5sum out/results.json 2>/dev/null || md5 out/results.json"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":301,"cache_read_input_tokens":11813,"output_tokens":2476,"output_tokens_details":{"thinking_tokens":0},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":301},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXnaim6Uoov2y5XpT9TH","requestRef":"5c451435-fd6b-4b02-a7fe-1ce852f6dbff","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6d992342-0a0e-44e4-bf1f-599b6df96369","timestamp":"2026-10-30T04:25:47.407Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0083","sessionId":"814de002-3f98-485a-bc50-5a0ac58ebbfe","version":"2.1.314","gitBranch":"HEAD"}35{"parentUuid":"6d992342-0a0e-44e4-bf1f-599b6df96369","isSidechain":false,"promptId":"d0ce3eab-219a-43dd-b949-c1a2dd555006","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_011G3WJUPsxXNirqqyERzn8H","type":"tool_result","content":"d7907b52ac880962a7c91ee70b79ad9a out/results.json","is_error":false}]},"uuid":"1c330fb9-88df-4789-a6fb-b1c27179cde8","timestamp":"2026-10-30T04:25:48.336Z","toolUseResult":{"stdout":"d7907b52ac880962a7c91ee70b79ad9a out/results.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"6d992342-0a0e-44e4-bf1f-599b6df96369","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0083","sessionId":"814de002-3f98-485a-bc50-5a0ac58ebbfe","version":"2.1.314","gitBranch":"HEAD"}36{"type":"api-request-blob","sessionId":"814de002-3f98-485a-bc50-5a0ac58ebbfe","hash":"6eba23095a59af235d4d408dcbfb4fde91e2b6c343e1ff7b8866d0a4c16150dc","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_011G3WJUPsxXNirqqyERzn8H","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F3-conf-04 — Multi-horizon forecasts of Canadian quarterly CPI inflation\n\n## Question\nOver 40 rolling origins (2015Q4–2025Q3), does a seasonal autoregression forecast Canadian quarterly CPI inflation (annualised, NSA) better than the seasonal-naive forecast at h = 1, 2, 4? And at h = 4, is the mean squared-error loss differential different from zero once we allow for the serial correlation that overlapping 4-step errors create?\n\n## Data and exclusions\n- `data/cpi_quarterly.csv`: 127 rows read (1995Q1–2026Q3). `data/cpi_monthly.csv`: 381 rows read. I used it only to check provenance: rebuilding `infl_annualised` from the monthly file matches the given series to within 5e-7.\n- The quarters run in an unbroken sequence and nothing is missing apart from 1995Q1 inflation, which cannot be computed because there is no earlier quarter. I dropped that row, so the usable series is 1995Q2 onward (126 observations).\n- Targets run from 2016Q1 to 2026Q3. Nothing else was excluded.\n\n## Method\n- **Model (`ar_seas_aic`)**: OLS of y_t on a constant, Q2/Q3/Q4 dummies and p own lags. At each origin p ∈ {0,…,4} is chosen by AIC, comparing all lag lengths on the same sample. The model is then re-estimated on all usable observations from 1995Q2 to the origin (expanding window). Multi-step forecasts are iterated, using the known seasonal dummies of the target quarters. Every estimation and selection step uses only quarters ≤ origin. AIC chose p = 2 for origins up to 2021Q3 and p = 1 after that. The last estimation sample has 121 observations.\n- **Seasonal naive**: the forecast for quarter t+h is y in quarter t+h−4.\n- **Metrics**: RMSE and MAE of the 40 errors per horizon, and relative RMSE improvement 1 − RMSE_model/RMSE_snaive.\n- **DM test at h = 4**: d_t = e²_snaive − e²_model. The standard error of d̄ uses a Newey–West (Bartlett kernel) long-run variance with truncation lag 3 (= h − 1), and the p-value is two-sided from N(0,1). I fixed this specification before seeing any results. Sensitivity checks are in `out/sensitivity.json`, which `analysis.py` also writes.\n\n## Results\n| h | RMSE snaive | RMSE model | MAE snaive | MAE model | rel. RMSE improvement |\n|---|---|---|---|---|---|\n| 1 | 2.849 | 2.193 | 2.137 | 1.519 | 0.230 |\n| 2 | 2.847 | 2.463 | 2.126 | 1.553 | 0.135 |\n| 4 | 2.882 | 2.343 | 2.181 | 1.597 | 0.187 |\n\n(Units: percentage points, annualised.) At all three horizons the model has lower RMSE and lower MAE than the seasonal-naive forecast.\n\nAt h = 4: d̄ = 2.818 squared pp, HAC SE = 2.086 (Bartlett, lag 3), DM = 1.35, two-sided p = 0.177. **The h = 4 improvement is not statistically distinguishable from zero at conventional levels.**\n\n## Uncertainty\n- How strong the h = 4 evidence looks depends on how the long-run variance is estimated:\n - Bartlett lag 4: DM 1.52, p = 0.13.\n - Rectangular lag 3: DM 1.66, p = 0.097.\n - Bartlett lag 6: DM 2.04, p = 0.041.\n - Harvey–Leybourne–Newbold small-sample correction with t(39): p = 0.23.\n- Only the longest lag (6) falls below 5%. That result is a post-hoc sensitivity check and should not replace the pre-specified test. With 40 overlapping errors the long-run variance is imprecisely estimated.\n- Descriptive DM tests at shorter horizons give p ≈ 0.10 at h = 1 and p ≈ 0.42 at h = 2.\n- The 2021–2023 inflation surge dominates the losses. Dropping h = 4 targets in 2021–2023 (28 origins remain) gives RMSE 2.03 for snaive and 1.52 for the model, so the model's ranking stays the same.\n\n## Limitations and open issues\n- I picked one model before looking at the evaluation results; I did not search over specifications. Other models might do better or worse.\n- Errors are computed on the current data vintage, so I make no claim about real-time performance. In reality the data are published about three weeks after quarter-end, and the CPI basket is periodically updated.\n- 40 origins is a small sample. The DM test relies on asymptotic approximations, and the standard error is sensitive to the kernel and lag choice.\n- The DM test treats forecasts as given. It does not adjust for parameter-estimation uncertainty, which is fine for comparing these particular forecasts (in the Giacomini–White sense).\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The seasonal AR model has lower out-of-sample RMSE than the seasonal-naive forecast at h=1, 2 and 4 (relative improvements 0.23, 0.13, 0.19).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_snaive_h1\",\"rmse_model_h2\",\"rmse_snaive_h2\",\"rmse_model_h4\",\"rmse_snaive_h4\",\"rel_improvement_rmse_h1\",\"rel_improvement_rmse_h2\",\"rel_improvement_rmse_h4\"],\"status\":\"supported\",\"caveat\":\"Point estimates over 40 origins; losses dominated by the 2021-2023 surge.\"},\n {\"id\":\"C2\",\"text\":\"The model also has lower MAE than seasonal naive at all three horizons.\",\"results_keys\":[\"mae_model_h1\",\"mae_snaive_h1\",\"mae_model_h2\",\"mae_snaive_h2\",\"mae_model_h4\",\"mae_snaive_h4\"],\"status\":\"supported\",\"caveat\":\"Descriptive only.\"},\n {\"id\":\"C3\",\"text\":\"At h=4 the mean squared-error loss differential (2.82) is not statistically distinguishable from zero using a Bartlett HAC SE with lag 3 (DM=1.35, p=0.18).\",\"results_keys\":[\"loss_diff_mean_h4\",\"loss_diff_se_h4\",\"hac_lags_h4\",\"hac_kernel_h4\",\"dm_stat_h4\",\"dm_pvalue_h4\"],\"status\":\"supported\",\"caveat\":\"Conclusion is sensitive to bandwidth: Bartlett lag 6 gives p=0.04 (post-hoc sensitivity); 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At the 4-quarter horizon, though, the gain is not statistically distinguishable from zero once the overlapping errors are accounted for (p = 0.177). All required files are in `out/`, and re-running `out/analysis.py` gave identical results.\n\n**The model (`ar_seas_aic`):** a least-squares regression of inflation on a constant, quarterly seasonal dummies and 0–4 of its own past values. At each origin the number of past values is chosen by AIC (a standard fit criterion). Each origin re-fits the model using only data up to that origin, and longer horizons are built by chaining one-step forecasts. I chose this one model before seeing any results and did not try alternatives.\n\n| Horizon | RMSE, seasonal naive | RMSE, model | RMSE improvement | MAE, seasonal naive | MAE, model |\n|---|---|---|---|---|---|\n| 1 quarter | 2.85 | 2.19 | 23% | 2.14 | 1.52 |\n| 2 quarters | 2.85 | 2.46 | 13% | 2.13 | 1.55 |\n| 4 quarters | 2.88 | 2.34 | 19% | 2.18 | 1.60 |\n\nErrors are in percentage points of annualised inflation.\n\n**Test at 4 quarters:**\n- **Main result:** the average loss difference in the model's favour is 2.82 (squared percentage points), with a standard error of 2.09. That gives a test statistic of 1.35 and p = 0.177.\n- **Specification:** the standard error uses a Newey–West estimator (Bartlett kernel) with a lag of 3, the minimum the task allows. I fixed this before seeing results.\n- **Sensitivity:** the conclusion depends on how the standard error is computed:\n\n| Alternative | p-value |\n|---|---|\n| Lag 4 | 0.13 |\n| Equal weighting of lags (rectangular kernel), lag 3 | 0.097 |\n| Small-sample correction (Harvey–Leybourne–Newbold) | 0.23 |\n| Lag 6 | 0.041 |\n\n Lag 6 is the only version below 5%, and it was a check I added afterwards, so it shouldn't replace the main result.\n- **2021–2023:** the inflation surge accounts for much of the error. Dropping those target quarters leaves 28 origins, and the model still does better (RMSE 1.52 vs 2.03).\n\n**Data:** the only gap is the missing 1995Q1 inflation value (there is no earlier quarter), so the series starts in 1995Q2. 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