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In the current working directory, `TASK.md` describes a bounded scientific task and the directory `out/` contains the deliverables submitted by another assistant (you have not seen how they were produced and you must not look for their working transcript). There is no network access. Use `~/wp29/venv/bin/python` if you need to re-run or test code. Do not modify any file under `out/` except that you must create `out/review/review.json`.\n\nReview the deliverables against `TASK.md` only. Specifically check:\n1. Does `out/results.json` contain every required key with legitimately computed values? Re-run `out/analysis.py` in a scratch copy if needed and compare.\n2. Are the information-availability rules of `TASK.md` respected by the code (for example no use of future information, no use of forbidden inputs)? Read the code to verify; do not trust the report.\n3. 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The estimands are the out-of-sample root-mean-squared error (RMSE) and mean absolute error (MAE) of (a) the naive forecast and (b) one model of your choice, computed over a fixed set of rolling (expanding-window) forecast origins, and the relative improvement of the model over the naive forecast, 1 − RMSE_model / RMSE_naive, at each horizon.\n\n## Inputs\n- `data/UNRATE.csv` — observed data: US unemployment rate (percent, seasonally adjusted, monthly), FRED series UNRATE (source BLS), retrieved 2026-10-30 (UTC) from https://fred.stlouisfed.org/graph/fredgraph.csv?id=UNRATE, exactly as served (header `observation_date,UNRATE`, one row per month dated YYYY-MM-01, 1948-01 to 2026-09). Missing observations appear as an empty value field. This is the current (final) vintage; see `data/README.md` for provenance, SHA-256 and terms.\n\n## Information-availability rules\n- Forecast origins: the 36 months t = 2023-07-01, 2023-08-01, …, 2026-06-01 (the `observation_date` of the origin month). Horizons h ∈ {1, 3} months; the target of origin t at horizon h is the month t + h.\n- A forecast made at origin t may use only observations dated ≤ t (expanding window: the training sample grows with t). Model selection, parameter estimation and any transformation (e.g. differencing, scaling) must use only observations dated ≤ t.\n- Naive baseline: the forecast for every horizon is the most recent available observation dated ≤ t (if the origin month itself is missing, use the latest earlier observation).\n- If the actual value at a target month is missing in the data, that (origin, horizon) pair still appears in the forecast ledger with an empty `actual`, but is excluded from all error statistics; report the number of evaluated pairs per horizon.\n- The evaluation errors are computed on the data as given (final vintage); do not claim real-time validity.\n\n## Required outputs\n- `out/forecasts.csv` — the forecast ledger, one row per (origin, horizon, model), with columns `origin_date` (YYYY-MM-DD), `target_date` (YYYY-MM-DD), `horizon` (integer), `forecast` (number), `actual` (number, empty if missing), `model` (string: `naive` for the baseline, and the value of `model_name` for your model). Expected: 36 origins × 2 horizons × 2 models = 144 rows.\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F3-dev-01\" |\n| `model_name` | string | — | short name of your model (e.g. \"AR2_diff\"), used in the `model` column |\n| `model_description` | string | — | one-sentence specification (lags, transformation, estimation sample start, estimation method) |\n| `n_origins` | integer | — | number of forecast origins (36) |\n| `first_origin`, `last_origin` | string | date | first and last origin dates |\n| `n_evaluated_h1`, `n_evaluated_h3` | integer | — | (origin, horizon) pairs with a non-missing actual, per horizon |\n| `rmse_naive_h1`, `mae_naive_h1`, `rmse_naive_h3`, `mae_naive_h3` | number | percentage points | naive-forecast errors per horizon |\n| `rmse_model_h1`, `mae_model_h1`, `rmse_model_h3`, `mae_model_h3` | number | percentage points | your model's errors per horizon |\n| `rel_improvement_rmse_h1`, `rel_improvement_rmse_h3` | number | fraction | 1 − rmse_model / rmse_naive (negative if the model is worse) |\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 | — | {\"UNRATE.csv\": number of data rows read, excluding the header} |\n| `n_analysed` | integer | — | observations used in the last training window |\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.\ntotal 72\ndrwxr-xr-x 10 simon-pierreboucher staff 320 oct. 30 00:01 .\ndrwxr-xr-x 7 simon-pierreboucher staff 224 oct. 29 23:59 ..\n-rw-r--r-- 1 simon-pierreboucher staff 6779 oct. 30 00:00 analysis.py\n-rw-r--r-- 1 simon-pierreboucher staff 1405 oct. 30 00:01 claims.json\n-rw-r--r-- 1 simon-pierreboucher staff 280 oct. 30 00:00 exclusions.csv\n-rw-r--r-- 1 simon-pierreboucher staff 7150 oct. 30 00:00 forecasts.csv\n-rw-r--r-- 1 simon-pierreboucher staff 5575 oct. 30 00:01 report.md\n-rw-r--r-- 1 simon-pierreboucher staff 2268 oct. 30 00:00 results.json\ndrwxr-xr-x 2 simon-pierreboucher staff 64 oct. 30 00:01 review\ndrwxr-xr-x 8 simon-pierreboucher staff 256 oct. 30 00:01 state\n{\n \"task_id\": \"F3-dev-01\",\n \"model_name\": \"AR2_diff\",\n \"model_description\": \"AR(2) with intercept on monthly first differences of UNRATE, estimated by OLS on an expanding window starting 1948-01 (regression rows touching missing values dropped), re-estimated at every origin; level forecasts by iterating the difference recursion.\",\n \"n_origins\": 36,\n \"first_origin\": \"2023-07-01\",\n \"last_origin\": \"2026-06-01\",\n \"n_evaluated_h1\": 35,\n \"rmse_naive_h1\": 0.11710800875382403,\n \"mae_naive_h1\": 0.09142857142857148,\n \"rmse_model_h1\": 0.11985758089022913,\n \"mae_model_h1\": 0.09565582574189531,\n \"n_evaluated_h3\": 35,\n \"rmse_naive_h3\": 0.15856499343441843,\n \"mae_naive_h3\": 0.12000000000000005,\n \"rmse_model_h3\": 0.15977032355322282,\n \"mae_model_h3\": 0.12128483318799818,\n \"rel_improvement_rmse_h1\": -0.023478941924331087,\n \"rel_improvement_rmse_h3\": -0.007601489412623064,\n \"dm_stat_h1\": 2.5036162781392184,\n \"dm_pvalue_h1\": 0.017257584632766314,\n \"mean_loss_diff_h1\": 0.000651553982572098,\n \"dm_stat_h3\": 1.3581793864758895,\n \"dm_pvalue_h3\": 0.18335155056438499,\n \"mean_loss_diff_h3\": 0.0003836991454443411,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"Missing UNRATE value(s) at 2025-10-01 (empty field).\",\n \"handling\": \"Origin 2025-10-01: naive uses 2025-09 value; AR forecasts iterated from last observed month (2025-09). Pairs with missing target (origin 2025-09 h1, origin 2025-07 h3) kept in ledger with empty actual and excluded from error statistics. In later training windows, regression rows touching the missing month are dropped; the forecasting state uses linear interpolation between observations dated <= origin.\"\n },\n {\n \"issue\": \"Final (revised) vintage, not real-time data.\",\n \"handling\": \"Errors measure forecastability of the revised series; no real-time validity claimed.\"\n },\n {\n \"issue\": \"COVID-19 spike 2020-03..2020-05 (4.4 -> 14.8 -> 13.2) inside every training window.\",\n \"handling\": \"Kept as genuine data; no outlier treatment (specification fixed a priori, not tuned on test errors).\"\n }\n ],\n \"n_input_rows\": {\n \"UNRATE.csv\": 945\n },\n \"n_analysed\": 941,\n \"n_regression_rows_last_window\": 935,\n \"random_seed\": null\n}[\n {\"id\":\"C1\",\"text\":\"At h=1 the AR2_diff model does not beat the naive forecast: its RMSE and MAE are higher (relative RMSE improvement -0.023).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_naive_h1\",\"mae_model_h1\",\"mae_naive_h1\",\"rel_improvement_rmse_h1\",\"n_evaluated_h1\"],\"status\":\"supported\",\"caveat\":\"35 evaluated pairs; final-vintage data; single a-priori specification.\"},\n {\"id\":\"C2\",\"text\":\"At h=3 the AR2_diff model does not beat the naive forecast: its RMSE and MAE are slightly higher (relative RMSE improvement -0.008).\",\"results_keys\":[\"rmse_model_h3\",\"rmse_naive_h3\",\"mae_model_h3\",\"mae_naive_h3\",\"rel_improvement_rmse_h3\",\"n_evaluated_h3\"],\"status\":\"supported\",\"caveat\":\"35 overlapping 3-month-ahead errors; final-vintage data.\"},\n {\"id\":\"C3\",\"text\":\"The h=1 loss difference is statistically significant at 5% (DM p=0.017, model worse); the h=3 difference is not (p=0.18).\",\"results_keys\":[\"dm_stat_h1\",\"dm_pvalue_h1\",\"mean_loss_diff_h1\",\"dm_stat_h3\",\"dm_pvalue_h3\",\"mean_loss_diff_h3\"],\"status\":\"supported\",\"caveat\":\"Approximate small-sample DM test; the magnitude of the difference is economically negligible.\"},\n {\"id\":\"C4\",\"text\":\"One missing observation (2025-10-01) reduces evaluated pairs to 35 per horizon; 941 observations are in the last training window.\",\"results_keys\":[\"n_evaluated_h1\",\"n_evaluated_h3\",\"n_analysed\",\"n_input_rows\",\"data_issues\"],\"status\":\"supported\",\"caveat\":\"\"}\n]","is_error":false}]},"uuid":"203b6974-04f2-4026-a677-7e00207fa509","timestamp":"2026-10-30T04:01:47.736Z","toolUseResult":{"stdout":"# F3-dev-01 — Rolling-origin forecasts of the US unemployment rate: can a simple time-series model beat the naive forecast?\n\n## Scientific question\nOver the last three years, does a simple autoregressive-type model forecast the US civilian unemployment rate better than the naive (no-change) forecast at one- and three-month horizons? The estimands are the out-of-sample root-mean-squared error (RMSE) and mean absolute error (MAE) of (a) the naive forecast and (b) one model of your choice, computed over a fixed set of rolling (expanding-window) forecast origins, and the relative improvement of the model over the naive forecast, 1 − RMSE_model / RMSE_naive, at each horizon.\n\n## Inputs\n- `data/UNRATE.csv` — observed data: US unemployment rate (percent, seasonally adjusted, monthly), FRED series UNRATE (source BLS), retrieved 2026-10-30 (UTC) from https://fred.stlouisfed.org/graph/fredgraph.csv?id=UNRATE, exactly as served (header `observation_date,UNRATE`, one row per month dated YYYY-MM-01, 1948-01 to 2026-09). Missing observations appear as an empty value field. This is the current (final) vintage; see `data/README.md` for provenance, SHA-256 and terms.\n\n## Information-availability rules\n- Forecast origins: the 36 months t = 2023-07-01, 2023-08-01, …, 2026-06-01 (the `observation_date` of the origin month). Horizons h ∈ {1, 3} months; the target of origin t at horizon h is the month t + h.\n- A forecast made at origin t may use only observations dated ≤ t (expanding window: the training sample grows with t). Model selection, parameter estimation and any transformation (e.g. differencing, scaling) must use only observations dated ≤ t.\n- Naive baseline: the forecast for every horizon is the most recent available observation dated ≤ t (if the origin month itself is missing, use the latest earlier observation).\n- If the actual value at a target month is missing in the data, that (origin, horizon) pair still appears in the forecast ledger with an empty `actual`, but is excluded from all error statistics; report the number of evaluated pairs per horizon.\n- The evaluation errors are computed on the data as given (final vintage); do not claim real-time validity.\n\n## Required outputs\n- `out/forecasts.csv` — the forecast ledger, one row per (origin, horizon, model), with columns `origin_date` (YYYY-MM-DD), `target_date` (YYYY-MM-DD), `horizon` (integer), `forecast` (number), `actual` (number, empty if missing), `model` (string: `naive` for the baseline, and the value of `model_name` for your model). Expected: 36 origins × 2 horizons × 2 models = 144 rows.\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F3-dev-01\" |\n| `model_name` | string | — | short name of your model (e.g. \"AR2_diff\"), used in the `model` column |\n| `model_description` | string | — | one-sentence specification (lags, transformation, estimation sample start, estimation method) |\n| `n_origins` | integer | — | number of forecast origins (36) |\n| `first_origin`, `last_origin` | string | date | first and last origin dates |\n| `n_evaluated_h1`, `n_evaluated_h3` | integer | — | (origin, horizon) pairs with a non-missing actual, per horizon |\n| `rmse_naive_h1`, `mae_naive_h1`, `rmse_naive_h3`, `mae_naive_h3` | number | percentage points | naive-forecast errors per horizon |\n| `rmse_model_h1`, `mae_model_h1`, `rmse_model_h3`, `mae_model_h3` | number | percentage points | your model's errors per horizon |\n| `rel_improvement_rmse_h1`, `rel_improvement_rmse_h3` | number | fraction | 1 − rmse_model / rmse_naive (negative if the model is worse) |\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 | — | {\"UNRATE.csv\": number of data rows read, excluding the header} |\n| `n_analysed` | integer | — | observations used in the last training window |\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.\ntotal 72\ndrwxr-xr-x 10 simon-pierreboucher staff 320 oct. 30 00:01 .\ndrwxr-xr-x 7 simon-pierreboucher staff 224 oct. 29 23:59 ..\n-rw-r--r-- 1 simon-pierreboucher staff 6779 oct. 30 00:00 analysis.py\n-rw-r--r-- 1 simon-pierreboucher staff 1405 oct. 30 00:01 claims.json\n-rw-r--r-- 1 simon-pierreboucher staff 280 oct. 30 00:00 exclusions.csv\n-rw-r--r-- 1 simon-pierreboucher staff 7150 oct. 30 00:00 forecasts.csv\n-rw-r--r-- 1 simon-pierreboucher staff 5575 oct. 30 00:01 report.md\n-rw-r--r-- 1 simon-pierreboucher staff 2268 oct. 30 00:00 results.json\ndrwxr-xr-x 2 simon-pierreboucher staff 64 oct. 30 00:01 review\ndrwxr-xr-x 8 simon-pierreboucher staff 256 oct. 30 00:01 state\n{\n \"task_id\": \"F3-dev-01\",\n \"model_name\": \"AR2_diff\",\n \"model_description\": \"AR(2) with intercept on monthly first differences of UNRATE, estimated by OLS on an expanding window starting 1948-01 (regression rows touching missing values dropped), re-estimated at every origin; level forecasts by iterating the difference recursion.\",\n \"n_origins\": 36,\n \"first_origin\": \"2023-07-01\",\n \"last_origin\": \"2026-06-01\",\n \"n_evaluated_h1\": 35,\n \"rmse_naive_h1\": 0.11710800875382403,\n \"mae_naive_h1\": 0.09142857142857148,\n \"rmse_model_h1\": 0.11985758089022913,\n \"mae_model_h1\": 0.09565582574189531,\n \"n_evaluated_h3\": 35,\n \"rmse_naive_h3\": 0.15856499343441843,\n \"mae_naive_h3\": 0.12000000000000005,\n \"rmse_model_h3\": 0.15977032355322282,\n \"mae_model_h3\": 0.12128483318799818,\n \"rel_improvement_rmse_h1\": -0.023478941924331087,\n \"rel_improvement_rmse_h3\": -0.007601489412623064,\n \"dm_stat_h1\": 2.5036162781392184,\n \"dm_pvalue_h1\": 0.017257584632766314,\n \"mean_loss_diff_h1\": 0.000651553982572098,\n \"dm_stat_h3\": 1.3581793864758895,\n \"dm_pvalue_h3\": 0.18335155056438499,\n \"mean_loss_diff_h3\": 0.0003836991454443411,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"Missing UNRATE value(s) at 2025-10-01 (empty field).\",\n \"handling\": \"Origin 2025-10-01: naive uses 2025-09 value; AR forecasts iterated from last observed month (2025-09). Pairs with missing target (origin 2025-09 h1, origin 2025-07 h3) kept in ledger with empty actual and excluded from error statistics. In later training windows, regression rows touching the missing month are dropped; the forecasting state uses linear interpolation between observations dated <= origin.\"\n },\n {\n \"issue\": \"Final (revised) vintage, not real-time data.\",\n \"handling\": \"Errors measure forecastability of the revised series; no real-time validity claimed.\"\n },\n {\n \"issue\": \"COVID-19 spike 2020-03..2020-05 (4.4 -> 14.8 -> 13.2) inside every training window.\",\n \"handling\": \"Kept as genuine data; no outlier treatment (specification fixed a priori, not tuned on test errors).\"\n }\n ],\n \"n_input_rows\": {\n \"UNRATE.csv\": 945\n },\n \"n_analysed\": 941,\n \"n_regression_rows_last_window\": 935,\n \"random_seed\": null\n}[\n {\"id\":\"C1\",\"text\":\"At h=1 the AR2_diff model does not beat the naive forecast: its RMSE and MAE are higher (relative RMSE improvement -0.023).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_naive_h1\",\"mae_model_h1\",\"mae_naive_h1\",\"rel_improvement_rmse_h1\",\"n_evaluated_h1\"],\"status\":\"supported\",\"caveat\":\"35 evaluated pairs; final-vintage data; single a-priori specification.\"},\n {\"id\":\"C2\",\"text\":\"At h=3 the AR2_diff model does not beat the naive forecast: its RMSE and MAE are slightly higher (relative RMSE improvement -0.008).\",\"results_keys\":[\"rmse_model_h3\",\"rmse_naive_h3\",\"mae_model_h3\",\"mae_naive_h3\",\"rel_improvement_rmse_h3\",\"n_evaluated_h3\"],\"status\":\"supported\",\"caveat\":\"35 overlapping 3-month-ahead errors; final-vintage data.\"},\n {\"id\":\"C3\",\"text\":\"The h=1 loss difference is statistically significant at 5% (DM p=0.017, model worse); the h=3 difference is not (p=0.18).\",\"results_keys\":[\"dm_stat_h1\",\"dm_pvalue_h1\",\"mean_loss_diff_h1\",\"dm_stat_h3\",\"dm_pvalue_h3\",\"mean_loss_diff_h3\"],\"status\":\"supported\",\"caveat\":\"Approximate small-sample DM test; the magnitude of the difference is economically negligible.\"},\n {\"id\":\"C4\",\"text\":\"One missing observation (2025-10-01) reduces evaluated pairs to 35 per horizon; 941 observations are in the last training window.\",\"results_keys\":[\"n_evaluated_h1\",\"n_evaluated_h3\",\"n_analysed\",\"n_input_rows\",\"data_issues\"],\"status\":\"supported\",\"caveat\":\"\"}\n]","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"8c9e6a98-bf86-42d6-bab6-0f6b531cc0d2","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0023","sessionId":"3c0817b8-c7e8-47f1-b003-1b4f1c3b06c0","version":"2.1.314","gitBranch":"HEAD"}15{"type":"api-request-blob","sessionId":"3c0817b8-c7e8-47f1-b003-1b4f1c3b06c0","hash":"ff8b4023217dbfe2fe7f34b34fc69763086e8e8612622def59617925a79945e2","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01QwydmBt2Gv7W4VC9UADaY3","name":"Bash","input":{"command":"cat TASK.md; 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writes out/results.json, out/forecasts.csv, out/exclusions.csv. No randomness.\"\"\"\nimport json, os\nimport numpy as np, pandas as pd\nfrom scipy import stats\n\nDATA = \"data/UNRATE.csv\"; OUT = \"out\"\nP = 2 # AR order on first differences (fixed a priori)\nHORIZONS = [1, 3]\nMODEL = \"AR2_diff\"\norigins = pd.date_range(\"2023-07-01\", \"2026-06-01\", freq=\"MS\")\n\nraw = pd.read_csv(DATA, dtype={\"observation_date\": str})\nn_raw = len(raw)\nraw[\"date\"] = pd.to_datetime(raw[\"observation_date\"], format=\"%Y-%m-%d\")\ny = raw.set_index(\"date\")[\"UNRATE\"].astype(float)\nassert y.index.is_monotonic_increasing and not y.index.duplicated().any()\nassert (y.index == pd.date_range(y.index[0], y.index[-1], freq=\"MS\")).all()\nmissing_dates = [d.strftime(\"%Y-%m-%d\") for d in y.index[y.isna()]]\n\ndef ar_forecast(s, steps):\n \"\"\"s: series with obs dated <= origin (may contain NaN). Returns forecasts 1..steps months\n ahead of the last *observed* month.\"\"\"\n s = s.loc[:s.last_valid_index()]\n d = s.diff()\n X = pd.concat({f\"l{i}\": d.shift(i) for i in range(1, P + 1)}, axis=1)\n reg = pd.concat([d.rename(\"y\"), X], axis=1).dropna() # drop rows touching missing values\n A = np.column_stack([np.ones(len(reg)), reg[[f\"l{i}\" for i in range(1, P + 1)]].values])\n beta, *_ = np.linalg.lstsq(A, reg[\"y\"].values, rcond=None)\n # forecasting state: interior missing values linearly interpolated using only obs <= origin\n si = s.interpolate(method=\"linear\", limit_area=\"inside\")\n lags = list(si.diff().values[-P:][::-1]) # [d_T, d_{T-1}]\n level, out = si.values[-1], []\n for _ in range(steps):\n dhat = beta[0] + np.dot(beta[1:], lags[:P])\n level += dhat; out.append(level); lags = [dhat] + lags[:P - 1]\n return np.array(out), len(reg)\n\nrows = []\nfor t in origins:\n s = y.loc[:t] # information rule: only obs dated <= t\n last_obs = s.last_valid_index()\n gap = (t.year - last_obs.year) * 12 + (t.month - last_obs.month) # months origin is ahead of last obs\n fc, nreg = ar_forecast(s, gap + max(HORIZONS))\n for h in HORIZONS:\n tgt = t + pd.DateOffset(months=h)\n act = y.get(tgt, np.nan)\n rows.append(dict(origin_date=t.strftime(\"%Y-%m-%d\"), target_date=tgt.strftime(\"%Y-%m-%d\"),\n horizon=h, forecast=float(s.loc[last_obs]), actual=act, model=\"naive\"))\n rows.append(dict(origin_date=t.strftime(\"%Y-%m-%d\"), target_date=tgt.strftime(\"%Y-%m-%d\"),\n horizon=h, forecast=float(fc[gap + h - 1]), actual=act, model=MODEL))\nfc_df = pd.DataFrame(rows)\nfc_df.to_csv(f\"{OUT}/forecasts.csv\", index=False, float_format=\"%.6f\")\n\nres = {\"task_id\": \"F3-dev-01\", \"model_name\": MODEL,\n \"model_description\": (\"AR(2) with intercept on monthly first differences of UNRATE, estimated by OLS on an \"\n \"expanding window starting 1948-01 (regression rows touching missing values dropped), \"\n \"re-estimated at every origin; level forecasts by iterating the difference recursion.\"),\n \"n_origins\": len(origins), \"first_origin\": origins[0].strftime(\"%Y-%m-%d\"),\n \"last_origin\": origins[-1].strftime(\"%Y-%m-%d\")}\ndm = {}\nfor h in HORIZONS:\n sub = fc_df[fc_df.horizon == h]\n ev = sub.dropna(subset=[\"actual\"])\n e = {m: (ev[ev.model == m].set_index(\"origin_date\")[\"actual\"] - ev[ev.model == m].set_index(\"origin_date\")[\"forecast\"])\n for m in [\"naive\", MODEL]}\n n = len(e[\"naive\"]); assert n == len(e[MODEL])\n res[f\"n_evaluated_h{h}\"] = int(n)\n for m, tag in [(\"naive\", \"naive\"), (MODEL, \"model\")]:\n res[f\"rmse_{tag}_h{h}\"] = float(np.sqrt(np.mean(e[m] ** 2)))\n res[f\"mae_{tag}_h{h}\"] = float(np.mean(np.abs(e[m])))\n # Diebold-Mariano (squared loss), HAC variance with h-1 Bartlett-free (rectangular) lags, HLN small-sample correction\n dl = (e[MODEL] ** 2 - e[\"naive\"] ** 2).values\n dbar = dl.mean(); dc = dl - dbar\n gam = [np.sum(dc[k:] * dc[:n - k]) / n for k in range(h)]\n var = (gam[0] + 2 * sum(gam[1:])) / n\n if var <= 0: var = gam[0] / n\n hln = np.sqrt((n + 1 - 2 * h + h * (h - 1) / n) / n)\n stat = hln * dbar / np.sqrt(var)\n dm[h] = (float(stat), float(2 * stats.t.sf(abs(stat), df=n - 1)), float(dbar))\nfor h in HORIZONS:\n res[f\"rel_improvement_rmse_h{h}\"] = 1 - res[f\"rmse_model_h{h}\"] / res[f\"rmse_naive_h{h}\"]\nfor h in HORIZONS:\n res[f\"dm_stat_h{h}\"], res[f\"dm_pvalue_h{h}\"], res[f\"mean_loss_diff_h{h}\"] = dm[h]\nres.update({\n \"feasibility\": \"complete\", \"feasibility_reason\": None,\n \"data_issues\": [\n {\"issue\": f\"Missing UNRATE value(s) at {', '.join(missing_dates)} (empty field).\",\n \"handling\": \"Origin 2025-10-01: naive uses 2025-09 value; AR forecasts iterated from last observed month (2025-09). \"\n \"Pairs with missing target (origin 2025-09 h1, origin 2025-07 h3) kept in ledger with empty actual and \"\n \"excluded from error statistics. In later training windows, regression rows touching the missing month are \"\n \"dropped; the forecasting state uses linear interpolation between observations dated <= origin.\"},\n {\"issue\": \"Final (revised) vintage, not real-time data.\",\n \"handling\": \"Errors measure forecastability of the revised series; no real-time validity claimed.\"},\n {\"issue\": \"COVID-19 spike 2020-03..2020-05 (4.4 -> 14.8 -> 13.2) inside every training window.\",\n \"handling\": \"Kept as genuine data; no outlier treatment (specification fixed a priori, not tuned on test errors).\"}],\n \"n_input_rows\": {\"UNRATE.csv\": int(n_raw)},\n})\nlast_win = y.loc[:origins[-1]]\nres[\"n_analysed\"] = int(last_win.notna().sum())\nres[\"n_regression_rows_last_window\"] = int(ar_forecast(last_win, 1)[1])\nres[\"random_seed\"] = None\nwith open(f\"{OUT}/results.json\", \"w\") as f:\n json.dump(res, f, indent=2)\n\n# exclusion ledger (training data for the last window)\nn1 = int(y.notna().sum()); n2 = res[\"n_analysed\"]\npd.DataFrame([\n dict(step=1, rule=\"drop rows with missing UNRATE\", n_before=n_raw, n_after=n1, n_removed=n_raw - n1,\n rationale=\"value not available (2025-10-01)\"),\n dict(step=2, rule=\"drop observations dated after last origin 2026-06-01\", n_before=n1, n_after=n2, n_removed=n1 - n2,\n rationale=\"information rule: training only on obs <= origin (these are used only as evaluation actuals)\"),\n]).to_csv(f\"{OUT}/exclusions.csv\", index=False)\nprint(json.dumps({k: v for k, v in res.items() if k not in (\"data_issues\", \"model_description\")}, indent=1))\n# F3-dev-01 — Rolling-origin forecasts of the US unemployment rate: AR(2) on differences vs naive\n\n## Question\nOver the 36 expanding-window forecast origins 2023-07-01 … 2026-06-01 (`n_origins`, `first_origin`, `last_origin`), does a simple autoregressive model forecast the US civilian unemployment rate (FRED UNRATE, SA, %) better than the naive no-change forecast at horizons of 1 and 3 months? Estimands: out-of-sample RMSE and MAE (percentage points) of both forecasts and the relative RMSE improvement 1 − RMSE_model/RMSE_naive per horizon.\n\n## Data and exclusions\n- `data/UNRATE.csv`, 945 data rows (`n_input_rows`), 1948-01 to 2026-09, SHA-256 matching the README; no duplicate or skipped months (see `out/state/data_audit.md`).\n- One missing value: 2025-10-01 (listed in `data_issues`). How it was handled: (i) at origin 2025-10-01 the naive forecast is the 2025-09 value, and the AR forecast is iterated from 2025-09; (ii) the pairs (origin 2025-09, h=1) and (origin 2025-07, h=3) have no actual. They stay in `out/forecasts.csv` with an empty `actual` and are excluded from the error statistics. So `n_evaluated_h1` = 35 and `n_evaluated_h3` = 35; (iii) in later training windows, regression rows that touch the missing month are dropped. The forecasting state uses linear interpolation between observations dated ≤ origin.\n- Exclusion ledger (`out/exclusions.csv`, last training window): 945 rows → drop 1 missing → drop 3 observations dated after the last origin (used only as actuals) → 941 = `n_analysed`. The AR regression in the last window uses 935 rows (`n_regression_rows_last_window`), because differencing, the two lags and the missing month each cost rows.\n- The COVID spike (2020-04: 14.8%) is kept as genuine data in every training window.\n\n## Method\n- **Naive**: the forecast at every horizon is the latest observation dated ≤ origin.\n- **Model `AR2_diff`** (`model_name`, `model_description`): AR(2) with intercept on monthly first differences, estimated by OLS on an expanding window that starts in 1948-01 and is re-estimated at every origin. Level forecasts come from iterating the difference recursion h steps ahead (plus one extra step at the origin with the missing value). I fixed the specification before looking at any evaluation errors. No model selection was done, so selection cannot leak test information.\n- **Information rule**: at every origin the code keeps only observations dated ≤ origin, before any estimation or transformation. A leakage test supports this: I set all values after 2024-12 to 9.9 in a temporary copy of the data, and the forecasts for origins ≤ 2024-12 did not change (`out/state/checks.md`).\n- **Errors**: actual − forecast on the final-vintage data, over pairs with a non-missing actual. The method is deterministic, so no random seed is used (`random_seed` = null).\n\n## Results\n| horizon | n evaluated | RMSE naive | RMSE AR2_diff | MAE naive | MAE AR2_diff | 1 − RMSE ratio |\n|---|---|---|---|---|---|---|\n| h=1 | 35 (`n_evaluated_h1`) | 0.1171 (`rmse_naive_h1`) | 0.1199 (`rmse_model_h1`) | 0.0914 (`mae_naive_h1`) | 0.0957 (`mae_model_h1`) | −0.0235 (`rel_improvement_rmse_h1`) |\n| h=3 | 35 (`n_evaluated_h3`) | 0.1586 (`rmse_naive_h3`) | 0.1598 (`rmse_model_h3`) | 0.1200 (`mae_naive_h3`) | 0.1213 (`mae_model_h3`) | −0.0076 (`rel_improvement_rmse_h3`) |\n\nThe AR(2)-on-differences model does **not** beat the naive forecast at either horizon. Its RMSE is about 2.3% higher at h=1 and 0.8% higher at h=3, and its MAE is also slightly higher at both horizons. In the last window the estimated coefficients are close to zero (intercept ≈ 0.0003, lag coefficients ≈ 0.04 and −0.04; recorded in `out/state/log.md`, not a results key). So the model behaves almost like a random walk, and its forecasts differ from the naive ones by only a few hundredths of a point.\n\n## Uncertainty\n- Diebold–Mariano test of equal squared-error loss (model minus naive), with the Harvey–Leybourne–Newbold small-sample correction, a rectangular HAC variance with h−1 lags, and t(n−1) reference:\n - h=1: mean loss difference 0.00065 (`mean_loss_diff_h1`), DM = 2.50 (`dm_stat_h1`), p = 0.017 (`dm_pvalue_h1`). At the 5% level the model is significantly *worse* than naive, but the difference in magnitude is tiny.\n - h=3: mean loss difference 0.00038 (`mean_loss_diff_h3`), DM = 1.36 (`dm_stat_h3`), p = 0.18 (`dm_pvalue_h3`). The difference is not significant.\n- With only 35 evaluated pairs per horizon, overlapping h=3 errors and a calm sample period (UNRATE stayed between 3.5% and 4.5% from 2023-07 to 2026-09; descriptive check recorded in `out/state/checks.md`, not a results key), these comparisons have little power and depend on the period chosen. They should not be generalised to other periods.\n\n## Limitations and open issues\n- **Final vintage**: the errors are computed on revised data. This measures how forecastable the revised series is, not real-time accuracy, and no real-time validity is claimed.\n- I evaluated only one model specification, chosen a priori. Other specifications (e.g. a shorter estimation window, or treating the COVID observations as outliers) might do differently. They were deliberately not tried, to avoid choosing a specification on the test errors. The 2020 spike probably pushes the full-sample AR coefficients towards zero.\n- The handling of the 2025-10 gap (interpolating the forecasting state, dropping regression rows) is a documented choice. It affects only a few origins.\n- The DM test with n = 35 and a HAC variance is approximate.\nstep,rule,n_before,n_after,n_removed,rationale\n1,drop rows with missing UNRATE,945,944,1,value not available (2025-10-01)\n2,drop observations dated after last origin 2026-06-01,944,941,3,information rule: training only on obs <= origin (these are used only as evaluation actuals)\nchecks.md\ncontract.md\ndata_audit.md\ngate_receipts\nlog.md\nphases.json\n# data/README.md — F3-dev-01\n\n## UNRATE.csv\n- **Series**: UNRATE — Unemployment Rate, United States, percent, seasonally adjusted, monthly. Source: U.S. Bureau of Labor Statistics, Current Population Survey, via FRED (Federal Reserve Bank of St. Louis).\n- **Retrieval URL**: https://fred.stlouisfed.org/graph/fredgraph.csv?id=UNRATE\n- **Retrieved (UTC)**: 2026-10-30T03:20:36Z\n- **SHA-256**: 621ff6fadf50910cb7a21ee20ba610c247cb043b29b4e05c4c1a72fadca2a06c\n- **Format**: exactly as served by FRED: header `observation_date,UNRATE`, one row per month dated on the first day of the month (YYYY-MM-01), 945 data rows from 1948-01-01 to 2026-09-01. Missing observations are served as an empty value field.\n- **Units**: percent of the civilian labour force.\n- **Vintage caveat**: this is the current (final) vintage as of the retrieval time. Values may have been revised since their first publication (annual seasonal-factor revisions). Rolling-origin results on this file therefore measure forecastability of the revised series, not historical real-time performance.\n- **License / terms**: FRED terms of use (https://fred.stlouisfed.org/legal/); BLS data are public domain.","is_error":false}]},"uuid":"7fc0bd48-fe1b-4a31-8788-040428564645","timestamp":"2026-10-30T04:01:49.290Z","toolUseResult":{"stdout":"\"\"\"Rolling-origin (expanding window) forecasts of US UNRATE: naive vs AR(2) on first differences.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nReads only data/UNRATE.csv; writes out/results.json, out/forecasts.csv, out/exclusions.csv. No randomness.\"\"\"\nimport json, os\nimport numpy as np, pandas as pd\nfrom scipy import stats\n\nDATA = \"data/UNRATE.csv\"; OUT = \"out\"\nP = 2 # AR order on first differences (fixed a priori)\nHORIZONS = [1, 3]\nMODEL = \"AR2_diff\"\norigins = pd.date_range(\"2023-07-01\", \"2026-06-01\", freq=\"MS\")\n\nraw = pd.read_csv(DATA, dtype={\"observation_date\": str})\nn_raw = len(raw)\nraw[\"date\"] = pd.to_datetime(raw[\"observation_date\"], format=\"%Y-%m-%d\")\ny = raw.set_index(\"date\")[\"UNRATE\"].astype(float)\nassert y.index.is_monotonic_increasing and not y.index.duplicated().any()\nassert (y.index == pd.date_range(y.index[0], y.index[-1], freq=\"MS\")).all()\nmissing_dates = [d.strftime(\"%Y-%m-%d\") for d in y.index[y.isna()]]\n\ndef ar_forecast(s, steps):\n \"\"\"s: series with obs dated <= origin (may contain NaN). Returns forecasts 1..steps months\n ahead of the last *observed* month.\"\"\"\n s = s.loc[:s.last_valid_index()]\n d = s.diff()\n X = pd.concat({f\"l{i}\": d.shift(i) for i in range(1, P + 1)}, axis=1)\n reg = pd.concat([d.rename(\"y\"), X], axis=1).dropna() # drop rows touching missing values\n A = np.column_stack([np.ones(len(reg)), reg[[f\"l{i}\" for i in range(1, P + 1)]].values])\n beta, *_ = np.linalg.lstsq(A, reg[\"y\"].values, rcond=None)\n # forecasting state: interior missing values linearly interpolated using only obs <= origin\n si = s.interpolate(method=\"linear\", limit_area=\"inside\")\n lags = list(si.diff().values[-P:][::-1]) # [d_T, d_{T-1}]\n level, out = si.values[-1], []\n for _ in range(steps):\n dhat = beta[0] + np.dot(beta[1:], lags[:P])\n level += dhat; out.append(level); lags = [dhat] + lags[:P - 1]\n return np.array(out), len(reg)\n\nrows = []\nfor t in origins:\n s = y.loc[:t] # information rule: only obs dated <= t\n last_obs = s.last_valid_index()\n gap = (t.year - last_obs.year) * 12 + (t.month - last_obs.month) # months origin is ahead of last obs\n fc, nreg = ar_forecast(s, gap + max(HORIZONS))\n for h in HORIZONS:\n tgt = t + pd.DateOffset(months=h)\n act = y.get(tgt, np.nan)\n rows.append(dict(origin_date=t.strftime(\"%Y-%m-%d\"), target_date=tgt.strftime(\"%Y-%m-%d\"),\n horizon=h, forecast=float(s.loc[last_obs]), actual=act, model=\"naive\"))\n rows.append(dict(origin_date=t.strftime(\"%Y-%m-%d\"), target_date=tgt.strftime(\"%Y-%m-%d\"),\n horizon=h, forecast=float(fc[gap + h - 1]), actual=act, model=MODEL))\nfc_df = pd.DataFrame(rows)\nfc_df.to_csv(f\"{OUT}/forecasts.csv\", index=False, float_format=\"%.6f\")\n\nres = {\"task_id\": \"F3-dev-01\", \"model_name\": MODEL,\n \"model_description\": (\"AR(2) with intercept on monthly first differences of UNRATE, estimated by OLS on an \"\n \"expanding window starting 1948-01 (regression rows touching missing values dropped), \"\n \"re-estimated at every origin; level forecasts by iterating the difference recursion.\"),\n \"n_origins\": len(origins), \"first_origin\": origins[0].strftime(\"%Y-%m-%d\"),\n \"last_origin\": origins[-1].strftime(\"%Y-%m-%d\")}\ndm = {}\nfor h in HORIZONS:\n sub = fc_df[fc_df.horizon == h]\n ev = sub.dropna(subset=[\"actual\"])\n e = {m: (ev[ev.model == m].set_index(\"origin_date\")[\"actual\"] - ev[ev.model == m].set_index(\"origin_date\")[\"forecast\"])\n for m in [\"naive\", MODEL]}\n n = len(e[\"naive\"]); assert n == len(e[MODEL])\n res[f\"n_evaluated_h{h}\"] = int(n)\n for m, tag in [(\"naive\", \"naive\"), (MODEL, \"model\")]:\n res[f\"rmse_{tag}_h{h}\"] = float(np.sqrt(np.mean(e[m] ** 2)))\n res[f\"mae_{tag}_h{h}\"] = float(np.mean(np.abs(e[m])))\n # Diebold-Mariano (squared loss), HAC variance with h-1 Bartlett-free (rectangular) lags, HLN small-sample correction\n dl = (e[MODEL] ** 2 - e[\"naive\"] ** 2).values\n dbar = dl.mean(); dc = dl - dbar\n gam = [np.sum(dc[k:] * dc[:n - k]) / n for k in range(h)]\n var = (gam[0] + 2 * sum(gam[1:])) / n\n if var <= 0: var = gam[0] / n\n hln = np.sqrt((n + 1 - 2 * h + h * (h - 1) / n) / n)\n stat = hln * dbar / np.sqrt(var)\n dm[h] = (float(stat), float(2 * stats.t.sf(abs(stat), df=n - 1)), float(dbar))\nfor h in HORIZONS:\n res[f\"rel_improvement_rmse_h{h}\"] = 1 - res[f\"rmse_model_h{h}\"] / res[f\"rmse_naive_h{h}\"]\nfor h in HORIZONS:\n res[f\"dm_stat_h{h}\"], res[f\"dm_pvalue_h{h}\"], res[f\"mean_loss_diff_h{h}\"] = dm[h]\nres.update({\n \"feasibility\": \"complete\", \"feasibility_reason\": None,\n \"data_issues\": [\n {\"issue\": f\"Missing UNRATE value(s) at {', '.join(missing_dates)} (empty field).\",\n \"handling\": \"Origin 2025-10-01: naive uses 2025-09 value; AR forecasts iterated from last observed month (2025-09). \"\n \"Pairs with missing target (origin 2025-09 h1, origin 2025-07 h3) kept in ledger with empty actual and \"\n \"excluded from error statistics. In later training windows, regression rows touching the missing month are \"\n \"dropped; the forecasting state uses linear interpolation between observations dated <= origin.\"},\n {\"issue\": \"Final (revised) vintage, not real-time data.\",\n \"handling\": \"Errors measure forecastability of the revised series; no real-time validity claimed.\"},\n {\"issue\": \"COVID-19 spike 2020-03..2020-05 (4.4 -> 14.8 -> 13.2) inside every training window.\",\n \"handling\": \"Kept as genuine data; no outlier treatment (specification fixed a priori, not tuned on test errors).\"}],\n \"n_input_rows\": {\"UNRATE.csv\": int(n_raw)},\n})\nlast_win = y.loc[:origins[-1]]\nres[\"n_analysed\"] = int(last_win.notna().sum())\nres[\"n_regression_rows_last_window\"] = int(ar_forecast(last_win, 1)[1])\nres[\"random_seed\"] = None\nwith open(f\"{OUT}/results.json\", \"w\") as f:\n json.dump(res, f, indent=2)\n\n# exclusion ledger (training data for the last window)\nn1 = int(y.notna().sum()); n2 = res[\"n_analysed\"]\npd.DataFrame([\n dict(step=1, rule=\"drop rows with missing UNRATE\", n_before=n_raw, n_after=n1, n_removed=n_raw - n1,\n rationale=\"value not available (2025-10-01)\"),\n dict(step=2, rule=\"drop observations dated after last origin 2026-06-01\", n_before=n1, n_after=n2, n_removed=n1 - n2,\n rationale=\"information rule: training only on obs <= origin (these are used only as evaluation actuals)\"),\n]).to_csv(f\"{OUT}/exclusions.csv\", index=False)\nprint(json.dumps({k: v for k, v in res.items() if k not in (\"data_issues\", \"model_description\")}, indent=1))\n# F3-dev-01 — Rolling-origin forecasts of the US unemployment rate: AR(2) on differences vs naive\n\n## Question\nOver the 36 expanding-window forecast origins 2023-07-01 … 2026-06-01 (`n_origins`, `first_origin`, `last_origin`), does a simple autoregressive model forecast the US civilian unemployment rate (FRED UNRATE, SA, %) better than the naive no-change forecast at horizons of 1 and 3 months? Estimands: out-of-sample RMSE and MAE (percentage points) of both forecasts and the relative RMSE improvement 1 − RMSE_model/RMSE_naive per horizon.\n\n## Data and exclusions\n- `data/UNRATE.csv`, 945 data rows (`n_input_rows`), 1948-01 to 2026-09, SHA-256 matching the README; no duplicate or skipped months (see `out/state/data_audit.md`).\n- One missing value: 2025-10-01 (listed in `data_issues`). How it was handled: (i) at origin 2025-10-01 the naive forecast is the 2025-09 value, and the AR forecast is iterated from 2025-09; (ii) the pairs (origin 2025-09, h=1) and (origin 2025-07, h=3) have no actual. They stay in `out/forecasts.csv` with an empty `actual` and are excluded from the error statistics. So `n_evaluated_h1` = 35 and `n_evaluated_h3` = 35; (iii) in later training windows, regression rows that touch the missing month are dropped. The forecasting state uses linear interpolation between observations dated ≤ origin.\n- Exclusion ledger (`out/exclusions.csv`, last training window): 945 rows → drop 1 missing → drop 3 observations dated after the last origin (used only as actuals) → 941 = `n_analysed`. The AR regression in the last window uses 935 rows (`n_regression_rows_last_window`), because differencing, the two lags and the missing month each cost rows.\n- The COVID spike (2020-04: 14.8%) is kept as genuine data in every training window.\n\n## Method\n- **Naive**: the forecast at every horizon is the latest observation dated ≤ origin.\n- **Model `AR2_diff`** (`model_name`, `model_description`): AR(2) with intercept on monthly first differences, estimated by OLS on an expanding window that starts in 1948-01 and is re-estimated at every origin. Level forecasts come from iterating the difference recursion h steps ahead (plus one extra step at the origin with the missing value). I fixed the specification before looking at any evaluation errors. No model selection was done, so selection cannot leak test information.\n- **Information rule**: at every origin the code keeps only observations dated ≤ origin, before any estimation or transformation. A leakage test supports this: I set all values after 2024-12 to 9.9 in a temporary copy of the data, and the forecasts for origins ≤ 2024-12 did not change (`out/state/checks.md`).\n- **Errors**: actual − forecast on the final-vintage data, over pairs with a non-missing actual. The method is deterministic, so no random seed is used (`random_seed` = null).\n\n## Results\n| horizon | n evaluated | RMSE naive | RMSE AR2_diff | MAE naive | MAE AR2_diff | 1 − RMSE ratio |\n|---|---|---|---|---|---|---|\n| h=1 | 35 (`n_evaluated_h1`) | 0.1171 (`rmse_naive_h1`) | 0.1199 (`rmse_model_h1`) | 0.0914 (`mae_naive_h1`) | 0.0957 (`mae_model_h1`) | −0.0235 (`rel_improvement_rmse_h1`) |\n| h=3 | 35 (`n_evaluated_h3`) | 0.1586 (`rmse_naive_h3`) | 0.1598 (`rmse_model_h3`) | 0.1200 (`mae_naive_h3`) | 0.1213 (`mae_model_h3`) | −0.0076 (`rel_improvement_rmse_h3`) |\n\nThe AR(2)-on-differences model does **not** beat the naive forecast at either horizon. Its RMSE is about 2.3% higher at h=1 and 0.8% higher at h=3, and its MAE is also slightly higher at both horizons. In the last window the estimated coefficients are close to zero (intercept ≈ 0.0003, lag coefficients ≈ 0.04 and −0.04; recorded in `out/state/log.md`, not a results key). So the model behaves almost like a random walk, and its forecasts differ from the naive ones by only a few hundredths of a point.\n\n## Uncertainty\n- Diebold–Mariano test of equal squared-error loss (model minus naive), with the Harvey–Leybourne–Newbold small-sample correction, a rectangular HAC variance with h−1 lags, and t(n−1) reference:\n - h=1: mean loss difference 0.00065 (`mean_loss_diff_h1`), DM = 2.50 (`dm_stat_h1`), p = 0.017 (`dm_pvalue_h1`). At the 5% level the model is significantly *worse* than naive, but the difference in magnitude is tiny.\n - h=3: mean loss difference 0.00038 (`mean_loss_diff_h3`), DM = 1.36 (`dm_stat_h3`), p = 0.18 (`dm_pvalue_h3`). The difference is not significant.\n- With only 35 evaluated pairs per horizon, overlapping h=3 errors and a calm sample period (UNRATE stayed between 3.5% and 4.5% from 2023-07 to 2026-09; descriptive check recorded in `out/state/checks.md`, not a results key), these comparisons have little power and depend on the period chosen. They should not be generalised to other periods.\n\n## Limitations and open issues\n- **Final vintage**: the errors are computed on revised data. This measures how forecastable the revised series is, not real-time accuracy, and no real-time validity is claimed.\n- I evaluated only one model specification, chosen a priori. Other specifications (e.g. a shorter estimation window, or treating the COVID observations as outliers) might do differently. They were deliberately not tried, to avoid choosing a specification on the test errors. The 2020 spike probably pushes the full-sample AR coefficients towards zero.\n- The handling of the 2025-10 gap (interpolating the forecasting state, dropping regression rows) is a documented choice. It affects only a few origins.\n- The DM test with n = 35 and a HAC variance is approximate.\nstep,rule,n_before,n_after,n_removed,rationale\n1,drop rows with missing UNRATE,945,944,1,value not available (2025-10-01)\n2,drop observations dated after last origin 2026-06-01,944,941,3,information rule: training only on obs <= origin (these are used only as evaluation actuals)\nchecks.md\ncontract.md\ndata_audit.md\ngate_receipts\nlog.md\nphases.json\n# data/README.md — F3-dev-01\n\n## UNRATE.csv\n- **Series**: UNRATE — Unemployment Rate, United States, percent, seasonally adjusted, monthly. Source: U.S. Bureau of Labor Statistics, Current Population Survey, via FRED (Federal Reserve Bank of St. Louis).\n- **Retrieval URL**: https://fred.stlouisfed.org/graph/fredgraph.csv?id=UNRATE\n- **Retrieved (UTC)**: 2026-10-30T03:20:36Z\n- **SHA-256**: 621ff6fadf50910cb7a21ee20ba610c247cb043b29b4e05c4c1a72fadca2a06c\n- **Format**: exactly as served by FRED: header `observation_date,UNRATE`, one row per month dated on the first day of the month (YYYY-MM-01), 945 data rows from 1948-01-01 to 2026-09-01. Missing observations are served as an empty value field.\n- **Units**: percent of the civilian labour force.\n- **Vintage caveat**: this is the current (final) vintage as of the retrieval time. Values may have been revised since their first publication (annual seasonal-factor revisions). Rolling-origin results on this file therefore measure forecastability of the revised series, not historical real-time performance.\n- **License / terms**: FRED terms of use (https://fred.stlouisfed.org/legal/); BLS data are public domain.","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"adfa46f5-1f94-49c6-bf20-f25a225039aa","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0023","sessionId":"3c0817b8-c7e8-47f1-b003-1b4f1c3b06c0","version":"2.1.314","gitBranch":"HEAD"}21{"type":"api-request-blob","sessionId":"3c0817b8-c7e8-47f1-b003-1b4f1c3b06c0","hash":"e2bb1f571b3cd57fec23e466971871b749f30e18af369e71d137c36d0924057c","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01B9KkspU8hn1HVp4DbZi92A","name":"Bash","input":{"command":"cat out/analysis.py; cat 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/tmp && rm -rf rv && mkdir rv && cd rv && cp -r ~/wp29/runs/RP0023/data . && mkdir out && cp ~/wp29/runs/RP0023/out/analysis.py out/ && ~/wp29/venv/bin/python out/analysis.py >/dev/null && diff out/results.json ~/wp29/runs/RP0023/out/results.json && diff out/forecasts.csv ~/wp29/runs/RP0023/out/forecasts.csv && echo SAME; shasum -a 256 data/UNRATE.csv; grep -n ',$\\|,,' data/UNRATE.csv; wc -l ~/wp29/runs/RP0023/out/forecasts.csv; grep -E '2025-(09|10|11)' ~/wp29/runs/RP0023/out/forecasts.csv; tail -15 data/UNRATE.csv","description":"Re-run analysis in scratch and 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PASS\n- exclusion ledger: 945-1-3=941=n_analysed: PASS\n- first_origin<last_origin; last target 2026-09 within data: PASS\n- naive RMSE h3 > h1 (plausible magnitude): PASS\n- Descriptive: UNRATE min 3.5 / max 4.5 over 2023-07..2026-09 (non-missing): computed, cited in report Uncertainty.\nShell cwd was reset to /Users/simon-pierreboucher/wp29/runs/RP0023","is_error":false}]},"uuid":"90a4c384-c0ca-453a-b6c3-9e066ad2d025","timestamp":"2026-10-30T04:02:03.871Z","toolUseResult":{"stdout":"1 AR2_diff 35 0.11985758509962682 0.09565579999999999\n1 naive 35 0.11710800875382403 0.09142857142857148\n3 AR2_diff 35 0.159770241753767 0.12128480000000005\n3 naive 35 0.15856499343441843 0.12000000000000005\n3.5 4.5\nleak-free True\n# Verification checks (P4)\n\n- Clean re-run (outputs deleted, analysis.py re-run): results.json and forecasts.csv byte-identical: PASS\n- Leakage test: all values after 2024-12-01 set to 9.9 in a temp copy; forecasts for origins <= 2024-12-01 identical, later ones change: PASS\n- 144 ledger rows: PASS\n- unique (origin,h,model): PASS\n- target=origin+h months: PASS\n- actuals match data: PASS\n- n_eval = non-missing actuals: PASS\n- naive = last obs <= origin: PASS\n- rmse/mae naive h1 recomputed from ledger: PASS\n- rmse/mae model h1 recomputed from ledger: PASS\n- rel_improvement h1 identity: PASS\n- rmse/mae naive h3 recomputed from ledger: PASS\n- rmse/mae model h3 recomputed from ledger: PASS\n- rel_improvement h3 identity: PASS\n- RMSE>=MAE>0: PASS\n- exclusion ledger: 945-1-3=941=n_analysed: PASS\n- first_origin<last_origin; last target 2026-09 within data: PASS\n- naive RMSE h3 > h1 (plausible magnitude): PASS\n- Descriptive: UNRATE min 3.5 / max 4.5 over 2023-07..2026-09 (non-missing): computed, cited in report Uncertainty.","stderr":"\nShell cwd was reset to 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> out/review/review.json <<'EOF'\n{\n \"verdict\": \"accept\",\n \"issues\": [\n {\n \"id\": \"R1\",\n \"severity\": \"minor\",\n \"location\": \"claims.json C3; report.md Uncertainty; results.json dm_*\",\n \"issue\": \"The naive random walk is nested in the AR(2)-on-differences model (it is the case where all coefficients are zero), so the Diebold-Mariano/HLN test with a t(n-1) reference does not have its usual null distribution. Calling the h=1 result 'statistically significant at 5%' (p=0.017) and marking C3 'supported' is stronger than the evidence. That p-value also comes from one of two horizon tests, with n=35 and a calm, short sample.\",\n \"suggested_fix\": \"Say that DM is only approximate for nested comparisons (or add a Clark-West test), describe the h=1 result as 'nominally significant', and add the nested-model caveat to C3.\"\n },\n {\n \"id\": \"R2\",\n \"severity\": \"minor\",\n \"location\": \"analysis.py data_issues handling string\",\n \"issue\": \"The missing-data handling text hardcodes the dates 2025-10 and 2025-09 and the affected pairs, while the issue text is built from the data. If the data changed, the description would no longer match the computation.\",\n \"suggested_fix\": \"Build the affected-pair list from the ledger rows that have an empty actual.\"\n },\n {\n \"id\": \"R3\",\n \"severity\": \"minor\",\n \"location\": \"report.md Results\",\n \"issue\": \"The report cites last-window AR coefficients (about 0.0003, 0.04, -0.04) from state/log.md. These are not results keys and analysis.py does not produce them, so the deliverables cannot reproduce them.\",\n \"suggested_fix\": \"Write the last-window coefficients to results.json, or remove the specific numbers.\"\n }\n ],\n \"summary\": \"All required keys are present. Re-running analysis.py on a scratch copy reproduces results.json and forecasts.csv byte for byte (144 rows; data SHA-256 matches the README). RMSE and MAE recomputed independently from the ledger match. The two missing-target pairs (targets in 2025-10) are kept in the ledger and excluded, giving n=35 per horizon. A leakage test I ran myself (setting values after 2024-12 to 9.9) left forecasts for origins up to 2024-12 unchanged. The naive rule, the expanding window and the handling of origins with a missing value follow TASK.md. The central claim, that the AR does not beat naive at h=1 or h=3, is supported, with honest caveats about the final vintage, small n and a calm period. The only remaining issues are minor: the significance wording for the nested-model DM test, a hardcoded handling string, and coefficients cited without being reproducible.\"\n}\nEOF\n~/wp29/venv/bin/python -m json.tool out/review/review.json >/dev/null && echo ok","description":"Write review JSON and 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Calling the h=1 result 'statistically significant at 5%' (p=0.017) and marking C3 'supported' is stronger than the evidence. That p-value also comes from one of two horizon tests, with n=35 and a calm, short sample.\",\n \"suggested_fix\": \"Say that DM is only approximate for nested comparisons (or add a Clark-West test), describe the h=1 result as 'nominally significant', and add the nested-model caveat to C3.\"\n },\n {\n \"id\": \"R2\",\n \"severity\": \"minor\",\n \"location\": \"analysis.py data_issues handling string\",\n \"issue\": \"The missing-data handling text hardcodes the dates 2025-10 and 2025-09 and the affected pairs, while the issue text is built from the data. If the data changed, the description would no longer match the computation.\",\n \"suggested_fix\": \"Build the affected-pair list from the ledger rows that have an empty actual.\"\n },\n {\n \"id\": \"R3\",\n \"severity\": \"minor\",\n \"location\": \"report.md Results\",\n \"issue\": \"The report cites last-window AR coefficients (about 0.0003, 0.04, -0.04) from state/log.md. These are not results keys and analysis.py does not produce them, so the deliverables cannot reproduce them.\",\n \"suggested_fix\": \"Write the last-window coefficients to results.json, or remove the specific numbers.\"\n }\n ],\n \"summary\": \"All required keys are present. Re-running analysis.py on a scratch copy reproduces results.json and forecasts.csv byte for byte (144 rows; data SHA-256 matches the README). RMSE and MAE recomputed independently from the ledger match. The two missing-target pairs (targets in 2025-10) are kept in the ledger and excluded, giving n=35 per horizon. 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The review is in `out/review/review.json`.\n\n**What I verified:**\n- **Reproducibility:** re-running `out/analysis.py` on a scratch copy gives byte-identical `results.json` and `forecasts.csv`.\n- **Ledger and counts:** the forecast file has the expected 144 rows, and the data file's checksum matches `data/README.md`. RMSE and MAE recomputed directly from the forecast file match the reported values.\n- **Missing month:** the only missing value is 2025-10. The two forecasts that target that month stay in the file with an empty actual and are left out of the error statistics, so 35 forecasts are scored at each horizon, as reported.\n- **No future information:** I ran my own test, setting every value after 2024-12 to 9.9. Forecasts made at or before 2024-12 did not change. Reading the code confirms that each forecast uses only data up to its origin month and that the naive forecast follows the task's rule.\n\nThe central claim holds: the autoregressive model does not beat the naive forecast at 1 or 3 months (RMSE 2.3% worse at 1 month, 0.8% worse at 3 months). The limitations are stated honestly: revised rather than real-time data, only 35 scored forecasts per horizon, a calm sample period, and a single model specification.\n\n**Minor issues:**\n1. **Significance wording is too strong.** The naive forecast is a special case of the model (all coefficients zero), and the Diebold–Mariano test used for \"significant at 5%, p = 0.017\" (claim C3) isn't strictly valid for that kind of comparison. The result should be called \"nominally significant\", or a Clark–West test added.\n2. **Hardcoded description.** The text describing how the missing month was handled names the dates and affected forecasts directly instead of deriving them from the data, so it would go stale if the data changed.\n3. **Unreproducible numbers in the report.** The final-window model coefficients quoted in the report come from a log file. The analysis script does not produce them."}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1746,"cache_read_input_tokens":15290,"output_tokens":714,"output_tokens_details":{"thinking_tokens":14},"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":1746},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXkpboo91ymFRGyD2WdF","requestRef":"d4ddd95a-abb7-4b9c-87f4-6920c3d7faef","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f5be6602-ab12-4186-8958-bde35e7209eb","timestamp":"2026-10-30T04:02:29.042Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0023","sessionId":"3c0817b8-c7e8-47f1-b003-1b4f1c3b06c0","version":"2.1.314","gitBranch":"HEAD"}44{"type":"last-prompt","lastPrompt":"Review","leafUuid":"f5be6602-ab12-4186-8958-bde35e7209eb","sessionId":"3c0817b8-c7e8-47f1-b003-1b4f1c3b06c0"}45{"type":"cost-state","sessionId":"3c0817b8-c7e8-47f1-b003-1b4f1c3b06c0","totalCostUSD":0.16751,"totalAPIDuration":42078,"totalAPIDurationWithoutRetries":42073,"totalToolDuration":1803,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":44034,"startTime":1793332905016,"modelUsage":{"claude-opus-5-5":{"inputTokens":14,"outputTokens":3972,"thinkingTokens":1062,"cacheReadInputTokens":51770,"cacheCreationInputTokens":15532,"cacheCreationEphemeral5mInputTokens":15532,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.16751}},"hasUnknownModelCost":false}46