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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 40\ndrwxr-xr-x 4 simon-pierreboucher staff 128 oct. 29 23:33 .\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:36 ..\n-rw-r--r-- 1 simon-pierreboucher staff 1174 oct. 29 23:33 README.md\n-rw-r--r-- 1 simon-pierreboucher staff 14211 oct. 29 23:33 UNRATE.csv\ndata\ndata/README.md\ndata/UNRATE.csv","is_error":false}]},"uuid":"c85813f5-3a65-4c3e-8da4-87199435e96c","timestamp":"2026-10-30T03:59:06.728Z","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). 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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.\nobservation_date,UNRATE\n1948-01-01,3.4\n1948-02-01,3.8\n2023-06-01,3.6\n2023-07-01,3.5\n2023-08-01,3.7\n2023-09-01,3.7\n2023-10-01,3.9\n2023-11-01,3.7\n2023-12-01,3.8\n2024-01-01,3.7\n2024-02-01,3.9\n2024-03-01,3.9\n2024-04-01,3.9\n2024-05-01,3.9\n2024-06-01,4.1\n2024-07-01,4.2\n2024-08-01,4.2\n2024-09-01,4.1\n2024-10-01,4.1\n2024-11-01,4.2\n2024-12-01,4.1\n2025-01-01,4.0\n2025-02-01,4.2\n2025-03-01,4.2\n2025-04-01,4.2\n2025-05-01,4.3\n2025-06-01,4.1\n2025-07-01,4.3\n2025-08-01,4.3\n2025-09-01,4.4\n2025-10-01,\n2025-11-01,4.5\n2025-12-01,4.4\n2026-01-01,4.3\n2026-02-01,4.4\n2026-03-01,4.3\n2026-04-01,4.3\n2026-05-01,4.3\n2026-06-01,4.2\n2026-07-01,4.1\n2026-08-01,4.1\n2026-09-01,4.2\n935:2025-10-01,\n 946 data/UNRATE.csv\n2.5\n14.8","is_error":false}]},"uuid":"65bf42ce-9dca-4197-9464-87021832ae9f","timestamp":"2026-10-30T03:59:08.785Z","toolUseResult":{"stdout":"# 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.\nobservation_date,UNRATE\n1948-01-01,3.4\n1948-02-01,3.8\n2023-06-01,3.6\n2023-07-01,3.5\n2023-08-01,3.7\n2023-09-01,3.7\n2023-10-01,3.9\n2023-11-01,3.7\n2023-12-01,3.8\n2024-01-01,3.7\n2024-02-01,3.9\n2024-03-01,3.9\n2024-04-01,3.9\n2024-05-01,3.9\n2024-06-01,4.1\n2024-07-01,4.2\n2024-08-01,4.2\n2024-09-01,4.1\n2024-10-01,4.1\n2024-11-01,4.2\n2024-12-01,4.1\n2025-01-01,4.0\n2025-02-01,4.2\n2025-03-01,4.2\n2025-04-01,4.2\n2025-05-01,4.3\n2025-06-01,4.1\n2025-07-01,4.3\n2025-08-01,4.3\n2025-09-01,4.4\n2025-10-01,\n2025-11-01,4.5\n2025-12-01,4.4\n2026-01-01,4.3\n2026-02-01,4.4\n2026-03-01,4.3\n2026-04-01,4.3\n2026-05-01,4.3\n2026-06-01,4.2\n2026-07-01,4.1\n2026-08-01,4.1\n2026-09-01,4.2\n935:2025-10-01,\n 946 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-p out; cat > out/analysis.py <<'EOF'\n\"\"\"F3-dev-01: rolling-origin (expanding window) forecasts of UNRATE, naive vs AR(2) on first differences.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\n\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\n\nDATA = \"data/UNRATE.csv\"\nOUT = \"out\"\nMODEL = \"AR2_diff\"\nP = 2\nHORIZONS = [1, 3]\nORIGINS = pd.date_range(\"2023-07-01\", \"2026-06-01\", freq=\"MS\")\n\nraw = pd.read_csv(DATA, dtype={\"observation_date\": str, \"UNRATE\": str}, keep_default_na=False)\nn_rows = len(raw)\ndf = pd.DataFrame({\"date\": pd.to_datetime(raw[\"observation_date\"], format=\"%Y-%m-%d\"),\n \"y\": pd.to_numeric(raw[\"UNRATE\"].replace(\"\", np.nan), errors=\"coerce\")})\nissues = []\nmiss = df.loc[df.y.isna(), \"date\"].dt.strftime(\"%Y-%m-%d\").tolist()\nassert df.date.is_unique and df.date.is_monotonic_increasing\nfull = pd.date_range(df.date.min(), df.date.max(), freq=\"MS\")\nassert len(full) == len(df), \"calendar gaps present\"\ns = df.set_index(\"date\")[\"y\"]\nif miss:\n issues.append({\"issue\": f\"Missing value(s) (empty field) at {', '.join(miss)}\",\n \"handling\": \"Excluded from estimation (any regression row whose dependent or lagged difference touches the missing month is dropped); \"\n \"naive uses latest earlier observation; when missing is the latest month at an origin the AR model iterates forward from the last observed month \"\n \"(extra steps); when it is interior to the window it is linearly interpolated from neighbours dated <= origin only to build lag inputs; \"\n \"(origin,horizon) pairs whose target is missing are kept in the ledger with empty actual and excluded from error statistics.\"})\ncovid = s[\"2020-03-01\":\"2020-06-01\"]\nissues.append({\"issue\": \"COVID-19 outlier: unemployment jumped from %.1f (2020-03) to %.1f (2020-04), extreme first differences in training sample\" % (s[\"2020-03-01\"], s[\"2020-04-01\"]),\n \"handling\": \"Retained in the primary specification (pre-specified, no outlier treatment); a sensitivity variant excluding 2020-03..2020-12 differences from estimation is reported in report.md only.\"})\n\n\ndef fit_ar_diff(y, p=P, exclude=None):\n \"\"\"OLS AR(p) with intercept on dy, using rows with no missing values. y: level Series up to origin.\"\"\"\n d = y.diff()\n X = pd.concat({f\"l{k}\": d.shift(k) for k in range(1, p + 1)}, axis=1)\n data = pd.concat([d.rename(\"dy\"), X], axis=1)\n if exclude is not None:\n data = data[~((data.index >= exclude[0]) & (data.index <= exclude[1]))]\n data = data.dropna()\n A = np.column_stack([np.ones(len(data)), data[[f\"l{k}\" for k in range(1, p + 1)]].values])\n beta, *_ = np.linalg.lstsq(A, data[\"dy\"].values, rcond=None)\n return beta, len(data)\n\n\ndef forecast_ar_diff(y, t, horizons, exclude=None):\n y = y[:t]\n beta, nobs = fit_ar_diff(y, exclude=exclude)\n last_obs = y.last_valid_index()\n yy = y[:last_obs].interpolate(method=\"linear\", limit_area=\"inside\") # interior gaps only, data <= t\n lev = list(yy.values)\n dif = list(np.diff(yy.values))\n steps_extra = (t.year - last_obs.year) * 12 + (t.month - last_obs.month)\n out = {}\n H = max(horizons) + steps_extra\n for step in range(1, H + 1):\n dnew = beta[0] + sum(beta[k] * dif[-k] for k in range(1, P + 1))\n dif.append(dnew)\n lev.append(lev[-1] + dnew)\n hh = step - steps_extra\n if hh in horizons:\n out[hh] = lev[-1]\n return out, nobs\n\n\ndef run(exclude=None):\n rows, nobs_last = [], None\n for t in ORIGINS:\n yt = s[:t]\n naive = yt.dropna().iloc[-1]\n fc, nobs = forecast_ar_diff(s, t, HORIZONS, exclude)\n nobs_last = nobs\n for h in HORIZONS:\n tgt = t + pd.DateOffset(months=h)\n act = s.get(tgt, np.nan)\n for m, f in ((\"naive\", naive), (MODEL, fc[h])):\n rows.append({\"origin_date\": t.strftime(\"%Y-%m-%d\"), \"target_date\": tgt.strftime(\"%Y-%m-%d\"),\n \"horizon\": h, \"forecast\": round(float(f), 6),\n \"actual\": act, \"model\": m})\n return pd.DataFrame(rows), nobs_last\n\n\ndef stats(led):\n r = {}\n for h in HORIZONS:\n for m, tag in ((\"naive\", \"naive\"), (MODEL, \"model\")):\n sub = led[(led.horizon == h) & (led.model == m) & led.actual.notna()]\n e = sub.actual - sub.forecast\n r[f\"rmse_{tag}_h{h}\"] = float(np.sqrt(np.mean(e ** 2)))\n r[f\"mae_{tag}_h{h}\"] = float(np.mean(np.abs(e)))\n r[f\"n_evaluated_h{h}\"] = int(len(sub))\n r[f\"rel_improvement_rmse_h{h}\"] = 1 - r[f\"rmse_model_h{h}\"] / r[f\"rmse_naive_h{h}\"]\n return r\n\n\nif __name__ == \"__main__\":\n led, nobs_last = run()\n st = stats(led)\n os.makedirs(OUT, exist_ok=True)\n led.to_csv(os.path.join(OUT, \"forecasts.csv\"), index=False, float_format=\"%.6g\")\n res = {\n \"task_id\": \"F3-dev-01\",\n \"model_name\": MODEL,\n \"model_description\": \"AR(2) with intercept on monthly first differences of UNRATE, estimated by OLS on an expanding window starting with the first available difference (1948-04 as dependent observation) up to the origin, iterated recursively and cumulated to levels for h-step forecasts.\",\n \"n_origins\": len(ORIGINS),\n \"first_origin\": ORIGINS[0].strftime(\"%Y-%m-%d\"),\n \"last_origin\": ORIGINS[-1].strftime(\"%Y-%m-%d\"),\n }\n for k in [\"n_evaluated_h1\", \"n_evaluated_h3\", \"rmse_naive_h1\", \"mae_naive_h1\", \"rmse_naive_h3\", \"mae_naive_h3\",\n \"rmse_model_h1\", \"mae_model_h1\", \"rmse_model_h3\", \"mae_model_h3\",\n \"rel_improvement_rmse_h1\", \"rel_improvement_rmse_h3\"]:\n res[k] = st[k]\n res.update({\"feasibility\": \"complete\", \"feasibility_reason\": None, \"data_issues\": issues,\n \"n_input_rows\": {\"UNRATE.csv\": n_rows}, \"n_analysed\": int(nobs_last), \"random_seed\": None})\n with open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n json.dump(res, f, indent=2)\n print(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py && wc -l out/forecasts.csv && grep -E '2025-(09|10|11|12)' 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\"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 with the first available difference (1948-04 as dependent observation) up to the origin, iterated recursively and cumulated to levels for h-step forecasts.\",\n \"n_origins\": 36,\n \"first_origin\": \"2023-07-01\",\n \"last_origin\": \"2026-06-01\",\n \"n_evaluated_h1\": 35,\n \"n_evaluated_h3\": 35,\n \"rmse_naive_h1\": 0.11710800875382403,\n \"mae_naive_h1\": 0.09142857142857148,\n \"rmse_naive_h3\": 0.15856499343441843,\n \"mae_naive_h3\": 0.12000000000000005,\n \"rmse_model_h1\": 0.11985758509962682,\n \"mae_model_h1\": 0.09565579999999999,\n \"rmse_model_h3\": 0.159770241753767,\n \"mae_model_h3\": 0.12128480000000005,\n \"rel_improvement_rmse_h1\": -0.023478977868906847,\n \"rel_improvement_rmse_h3\": -0.007600973539263922,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"Missing value(s) (empty field) at 2025-10-01\",\n \"handling\": \"Excluded from estimation (any regression row whose dependent or lagged difference touches the missing month is dropped); naive uses latest earlier observation; when missing is the latest month at an origin the AR model iterates forward from the last observed month (extra steps); when it is interior to the window it is linearly interpolated from neighbours dated <= origin only to build lag inputs; (origin,horizon) pairs whose target is missing are kept in the ledger with empty actual and excluded from error statistics.\"\n },\n {\n \"issue\": \"COVID-19 outlier: unemployment jumped from 4.4 (2020-03) to 14.8 (2020-04), extreme first differences in training sample\",\n \"handling\": \"Retained in the primary specification (pre-specified, no outlier treatment); a sensitivity variant excluding 2020-03..2020-12 differences from estimation is reported in report.md only.\"\n }\n ],\n \"n_input_rows\": {\n \"UNRATE.csv\": 945\n },\n \"n_analysed\": 935,\n \"random_seed\": null\n}\n 145 out/forecasts.csv\n2025-06-01,2025-09-01,3,4.1,4.4,naive\n2025-06-01,2025-09-01,3,4.09759,4.4,AR2_diff\n2025-07-01,2025-10-01,3,4.3,,naive\n2025-07-01,2025-10-01,3,4.30804,,AR2_diff\n2025-08-01,2025-09-01,1,4.3,4.4,naive\n2025-08-01,2025-09-01,1,4.29186,4.4,AR2_diff\n2025-08-01,2025-11-01,3,4.3,4.5,naive\n2025-08-01,2025-11-01,3,4.29258,4.5,AR2_diff\n2025-09-01,2025-10-01,1,4.4,,naive\n2025-09-01,2025-10-01,1,4.40412,,AR2_diff\n2025-09-01,2025-12-01,3,4.4,4.4,naive\n2025-09-01,2025-12-01,3,4.40065,4.4,AR2_diff\n2025-10-01,2025-11-01,1,4.4,4.5,naive\n2025-10-01,2025-11-01,1,4.4005,4.5,AR2_diff\n2025-10-01,2026-01-01,3,4.4,4.3,naive\n2025-10-01,2026-01-01,3,4.40126,4.3,AR2_diff\n2025-11-01,2025-12-01,1,4.5,4.4,naive\n2025-11-01,2025-12-01,1,4.50018,4.4,AR2_diff\n2025-11-01,2026-02-01,3,4.5,4.4,naive\n2025-11-01,2026-02-01,3,4.4989,4.4,AR2_diff\n2025-12-01,2026-01-01,1,4.4,4.3,naive\n2025-12-01,2026-01-01,1,4.39467,4.3,AR2_diff\n2025-12-01,2026-03-01,3,4.4,4.3,naive\n2025-12-01,2026-03-01,3,4.39999,4.3,AR2_diff","is_error":false}]},"uuid":"d3a7b551-d699-4491-8e10-d56522280b6f","timestamp":"2026-10-30T03:59:40.188Z","toolUseResult":{"stdout":"{\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 with the first available difference (1948-04 as dependent observation) up to the origin, iterated recursively and cumulated to levels for h-step forecasts.\",\n \"n_origins\": 36,\n \"first_origin\": \"2023-07-01\",\n \"last_origin\": \"2026-06-01\",\n \"n_evaluated_h1\": 35,\n \"n_evaluated_h3\": 35,\n \"rmse_naive_h1\": 0.11710800875382403,\n \"mae_naive_h1\": 0.09142857142857148,\n \"rmse_naive_h3\": 0.15856499343441843,\n \"mae_naive_h3\": 0.12000000000000005,\n \"rmse_model_h1\": 0.11985758509962682,\n \"mae_model_h1\": 0.09565579999999999,\n \"rmse_model_h3\": 0.159770241753767,\n \"mae_model_h3\": 0.12128480000000005,\n \"rel_improvement_rmse_h1\": -0.023478977868906847,\n \"rel_improvement_rmse_h3\": -0.007600973539263922,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"Missing value(s) (empty field) at 2025-10-01\",\n \"handling\": \"Excluded from estimation (any regression row whose dependent or lagged difference touches the missing month is dropped); naive uses latest earlier observation; when missing is the latest month at an origin the AR model iterates forward from the last observed month (extra steps); when it is interior to the window it is linearly interpolated from neighbours dated <= origin only to build lag inputs; (origin,horizon) pairs whose target is missing are kept in the ledger with empty actual and excluded from error statistics.\"\n },\n {\n \"issue\": \"COVID-19 outlier: unemployment jumped from 4.4 (2020-03) to 14.8 (2020-04), extreme first differences in training sample\",\n \"handling\": \"Retained in the primary specification (pre-specified, no outlier treatment); a sensitivity variant excluding 2020-03..2020-12 differences from estimation is reported in report.md only.\"\n }\n ],\n \"n_input_rows\": {\n \"UNRATE.csv\": 945\n },\n \"n_analysed\": 935,\n \"random_seed\": null\n}\n 145 out/forecasts.csv\n2025-06-01,2025-09-01,3,4.1,4.4,naive\n2025-06-01,2025-09-01,3,4.09759,4.4,AR2_diff\n2025-07-01,2025-10-01,3,4.3,,naive\n2025-07-01,2025-10-01,3,4.30804,,AR2_diff\n2025-08-01,2025-09-01,1,4.3,4.4,naive\n2025-08-01,2025-09-01,1,4.29186,4.4,AR2_diff\n2025-08-01,2025-11-01,3,4.3,4.5,naive\n2025-08-01,2025-11-01,3,4.29258,4.5,AR2_diff\n2025-09-01,2025-10-01,1,4.4,,naive\n2025-09-01,2025-10-01,1,4.40412,,AR2_diff\n2025-09-01,2025-12-01,3,4.4,4.4,naive\n2025-09-01,2025-12-01,3,4.40065,4.4,AR2_diff\n2025-10-01,2025-11-01,1,4.4,4.5,naive\n2025-10-01,2025-11-01,1,4.4005,4.5,AR2_diff\n2025-10-01,2026-01-01,3,4.4,4.3,naive\n2025-10-01,2026-01-01,3,4.40126,4.3,AR2_diff\n2025-11-01,2025-12-01,1,4.5,4.4,naive\n2025-11-01,2025-12-01,1,4.50018,4.4,AR2_diff\n2025-11-01,2026-02-01,3,4.5,4.4,naive\n2025-11-01,2026-02-01,3,4.4989,4.4,AR2_diff\n2025-12-01,2026-01-01,1,4.4,4.3,naive\n2025-12-01,2026-01-01,1,4.39467,4.3,AR2_diff\n2025-12-01,2026-03-01,3,4.4,4.3,naive\n2025-12-01,2026-03-01,3,4.39999,4.3,AR2_diff","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"c971d0b0-8b41-424d-9180-14c49b0906ef","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0024","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","version":"2.1.314","gitBranch":"HEAD"}25{"type":"api-request-blob","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","hash":"596ffe8f452f0ef1e4c19159711536fddecbe0fc6f56f73b47b60c6f0d99d1ea","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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-p out; cat > out/analysis.py <<'EOF'\n\"\"\"F3-dev-01: rolling-origin (expanding window) forecasts of UNRATE, naive vs AR(2) on first differences.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\n\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\n\nDATA = \"data/UNRATE.csv\"\nOUT = \"out\"\nMODEL = \"AR2_diff\"\nP = 2\nHORIZONS = [1, 3]\nORIGINS = pd.date_range(\"2023-07-01\", \"2026-06-01\", freq=\"MS\")\n\nraw = pd.read_csv(DATA, dtype={\"observation_date\": str, \"UNRATE\": str}, keep_default_na=False)\nn_rows = len(raw)\ndf = pd.DataFrame({\"date\": pd.to_datetime(raw[\"observation_date\"], format=\"%Y-%m-%d\"),\n \"y\": pd.to_numeric(raw[\"UNRATE\"].replace(\"\", np.nan), errors=\"coerce\")})\nissues = []\nmiss = df.loc[df.y.isna(), \"date\"].dt.strftime(\"%Y-%m-%d\").tolist()\nassert df.date.is_unique and df.date.is_monotonic_increasing\nfull = pd.date_range(df.date.min(), df.date.max(), freq=\"MS\")\nassert len(full) == len(df), \"calendar gaps present\"\ns = df.set_index(\"date\")[\"y\"]\nif miss:\n issues.append({\"issue\": f\"Missing value(s) (empty field) at {', '.join(miss)}\",\n \"handling\": \"Excluded from estimation (any regression row whose dependent or lagged difference touches the missing month is dropped); \"\n \"naive uses latest earlier observation; when missing is the latest month at an origin the AR model iterates forward from the last observed month \"\n \"(extra steps); when it is interior to the window it is linearly interpolated from neighbours dated <= origin only to build lag inputs; \"\n \"(origin,horizon) pairs whose target is missing are kept in the ledger with empty actual and excluded from error statistics.\"})\ncovid = s[\"2020-03-01\":\"2020-06-01\"]\nissues.append({\"issue\": \"COVID-19 outlier: unemployment jumped from %.1f (2020-03) to %.1f (2020-04), extreme first differences in training sample\" % (s[\"2020-03-01\"], s[\"2020-04-01\"]),\n \"handling\": \"Retained in the primary specification (pre-specified, no outlier treatment); a sensitivity variant excluding 2020-03..2020-12 differences from estimation is reported in report.md only.\"})\n\n\ndef fit_ar_diff(y, p=P, exclude=None):\n \"\"\"OLS AR(p) with intercept on dy, using rows with no missing values. y: level Series up to origin.\"\"\"\n d = y.diff()\n X = pd.concat({f\"l{k}\": d.shift(k) for k in range(1, p + 1)}, axis=1)\n data = pd.concat([d.rename(\"dy\"), X], axis=1)\n if exclude is not None:\n data = data[~((data.index >= exclude[0]) & (data.index <= exclude[1]))]\n data = data.dropna()\n A = np.column_stack([np.ones(len(data)), data[[f\"l{k}\" for k in range(1, p + 1)]].values])\n beta, *_ = np.linalg.lstsq(A, data[\"dy\"].values, rcond=None)\n return beta, len(data)\n\n\ndef forecast_ar_diff(y, t, horizons, exclude=None):\n y = y[:t]\n beta, nobs = fit_ar_diff(y, exclude=exclude)\n last_obs = y.last_valid_index()\n yy = y[:last_obs].interpolate(method=\"linear\", limit_area=\"inside\") # interior gaps only, data <= t\n lev = list(yy.values)\n dif = list(np.diff(yy.values))\n steps_extra = (t.year - last_obs.year) * 12 + (t.month - last_obs.month)\n out = {}\n H = max(horizons) + steps_extra\n for step in range(1, H + 1):\n dnew = beta[0] + sum(beta[k] * dif[-k] for k in range(1, P + 1))\n dif.append(dnew)\n lev.append(lev[-1] + dnew)\n hh = step - steps_extra\n if hh in horizons:\n out[hh] = lev[-1]\n return out, nobs\n\n\ndef run(exclude=None):\n rows, nobs_last = [], None\n for t in ORIGINS:\n yt = s[:t]\n naive = yt.dropna().iloc[-1]\n fc, nobs = forecast_ar_diff(s, t, HORIZONS, exclude)\n nobs_last = nobs\n for h in HORIZONS:\n tgt = t + pd.DateOffset(months=h)\n act = s.get(tgt, np.nan)\n for m, f in ((\"naive\", naive), (MODEL, fc[h])):\n rows.append({\"origin_date\": t.strftime(\"%Y-%m-%d\"), \"target_date\": tgt.strftime(\"%Y-%m-%d\"),\n \"horizon\": h, \"forecast\": round(float(f), 6),\n \"actual\": act, \"model\": m})\n return pd.DataFrame(rows), nobs_last\n\n\ndef stats(led):\n r = {}\n for h in HORIZONS:\n for m, tag in ((\"naive\", \"naive\"), (MODEL, \"model\")):\n sub = led[(led.horizon == h) & (led.model == m) & led.actual.notna()]\n e = sub.actual - sub.forecast\n r[f\"rmse_{tag}_h{h}\"] = float(np.sqrt(np.mean(e ** 2)))\n r[f\"mae_{tag}_h{h}\"] = float(np.mean(np.abs(e)))\n r[f\"n_evaluated_h{h}\"] = int(len(sub))\n r[f\"rel_improvement_rmse_h{h}\"] = 1 - r[f\"rmse_model_h{h}\"] / r[f\"rmse_naive_h{h}\"]\n return r\n\n\nif __name__ == \"__main__\":\n led, nobs_last = run()\n st = stats(led)\n os.makedirs(OUT, exist_ok=True)\n led.to_csv(os.path.join(OUT, \"forecasts.csv\"), index=False, float_format=\"%.6g\")\n res = {\n \"task_id\": \"F3-dev-01\",\n \"model_name\": MODEL,\n \"model_description\": \"AR(2) with intercept on monthly first differences of UNRATE, estimated by OLS on an expanding window starting with the first available difference (1948-04 as dependent observation) up to the origin, iterated recursively and cumulated to levels for h-step forecasts.\",\n \"n_origins\": len(ORIGINS),\n \"first_origin\": ORIGINS[0].strftime(\"%Y-%m-%d\"),\n \"last_origin\": ORIGINS[-1].strftime(\"%Y-%m-%d\"),\n }\n for k in [\"n_evaluated_h1\", \"n_evaluated_h3\", \"rmse_naive_h1\", \"mae_naive_h1\", \"rmse_naive_h3\", \"mae_naive_h3\",\n \"rmse_model_h1\", \"mae_model_h1\", \"rmse_model_h3\", \"mae_model_h3\",\n \"rel_improvement_rmse_h1\", \"rel_improvement_rmse_h3\"]:\n res[k] = st[k]\n res.update({\"feasibility\": \"complete\", \"feasibility_reason\": None, \"data_issues\": issues,\n \"n_input_rows\": {\"UNRATE.csv\": n_rows}, \"n_analysed\": int(nobs_last), \"random_seed\": None})\n with open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n json.dump(res, f, indent=2)\n print(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py && wc -l out/forecasts.csv && grep -E '2025-(09|10|11|12)' out/forecasts.csv"}}]}}26{"type":"api-request","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","id":"a90d04b5-e506-4731-a629-b5c371816d94","timestamp":"2026-10-30T03:59:40.190Z","version":"2.1.314","querySource":"sdk","shapeHash":"44a939a0b6e8cd148d8e4900dd77ad6a5ae0572a185aea2b7be1a177eb0ee48e","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":"875f8813-455d-4ae0-bf58-c12acdf03ab1","keep":6,"tail":["596ffe8f452f0ef1e4c19159711536fddecbe0fc6f56f73b47b60c6f0d99d1ea","7b42f7f592eb7077523d2ef4e89f7f57f6f1235278c001f573339e50f08e26e1"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"f096810f2120d1d34423cd49adcb55cf4aefd8448b1476d4146c10b5848590cc"}27{"parentUuid":"d3a7b551-d699-4491-8e10-d56522280b6f","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXkciZkuURBjHVgkfqoY","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":5100,"cache_read_input_tokens":5543,"output_tokens":1586,"output_tokens_details":{"thinking_tokens":240},"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":5100},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":2089,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXkciF9nzJhbkeU13rhN","requestRef":"a90d04b5-e506-4731-a629-b5c371816d94","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"e1c9a278-1884-41fc-9750-55041d06cb09","timestamp":"2026-10-30T03:59:43.562Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0024","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","version":"2.1.314","gitBranch":"HEAD"}28{"parentUuid":"e1c9a278-1884-41fc-9750-55041d06cb09","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXkciZkuURBjHVgkfqoY","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01RmP7qLbPemFrF9f1tsJyBj","name":"Bash","input":{"command":"cat >> out/analysis.py <<'EOF'\n\n # ---------------- supplementary (report only) ----------------\n from scipy import stats as sps\n sup = {}\n beta_last, _ = fit_ar_diff(s[:ORIGINS[-1]])\n beta_first, _ = fit_ar_diff(s[:ORIGINS[0]])\n sup[\"coef_first_origin\"] = [float(b) for b in beta_first]\n sup[\"coef_last_origin\"] = [float(b) for b in beta_last]\n\n def dm(led, h):\n a = led[(led.horizon == h) & (led.model == \"naive\") & led.actual.notna()].reset_index(drop=True)\n b = led[(led.horizon == h) & (led.model == MODEL) & led.actual.notna()].reset_index(drop=True)\n d = (a.actual - b.forecast) ** 2 - (a.actual - a.forecast) ** 2 # model loss - naive loss\n n = len(d); dbar = d.mean(); dc = d - dbar\n lrv = np.sum(dc ** 2) / n\n for k in range(1, h): # rectangular HAC with h-1 lags\n lrv += 2 * np.sum(dc[k:].values * dc[:-k].values) / n\n stat = dbar / np.sqrt(lrv / n)\n hln = np.sqrt((n + 1 - 2 * h + h * (h - 1) / n) / n) # Harvey-Leybourne-Newbold correction\n stat *= hln\n p = 2 * sps.t.sf(abs(stat), df=n - 1)\n return {\"mean_loss_diff_model_minus_naive\": float(dbar), \"dm_hln_stat\": float(stat), \"p_value_two_sided\": float(p), \"n\": int(n)}\n sup[\"dm_h1\"] = dm(led, 1); sup[\"dm_h3\"] = dm(led, 3)\n\n # bootstrap-free descriptive: share of origins where model abs error < naive abs error\n for h in HORIZONS:\n a = led[(led.horizon == h) & (led.model == \"naive\") & led.actual.notna()].reset_index(drop=True)\n b = led[(led.horizon == h) & (led.model == MODEL) & led.actual.notna()].reset_index(drop=True)\n sup[f\"share_model_better_abs_h{h}\"] = float(np.mean(np.abs(b.actual - b.forecast) < np.abs(a.actual - a.forecast)))\n sup[f\"share_ties_abs_h{h}\"] = float(np.mean(np.isclose(np.abs(b.actual - b.forecast), np.abs(a.actual - a.forecast))))\n\n led2, _ = run(exclude=(pd.Timestamp(\"2020-03-01\"), pd.Timestamp(\"2020-12-01\")))\n st2 = stats(led2)\n sup[\"sensitivity_exclude_covid_2020\"] = {k: st2[k] for k in st2 if k.startswith((\"rmse_model\", \"mae_model\", \"rel_\"))}\n sup[\"sensitivity_exclude_covid_coef_last_origin\"] = [float(b) for b in fit_ar_diff(s[:ORIGINS[-1]], exclude=(pd.Timestamp(\"2020-03-01\"), pd.Timestamp(\"2020-12-01\")))[0]]\n with open(os.path.join(OUT, \"supplementary.json\"), \"w\") as f:\n json.dump(sup, f, indent=2)\n print(json.dumps(sup, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py | sed -n '/coef_first/,$p'; ~/wp29/venv/bin/python out/analysis.py >/dev/null; md5 out/results.json 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\"coef_first_origin\": [\n -0.000535192175988547,\n 0.03795097312802282,\n -0.04298039140375718\n ],\n \"coef_last_origin\": [\n 0.0003368050557942884,\n 0.036584777952152876,\n -0.04220948335502803\n ],\n \"dm_h1\": {\n \"mean_loss_diff_model_minus_naive\": 0.0006515549916285615,\n \"dm_hln_stat\": 2.5036115978683102,\n \"p_value_two_sided\": 0.0172577765361148,\n \"n\": 35\n },\n \"dm_h3\": {\n \"mean_loss_diff_model_minus_naive\": 0.0003836730071999882,\n \"dm_hln_stat\": 1.358099191951314,\n \"p_value_two_sided\": 0.18337674877793833,\n \"n\": 35\n },\n \"share_model_better_abs_h1\": 0.2857142857142857,\n \"share_ties_abs_h1\": 0.0,\n \"share_model_better_abs_h3\": 0.2857142857142857,\n \"share_ties_abs_h3\": 0.0,\n \"sensitivity_exclude_covid_2020\": {\n \"rmse_model_h1\": 0.11861155669206222,\n \"mae_model_h1\": 0.09794017142857145,\n \"rel_improvement_rmse_h1\": -0.012838984747822302,\n \"rmse_model_h3\": 0.17561730831457695,\n \"mae_model_h3\": 0.14061548571428575,\n \"rel_improvement_rmse_h3\": -0.10754148510851014\n },\n \"sensitivity_exclude_covid_coef_last_origin\": [\n -0.0021042781557614612,\n 0.08212921988039322,\n 0.2814591585552241\n ]\n}\nMD5 (out/results.json) = f86d70051817679d8fc7e5b63513d210\nMD5 (out/forecasts.csv) = a12f8f76c103e0a207eb2c475a20811f","is_error":false}]},"uuid":"6b7ef86f-0242-4ccd-a904-205309b51b53","timestamp":"2026-10-30T03:59:54.440Z","toolUseResult":{"stdout":" \"coef_first_origin\": [\n -0.000535192175988547,\n 0.03795097312802282,\n -0.04298039140375718\n ],\n \"coef_last_origin\": [\n 0.0003368050557942884,\n 0.036584777952152876,\n -0.04220948335502803\n ],\n \"dm_h1\": {\n \"mean_loss_diff_model_minus_naive\": 0.0006515549916285615,\n \"dm_hln_stat\": 2.5036115978683102,\n \"p_value_two_sided\": 0.0172577765361148,\n \"n\": 35\n },\n \"dm_h3\": {\n \"mean_loss_diff_model_minus_naive\": 0.0003836730071999882,\n \"dm_hln_stat\": 1.358099191951314,\n \"p_value_two_sided\": 0.18337674877793833,\n \"n\": 35\n },\n 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> out/report.md <<'EOF'\n# F3-dev-01 — Can an AR model beat the naive forecast of US unemployment? (Rolling origins 2023-07 to 2026-06)\n\n## Question\nOver the 36 monthly forecast origins 2023-07-01 … 2026-06-01, does a simple autoregressive model forecast the US unemployment rate (FRED UNRATE, SA, %) better than the naive no-change forecast at horizons h = 1 and h = 3 months? We compare out-of-sample RMSE and MAE and report 1 − RMSE_model/RMSE_naive.\n\n## Data and exclusions\n- `data/UNRATE.csv`: 945 data rows, 1948-01 to 2026-09. Dates are unique, in order and have no calendar gaps.\n- **Missing value:** 2025-10-01 has an empty field (no October 2025 observation). How it was handled:\n - The 2025-10 target is not scored. Two (origin, horizon) pairs are affected: origin 2025-09 at h=1 and origin 2025-07 at h=3. They stay in `forecasts.csv` with an empty `actual`. This leaves **35 evaluated pairs per horizon**.\n - In estimation, any regression row whose dependent or lagged difference involves 2025-10 is dropped.\n - At origin 2025-10, the naive forecast uses 2025-09 (4.4). The AR model iterates forward from 2025-09, adding one extra step.\n - At later origins, 2025-10 is linearly interpolated from 2025-09 and 2025-11, both dated ≤ origin. This is used only to build lag inputs and is never used as an estimation observation.\n- **COVID-19 outlier:** unemployment rose from 4.4 (2020-03) to 14.8 (2020-04). In the primary specification this outlier was kept, a choice made in advance. A sensitivity check is reported below.\n- Every error is computed on the final vintage, so none of these results are valid in real time.\n\n## Method\n- **Naive:** the forecast for all h is the latest observation dated ≤ origin.\n- **Model `AR2_diff`:** an AR(2) with intercept on monthly first differences Δy_t.\n - Estimated by OLS on an expanding window that starts at the beginning of the series and ends at the origin. It is re-estimated at every origin using only data dated ≤ origin.\n - h-step forecasts come from iterating the difference equation and adding the steps to the last level.\n - The specification was fixed before looking at any results, with no model selection. The last training window (origin 2026-06) has 935 regression observations.\n- **Uncertainty:** Diebold–Mariano test on squared-error loss differentials, with HAC variance (h−1 lags) and the Harvey–Leybourne–Newbold small-sample correction, compared against a t(n−1) distribution.\n- **Reproducibility:** `out/analysis.py` writes `results.json`, `forecasts.csv` and `supplementary.json`. It is deterministic and uses no random numbers.\n\n## Results\n| horizon | n | RMSE naive | RMSE AR2_diff | MAE naive | MAE AR2_diff | 1 − RMSE ratio |\n|---|---|---|---|---|---|---|\n| h=1 | 35 | 0.1171 | 0.1199 | 0.0914 | 0.0957 | −0.0235 |\n| h=3 | 35 | 0.1586 | 0.1598 | 0.1200 | 0.1213 | −0.0076 |\n\nThe AR model **does not beat** the naive forecast. It is slightly worse on both RMSE and MAE at both horizons: about 2.3% higher RMSE at h=1 and 0.8% at h=3. Its absolute error was smaller than the naive error at only 10 of 35 origins (28.6%) at each horizon.\n\nWhy: the estimated AR coefficients are close to zero. At the last origin they are intercept 0.0003, lag 1 0.037 and lag 2 −0.042, and they are almost the same at the first origin. The 2020 spike dominates the full-sample OLS fit and pushes them towards zero. As a result the model is close to a random walk, and its forecasts differ from the naive one by only a few thousandths of a point. The data are recorded to 0.1 pp.\n\n## Uncertainty\n- **h=1:** DM-HLN statistic = 2.50, two-sided p = 0.017. Positive means the model's loss is higher. The model's (small) inferiority is nominally significant at the 5% level.\n- **h=3:** statistic = 1.36, p = 0.18, so there is no significant difference.\n- Treat these tests with caution:\n - n = 35, and the two forecasts are nearly identical, so the loss differentials are tiny (mean 0.00065 pp² at h=1).\n - The DM test's assumptions are only approximately met.\n - The economic difference is negligible.\n- **Sensitivity (not pre-specified; report only):** I dropped 2020-03…2020-12 differences from estimation. The AR coefficients then become substantial (lag 1 0.08, lag 2 0.28 at the last origin), but out-of-sample performance gets *worse*:\n - h=1: RMSE 0.1186, relative improvement −0.013.\n - h=3: RMSE 0.1756, relative improvement −0.108.\n- The conclusion \"no improvement over naive\" therefore holds up under this alternative.\n\n## Limitations and open issues\n- The evaluation covers only 36 origins in one fairly calm, slowly rising unemployment period. The results may not carry over to recessions.\n- Final-vintage data were used, not real-time vintages. Seasonal-factor revisions may change the errors.\n- Only one model specification was evaluated. The primary model's near-zero coefficients largely reflect the influence of the COVID outlier, so the comparison is effectively \"random walk with tiny drift vs random walk\".\n- The missing 2025-10 value reduces each horizon to 35 evaluated pairs. Interpolating it as a lag input is a modelling choice.\n- The HAC/DM inference is approximate in small samples.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"At h=1 the AR(2)-on-differences model does not beat the naive forecast: RMSE 0.1199 vs 0.1171 (relative improvement -0.023).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_naive_h1\",\"rel_improvement_rmse_h1\",\"n_evaluated_h1\"],\"status\":\"supported\",\"caveat\":\"35 evaluated pairs, final-vintage data; DM-HLN p=0.017 but economically negligible difference.\"},\n {\"id\":\"C2\",\"text\":\"At h=3 the model does not beat the naive forecast: RMSE 0.1598 vs 0.1586 (relative improvement -0.008), difference not statistically significant.\",\"results_keys\":[\"rmse_model_h3\",\"rmse_naive_h3\",\"rel_improvement_rmse_h3\",\"n_evaluated_h3\"],\"status\":\"supported\",\"caveat\":\"DM-HLN p=0.18; small sample.\"},\n {\"id\":\"C3\",\"text\":\"MAE ranks the forecasts the same way: the naive forecast has lower MAE at both horizons.\",\"results_keys\":[\"mae_naive_h1\",\"mae_model_h1\",\"mae_naive_h3\",\"mae_model_h3\"],\"status\":\"supported\",\"caveat\":\"Differences are a few thousandths of a percentage point.\"},\n {\"id\":\"C4\",\"text\":\"The finding of no improvement holds up when COVID-2020 differences are excluded from estimation (model becomes worse, especially at h=3).\",\"results_keys\":[],\"status\":\"supported\",\"caveat\":\"Sensitivity analysis not pre-specified; numbers in out/supplementary.json, not in results.json.\"},\n {\"id\":\"C5\",\"text\":\"The 2025-10 missing observation is excluded from evaluation, leaving 35 evaluated pairs per horizon.\",\"results_keys\":[\"n_evaluated_h1\",\"n_evaluated_h3\",\"data_issues\"],\"status\":\"supported\",\"caveat\":\"\"}\n]\nEOF\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'))\"; ls out"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":251,"cache_read_input_tokens":12907,"output_tokens":2829,"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":251},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXkdz2TSVN42QnP9KGmK","requestRef":"88b8aabd-27b8-4a38-ae57-57e7651fcef5","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"cc3adeb9-5374-4bce-a7ae-47b12b529ac6","timestamp":"2026-10-30T04:00:22.519Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0024","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","version":"2.1.314","gitBranch":"HEAD"}40{"parentUuid":"cc3adeb9-5374-4bce-a7ae-47b12b529ac6","isSidechain":false,"promptId":"3ee256e1-e8df-4565-999b-376f641ddd55","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01EAU7w1vF8xC23E2qPE9wqD","type":"tool_result","content":"analysis.py\nclaims.json\nforecasts.csv\nreport.md\nresults.json\nsupplementary.json","is_error":false}]},"uuid":"eb6f146d-1932-4994-b8fc-7b26c6d57997","timestamp":"2026-10-30T04:00:22.571Z","toolUseResult":{"stdout":"analysis.py\nclaims.json\nforecasts.csv\nreport.md\nresults.json\nsupplementary.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"cc3adeb9-5374-4bce-a7ae-47b12b529ac6","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0024","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"eb6f146d-1932-4994-b8fc-7b26c6d57997","isSidechain":false,"attachment":{"type":"date","date":"2026-10-30","changed":true},"type":"attachment","uuid":"4ef1c009-fbb1-45af-8c28-0154432937a3","timestamp":"2026-10-30T04:00:22.572Z","rendered":[{"content":"<system-reminder>\nThe date has changed. Today's date is now 2026-10-30. No need to announce the new date — the user's own clock shows it.\n</system-reminder>"}],"renderedRole":"system","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0024","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","version":"2.1.314","gitBranch":"HEAD"}42{"type":"api-request-blob","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","hash":"c3f52db55744807bc6348058f3826501296a2ac78fd78eb3fa2bcd31688fcc63","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01EAU7w1vF8xC23E2qPE9wqD","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F3-dev-01 — Can an AR model beat the naive forecast of US unemployment? (Rolling origins 2023-07 to 2026-06)\n\n## Question\nOver the 36 monthly forecast origins 2023-07-01 … 2026-06-01, does a simple autoregressive model forecast the US unemployment rate (FRED UNRATE, SA, %) better than the naive no-change forecast at horizons h = 1 and h = 3 months? We compare out-of-sample RMSE and MAE and report 1 − RMSE_model/RMSE_naive.\n\n## Data and exclusions\n- `data/UNRATE.csv`: 945 data rows, 1948-01 to 2026-09. Dates are unique, in order and have no calendar gaps.\n- **Missing value:** 2025-10-01 has an empty field (no October 2025 observation). How it was handled:\n - The 2025-10 target is not scored. Two (origin, horizon) pairs are affected: origin 2025-09 at h=1 and origin 2025-07 at h=3. They stay in `forecasts.csv` with an empty `actual`. This leaves **35 evaluated pairs per horizon**.\n - In estimation, any regression row whose dependent or lagged difference involves 2025-10 is dropped.\n - At origin 2025-10, the naive forecast uses 2025-09 (4.4). The AR model iterates forward from 2025-09, adding one extra step.\n - At later origins, 2025-10 is linearly interpolated from 2025-09 and 2025-11, both dated ≤ origin. This is used only to build lag inputs and is never used as an estimation observation.\n- **COVID-19 outlier:** unemployment rose from 4.4 (2020-03) to 14.8 (2020-04). In the primary specification this outlier was kept, a choice made in advance. A sensitivity check is reported below.\n- Every error is computed on the final vintage, so none of these results are valid in real time.\n\n## Method\n- **Naive:** the forecast for all h is the latest observation dated ≤ origin.\n- **Model `AR2_diff`:** an AR(2) with intercept on monthly first differences Δy_t.\n - Estimated by OLS on an expanding window that starts at the beginning of the series and ends at the origin. It is re-estimated at every origin using only data dated ≤ origin.\n - h-step forecasts come from iterating the difference equation and adding the steps to the last level.\n - The specification was fixed before looking at any results, with no model selection. The last training window (origin 2026-06) has 935 regression observations.\n- **Uncertainty:** Diebold–Mariano test on squared-error loss differentials, with HAC variance (h−1 lags) and the Harvey–Leybourne–Newbold small-sample correction, compared against a t(n−1) distribution.\n- **Reproducibility:** `out/analysis.py` writes `results.json`, `forecasts.csv` and `supplementary.json`. It is deterministic and uses no random numbers.\n\n## Results\n| horizon | n | RMSE naive | RMSE AR2_diff | MAE naive | MAE AR2_diff | 1 − RMSE ratio |\n|---|---|---|---|---|---|---|\n| h=1 | 35 | 0.1171 | 0.1199 | 0.0914 | 0.0957 | −0.0235 |\n| h=3 | 35 | 0.1586 | 0.1598 | 0.1200 | 0.1213 | −0.0076 |\n\nThe AR model **does not beat** the naive forecast. It is slightly worse on both RMSE and MAE at both horizons: about 2.3% higher RMSE at h=1 and 0.8% at h=3. Its absolute error was smaller than the naive error at only 10 of 35 origins (28.6%) at each horizon.\n\nWhy: the estimated AR coefficients are close to zero. At the last origin they are intercept 0.0003, lag 1 0.037 and lag 2 −0.042, and they are almost the same at the first origin. The 2020 spike dominates the full-sample OLS fit and pushes them towards zero. As a result the model is close to a random walk, and its forecasts differ from the naive one by only a few thousandths of a point. The data are recorded to 0.1 pp.\n\n## Uncertainty\n- **h=1:** DM-HLN statistic = 2.50, two-sided p = 0.017. Positive means the model's loss is higher. The model's (small) inferiority is nominally significant at the 5% level.\n- **h=3:** statistic = 1.36, p = 0.18, so there is no significant difference.\n- Treat these tests with caution:\n - n = 35, and the two forecasts are nearly identical, so the loss differentials are tiny (mean 0.00065 pp² at h=1).\n - The DM test's assumptions are only approximately met.\n - The economic difference is negligible.\n- **Sensitivity (not pre-specified; report only):** I dropped 2020-03…2020-12 differences from estimation. The AR coefficients then become substantial (lag 1 0.08, lag 2 0.28 at the last origin), but out-of-sample performance gets *worse*:\n - h=1: RMSE 0.1186, relative improvement −0.013.\n - h=3: RMSE 0.1756, relative improvement −0.108.\n- The conclusion \"no improvement over naive\" therefore holds up under this alternative.\n\n## Limitations and open issues\n- The evaluation covers only 36 origins in one fairly calm, slowly rising unemployment period. The results may not carry over to recessions.\n- Final-vintage data were used, not real-time vintages. Seasonal-factor revisions may change the errors.\n- Only one model specification was evaluated. The primary model's near-zero coefficients largely reflect the influence of the COVID outlier, so the comparison is effectively \"random walk with tiny drift vs random walk\".\n- The missing 2025-10 value reduces each horizon to 35 evaluated pairs. Interpolating it as a lag input is a modelling choice.\n- The HAC/DM inference is approximate in small samples.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"At h=1 the AR(2)-on-differences model does not beat the naive forecast: RMSE 0.1199 vs 0.1171 (relative improvement -0.023).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_naive_h1\",\"rel_improvement_rmse_h1\",\"n_evaluated_h1\"],\"status\":\"supported\",\"caveat\":\"35 evaluated pairs, final-vintage data; DM-HLN p=0.017 but economically negligible difference.\"},\n {\"id\":\"C2\",\"text\":\"At h=3 the model does not beat the naive forecast: RMSE 0.1598 vs 0.1586 (relative improvement -0.008), difference not statistically significant.\",\"results_keys\":[\"rmse_model_h3\",\"rmse_naive_h3\",\"rel_improvement_rmse_h3\",\"n_evaluated_h3\"],\"status\":\"supported\",\"caveat\":\"DM-HLN p=0.18; small sample.\"},\n {\"id\":\"C3\",\"text\":\"MAE ranks the forecasts the same way: the naive forecast has lower MAE at both horizons.\",\"results_keys\":[\"mae_naive_h1\",\"mae_model_h1\",\"mae_naive_h3\",\"mae_model_h3\"],\"status\":\"supported\",\"caveat\":\"Differences are a few thousandths of a percentage point.\"},\n {\"id\":\"C4\",\"text\":\"The finding of no improvement holds up when COVID-2020 differences are excluded from estimation (model becomes worse, especially at h=3).\",\"results_keys\":[],\"status\":\"supported\",\"caveat\":\"Sensitivity analysis not pre-specified; numbers in out/supplementary.json, not in results.json.\"},\n {\"id\":\"C5\",\"text\":\"The 2025-10 missing observation is excluded from evaluation, leaving 35 evaluated pairs per horizon.\",\"results_keys\":[\"n_evaluated_h1\",\"n_evaluated_h3\",\"data_issues\"],\"status\":\"supported\",\"caveat\":\"\"}\n]\nEOF\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'))\"; ls out"}}]}}43{"type":"api-request","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","id":"23588bae-1dd9-4fb6-9463-7fc99fe71cc3","timestamp":"2026-10-30T04:00:22.574Z","version":"2.1.314","querySource":"sdk","shapeHash":"44a939a0b6e8cd148d8e4900dd77ad6a5ae0572a185aea2b7be1a177eb0ee48e","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":"88b8aabd-27b8-4a38-ae57-57e7651fcef5","keep":12,"tail":["c3f52db55744807bc6348058f3826501296a2ac78fd78eb3fa2bcd31688fcc63","e86996ac539c913a7aa355321579875267e9262302635c4327413b7e37a674a4"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",13,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"e0ef41477d2204d11323e949e9726d43378b689082b217ea749d020efbf5cb89"}44{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"4ef1c009-fbb1-45af-8c28-0154432937a3","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508"}45{"type":"atis-latch","atis":"","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508"}46{"parentUuid":"4ef1c009-fbb1-45af-8c28-0154432937a3","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXkfr4YUuRSaueQA8HRF","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2867,"cache_read_input_tokens":13158,"output_tokens":925,"output_tokens_details":{"thinking_tokens":27},"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":2867},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":6858,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXkfqmftjdBy63ptKsxS","requestRef":"23588bae-1dd9-4fb6-9463-7fc99fe71cc3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6bd8fcc3-4b88-4235-96e5-b33f00af9da9","timestamp":"2026-10-30T04:00:30.712Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0024","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","version":"2.1.314","gitBranch":"HEAD"}47{"parentUuid":"6bd8fcc3-4b88-4235-96e5-b33f00af9da9","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXkfr4YUuRSaueQA8HRF","type":"message","role":"assistant","content":[{"type":"text","text":"The AR model I tested does not beat the naive (no-change) forecast. It is slightly worse at both the one-month and three-month horizons.\n\nI used an AR(2) on monthly changes in the unemployment rate, called `AR2_diff`. It is re-estimated by ordinary least squares at each of the 36 forecast origins (2023-07 to 2026-06), using only data up to that origin. I fixed this specification before looking at any results.\n\n| Horizon | Pairs scored | RMSE naive | RMSE AR2_diff | MAE naive | MAE AR2_diff | 1 − RMSE ratio |\n|---|---|---|---|---|---|---|\n| 1 month | 35 | 0.117 | 0.120 | 0.091 | 0.096 | −0.023 |\n| 3 months | 35 | 0.159 | 0.160 | 0.120 | 0.121 | −0.008 |\n\n- **How often the model wins:** its error was smaller than the naive one at only 10 of 35 origins at each horizon.\n- **Significance:** a Diebold–Mariano test (with a small-sample correction) finds the model's extra error nominally significant at one month (p = 0.017) but not at three months (p = 0.18). The size of the difference is negligible in practice: a few thousandths of a percentage point, while the data are recorded to 0.1.\n- **Why the model behaves like the naive forecast:** the 2020 COVID spike (4.4% to 14.8% in one month) dominates the fit and pushes the AR coefficients close to zero. The model ends up almost a random walk.\n- **Sensitivity check:** I added this after seeing the results, so it is not pre-specified. Leaving the 2020 changes out of estimation gives the model real coefficients, but it then does worse: −0.013 at one month and −0.108 at three months. The \"no improvement\" conclusion holds either way.\n\n**Limitations:**\n- **Missing month:** there is no value for October 2025. The two forecasts that target it are kept in the forecast file with an empty actual and left out of the scores, which is why each horizon has 35 scored pairs rather than 36. For later origins I filled October 2025 by interpolating between its neighbours, but only to supply lag values, never as an estimation data point.\n- **Scope:** the results are on the current revised data, so they are not real-time results. They cover a short, calm period, and only one model was tested.\n\nRunning `analysis.py` twice gave identical outputs.\n\nFiles are in `out/`:\n- `analysis.py`\n- `results.json`\n- `forecasts.csv` (144 rows)\n- `report.md`\n- `claims.json`\n- `supplementary.json` (test results, AR coefficients and the sensitivity check)"}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2867,"cache_read_input_tokens":13158,"output_tokens":925,"output_tokens_details":{"thinking_tokens":27},"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":2867},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXkfqmftjdBy63ptKsxS","requestRef":"23588bae-1dd9-4fb6-9463-7fc99fe71cc3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"a374d1b1-ba6b-4299-a14a-2a98bf6e09ee","timestamp":"2026-10-30T04:00:32.085Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0024","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","version":"2.1.314","gitBranch":"HEAD"}48{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"a374d1b1-ba6b-4299-a14a-2a98bf6e09ee","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508"}49{"type":"cost-state","sessionId":"9b17892a-17dd-4863-9fe8-7564f240c508","totalCostUSD":0.2685016,"totalAPIDuration":86324,"totalAPIDurationWithoutRetries":86321,"totalToolDuration":1925,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":88366,"startTime":1793332743743,"modelUsage":{"claude-opus-5-5":{"inputTokens":16,"outputTokens":9288,"thinkingTokens":1062,"cacheReadInputTokens":50363,"cacheCreationInputTokens":14521,"cacheCreationEphemeral5mInputTokens":14521,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.2685016}},"hasUnknownModelCost":false}50