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The estimands are the out-of-sample RMSE and MAE, over a fixed set of 48 rolling (expanding-window) origins and horizons h ∈ {1, 3}, of (a) the naive forecast and (b) one model of your choice, and the relative improvement 1 − RMSE_model / RMSE_naive per horizon.\n\n## Inputs\n- `data/canada_gdp_employment.csv` — observed data (Statistics Canada, current vintage, retrieved 2026-10-30 UTC via the Web Data Service; see `data/README.md` for vectors, URL, SHA-256 and licence). Columns: `month` (YYYY-MM-01), `gdp_level` (monthly real GDP at basic prices, chained 2017 dollars, SA, millions), `gdp_yoy` (target: year-over-year growth of `gdp_level`, percent, 4 decimals), `emp_level` (LFS employment, SA, thousands), `emp_yoy` (predictor: year-over-year employment growth, percent, 4 decimals). 345 monthly rows, 1998-01 to 2026-09; GDP columns are empty after the last published GDP month (2026-07), employment runs to 2026-09.\n\n## Information-availability rules\n- Forecast origins: the 48 months t = 2022-05-01, 2022-06-01, …, 2026-04-01 (identified by their `month` value). The origin is the **end** of month t. Horizons h ∈ {1, 3}; the target of origin t at horizon h is `gdp_yoy` of month t + h.\n- Publication lags (documented in `data/README.md`): monthly GDP for a reference month is published about two months after the end of that month; LFS employment for a reference month is published in the first/second week of the following month. Therefore, at origin t, **the GDP columns are available only for months ≤ t − 2 and the employment columns only for months ≤ t − 1**. A forecast made at origin t (its estimation sample, its model selection, its transformations and the values plugged into the forecast) may use only these observations. Training targets must also be observed at the origin.\n- Naive baseline: for both horizons, the forecast is the most recent GDP growth value available at the origin, i.e. `gdp_yoy` of month t − 2.\n- The errors are computed on the data as given (current vintage); the exercise simulates publication timing, not historical first-release values — do not claim real-time validity.\n\n## Required outputs\n- `out/forecasts.csv` — the forecast ledger, one row per (origin, horizon, model), columns: `origin_date` (YYYY-MM-DD, the `month` of the origin), `target_date`, `horizon` (integer), `forecast`, `actual` (the `gdp_yoy` value of the target month), `model` (`naive` or the value of `model_name`), `last_target_date_used` (YYYY-MM-DD: the latest `gdp_yoy` month entering the forecast, estimation included), `last_predictor_date_used` (YYYY-MM-DD: the latest `emp_yoy` month used, or empty if the model does not use employment). Expected: 48 × 2 × 2 = 192 rows.\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F3-conf-01\" |\n| `model_name` | string | — | short name of your model, used in the `model` column |\n| `model_description` | string | — | one-sentence specification (lags, predictors, estimation sample, method) |\n| `n_origins` | integer | — | 48 |\n| `first_origin`, `last_origin` | string | date | first and last origin dates |\n| `last_target_date_available` | string | date | latest `gdp_yoy` month available at the last origin (2026-04-01) under the rules |\n| `last_predictor_date_available` | string | date | latest `emp_yoy` month available at the last origin under the rules |\n| `rmse_naive_h1`, `mae_naive_h1`, `rmse_naive_h3`, `mae_naive_h3` | number | percentage points | naive 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 |\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 | — | {\"canada_gdp_employment.csv\": number of data rows read, excluding the header} |\n| `n_analysed` | integer | — | observations in the last estimation sample |\n| `random_seed` | integer or null | — | seed used, if any |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` and `out/forecasts.csv` from `data/` only, deterministically.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}].\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels available). Do not modify `data/`.\n- This task is designed to be completed in well under 20 minutes of work.\ntotal 88\ndrwxr-xr-x@ 10 simon-pierreboucher staff 320 oct. 30 01:03 .\ndrwxr-xr-x 7 simon-pierreboucher staff 224 oct. 30 01:00 ..\n-rw-r--r--@ 1 simon-pierreboucher staff 7953 oct. 30 01:01 analysis.py\n-rw-r--r--@ 1 simon-pierreboucher staff 1633 oct. 30 01:02 claims.json\n-rw-r--r--@ 1 simon-pierreboucher staff 333 oct. 30 01:01 exclusions.csv\n-rw-r--r--@ 1 simon-pierreboucher staff 13445 oct. 30 01:01 forecasts.csv\n-rw-r--r--@ 1 simon-pierreboucher staff 5453 oct. 30 01:02 report.md\n-rw-r--r--@ 1 simon-pierreboucher staff 2597 oct. 30 01:01 results.json\ndrwxr-xr-x 2 simon-pierreboucher staff 64 oct. 30 01:03 review\ndrwxr-xr-x@ 8 simon-pierreboucher staff 256 oct. 30 01:02 state\n{\n \"task_id\": \"F3-conf-01\",\n \"model_name\": \"adl_direct_emp\",\n \"model_description\": \"Direct (per-horizon) OLS regression of gdp_yoy(t+h) on a constant, gdp_yoy(t-2) and emp_yoy(t-1), re-estimated at each origin on an expanding window of training rows (from 1998-03) whose target month is <= t-2, excluding rows touching 2020-03..2021-12.\",\n \"n_origins\": 48,\n \"first_origin\": \"2022-05-01\",\n \"last_origin\": \"2026-04-01\",\n \"last_target_date_available\": \"2026-02-01\",\n \"last_predictor_date_available\": \"2026-03-01\",\n \"rmse_naive_h1\": 0.813620914876824,\n \"mae_naive_h1\": 0.6421395833333333,\n \"rmse_model_h1\": 0.7429391714223801,\n \"mae_model_h1\": 0.6039917578066155,\n \"rmse_naive_h3\": 1.1399827160604965,\n \"mae_naive_h3\": 0.8715583333333333,\n \"rmse_model_h3\": 0.9023000239646665,\n \"mae_model_h3\": 0.7534546734385598,\n \"rel_improvement_rmse_h1\": 0.08687306602134803,\n \"rel_improvement_rmse_h3\": 0.20849675065004825,\n \"dm_test\": {\n \"h1\": {\n \"mean_loss_diff_model_minus_naive\": -0.11002038069122726,\n \"dm_stat_hln\": -1.3266201174612682,\n \"p_value_two_sided\": 0.191044366683287,\n \"nw_lags\": 2\n },\n \"h3\": {\n \"mean_loss_diff_model_minus_naive\": -0.485415259670029,\n \"dm_stat_hln\": -1.3657496075270925,\n \"p_value_two_sided\": 0.178518085003236,\n \"nw_lags\": 4\n }\n },\n \"n_training_last_origin_h3\": 306,\n \"sensitivity_no_covid_exclusion\": {\n \"rmse_h1\": 0.8040049585200156,\n \"rel_improvement_rmse_h1\": 0.011818718251932037,\n \"rmse_h3\": 0.7937029596656197,\n \"rel_improvement_rmse_h3\": 0.3037587776694858\n },\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"README states gdp_yoy is empty for the first 12 months, but the file contains yoy values for 1998 (both series).\",\n \"handling\": \"Used as given; yoy recomputed from levels agrees to rounding (<5e-5) where possible.\"\n },\n {\n \"issue\": \"gdp columns missing for 2026-08 and 2026-09 (not yet published).\",\n \"handling\": \"Not needed: latest target (2026-07) and latest GDP input (2026-02) are present.\"\n },\n {\n \"issue\": \"COVID-19 outliers (gdp_yoy from -16.2 to +18.5 in 2020-2021).\",\n \"handling\": \"Model training rows touching 2020-03..2021-12 excluded; naive unaffected; see out/exclusions.csv.\"\n },\n {\n \"issue\": \"Current-vintage data (revised), not first releases.\",\n \"handling\": \"Exercise simulates publication timing only; no real-time validity claimed.\"\n }\n ],\n \"n_input_rows\": {\n \"canada_gdp_employment.csv\": 345\n },\n \"n_analysed\": 310,\n \"random_seed\": null\n}[\n {\"id\":\"C1\",\"text\":\"The naive forecast gdp_yoy(t-2) has RMSE 0.814 pp at h=1 and 1.140 pp at h=3 over 48 origins (MAE 0.642 and 0.872).\",\"results_keys\":[\"rmse_naive_h1\",\"rmse_naive_h3\",\"mae_naive_h1\",\"mae_naive_h3\",\"n_origins\"],\"status\":\"supported\",\"caveat\":\"Current-vintage data; timing simulation only.\"},\n {\"id\":\"C2\",\"text\":\"The employment-augmented direct ADL model has lower RMSE and MAE than the naive forecast at both horizons (RMSE 0.743 and 0.902 pp; relative improvement 0.087 at h=1 and 0.208 at h=3).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_model_h3\",\"mae_model_h1\",\"mae_model_h3\",\"rel_improvement_rmse_h1\",\"rel_improvement_rmse_h3\"],\"status\":\"supported\",\"caveat\":\"Point estimates only; see C3.\"},\n {\"id\":\"C3\",\"text\":\"The improvements are not statistically significant: Diebold-Mariano (HLN-corrected) p-values are about 0.19 (h=1) and 0.18 (h=3).\",\"results_keys\":[\"dm_test\"],\"status\":\"supported\",\"caveat\":\"Low power with 48 overlapping errors.\"},\n {\"id\":\"C4\",\"text\":\"How large the gain is depends on the COVID-period training exclusion; without it the relative RMSE improvement is 0.012 at h=1 and 0.304 at h=3, but the model still beats naive at both horizons.\",\"results_keys\":[\"sensitivity_no_covid_exclusion\"],\"status\":\"supported\",\"caveat\":\"Sensitivity only, not the headline model.\"},\n {\"id\":\"C5\",\"text\":\"All forecasts use GDP only through t-2 and employment only through t-1; at the last origin these are 2026-02-01 and 2026-03-01.\",\"results_keys\":[\"last_target_date_available\",\"last_predictor_date_available\",\"last_origin\"],\"status\":\"supported\",\"caveat\":\"Enforced in code and verified in out/state/checks.md.\"}\n]","is_error":false}]},"uuid":"8cdb29b4-d4d6-44f2-a95e-59482b7f376a","timestamp":"2026-10-30T05:03:08.477Z","toolUseResult":{"stdout":"# F3-conf-01 — Forecasting Canadian monthly GDP growth under publication lags\n\n## Scientific question\nAt the end of each month, how well can the year-over-year growth of Canadian monthly real GDP one and three months ahead be forecast from the information that is actually published at that time, and does a model that also uses the (more timely) Labour Force Survey employment growth beat the naive forecast? The estimands are the out-of-sample RMSE and MAE, over a fixed set of 48 rolling (expanding-window) origins and horizons h ∈ {1, 3}, of (a) the naive forecast and (b) one model of your choice, and the relative improvement 1 − RMSE_model / RMSE_naive per horizon.\n\n## Inputs\n- `data/canada_gdp_employment.csv` — observed data (Statistics Canada, current vintage, retrieved 2026-10-30 UTC via the Web Data Service; see `data/README.md` for vectors, URL, SHA-256 and licence). Columns: `month` (YYYY-MM-01), `gdp_level` (monthly real GDP at basic prices, chained 2017 dollars, SA, millions), `gdp_yoy` (target: year-over-year growth of `gdp_level`, percent, 4 decimals), `emp_level` (LFS employment, SA, thousands), `emp_yoy` (predictor: year-over-year employment growth, percent, 4 decimals). 345 monthly rows, 1998-01 to 2026-09; GDP columns are empty after the last published GDP month (2026-07), employment runs to 2026-09.\n\n## Information-availability rules\n- Forecast origins: the 48 months t = 2022-05-01, 2022-06-01, …, 2026-04-01 (identified by their `month` value). The origin is the **end** of month t. Horizons h ∈ {1, 3}; the target of origin t at horizon h is `gdp_yoy` of month t + h.\n- Publication lags (documented in `data/README.md`): monthly GDP for a reference month is published about two months after the end of that month; LFS employment for a reference month is published in the first/second week of the following month. Therefore, at origin t, **the GDP columns are available only for months ≤ t − 2 and the employment columns only for months ≤ t − 1**. A forecast made at origin t (its estimation sample, its model selection, its transformations and the values plugged into the forecast) may use only these observations. Training targets must also be observed at the origin.\n- Naive baseline: for both horizons, the forecast is the most recent GDP growth value available at the origin, i.e. `gdp_yoy` of month t − 2.\n- The errors are computed on the data as given (current vintage); the exercise simulates publication timing, not historical first-release values — do not claim real-time validity.\n\n## Required outputs\n- `out/forecasts.csv` — the forecast ledger, one row per (origin, horizon, model), columns: `origin_date` (YYYY-MM-DD, the `month` of the origin), `target_date`, `horizon` (integer), `forecast`, `actual` (the `gdp_yoy` value of the target month), `model` (`naive` or the value of `model_name`), `last_target_date_used` (YYYY-MM-DD: the latest `gdp_yoy` month entering the forecast, estimation included), `last_predictor_date_used` (YYYY-MM-DD: the latest `emp_yoy` month used, or empty if the model does not use employment). Expected: 48 × 2 × 2 = 192 rows.\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F3-conf-01\" |\n| `model_name` | string | — | short name of your model, used in the `model` column |\n| `model_description` | string | — | one-sentence specification (lags, predictors, estimation sample, method) |\n| `n_origins` | integer | — | 48 |\n| `first_origin`, `last_origin` | string | date | first and last origin dates |\n| `last_target_date_available` | string | date | latest `gdp_yoy` month available at the last origin (2026-04-01) under the rules |\n| `last_predictor_date_available` | string | date | latest `emp_yoy` month available at the last origin under the rules |\n| `rmse_naive_h1`, `mae_naive_h1`, `rmse_naive_h3`, `mae_naive_h3` | number | percentage points | naive 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 |\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 | — | {\"canada_gdp_employment.csv\": number of data rows read, excluding the header} |\n| `n_analysed` | integer | — | observations in the last estimation sample |\n| `random_seed` | integer or null | — | seed used, if any |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` and `out/forecasts.csv` from `data/` only, deterministically.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}].\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels available). Do not modify `data/`.\n- This task is designed to be completed in well under 20 minutes of work.\ntotal 88\ndrwxr-xr-x@ 10 simon-pierreboucher staff 320 oct. 30 01:03 .\ndrwxr-xr-x 7 simon-pierreboucher staff 224 oct. 30 01:00 ..\n-rw-r--r--@ 1 simon-pierreboucher staff 7953 oct. 30 01:01 analysis.py\n-rw-r--r--@ 1 simon-pierreboucher staff 1633 oct. 30 01:02 claims.json\n-rw-r--r--@ 1 simon-pierreboucher staff 333 oct. 30 01:01 exclusions.csv\n-rw-r--r--@ 1 simon-pierreboucher staff 13445 oct. 30 01:01 forecasts.csv\n-rw-r--r--@ 1 simon-pierreboucher staff 5453 oct. 30 01:02 report.md\n-rw-r--r--@ 1 simon-pierreboucher staff 2597 oct. 30 01:01 results.json\ndrwxr-xr-x 2 simon-pierreboucher staff 64 oct. 30 01:03 review\ndrwxr-xr-x@ 8 simon-pierreboucher staff 256 oct. 30 01:02 state\n{\n \"task_id\": \"F3-conf-01\",\n \"model_name\": \"adl_direct_emp\",\n \"model_description\": \"Direct (per-horizon) OLS regression of gdp_yoy(t+h) on a constant, gdp_yoy(t-2) and emp_yoy(t-1), re-estimated at each origin on an expanding window of training rows (from 1998-03) whose target month is <= t-2, excluding rows touching 2020-03..2021-12.\",\n \"n_origins\": 48,\n \"first_origin\": \"2022-05-01\",\n \"last_origin\": \"2026-04-01\",\n \"last_target_date_available\": \"2026-02-01\",\n \"last_predictor_date_available\": \"2026-03-01\",\n \"rmse_naive_h1\": 0.813620914876824,\n \"mae_naive_h1\": 0.6421395833333333,\n \"rmse_model_h1\": 0.7429391714223801,\n \"mae_model_h1\": 0.6039917578066155,\n \"rmse_naive_h3\": 1.1399827160604965,\n \"mae_naive_h3\": 0.8715583333333333,\n \"rmse_model_h3\": 0.9023000239646665,\n \"mae_model_h3\": 0.7534546734385598,\n \"rel_improvement_rmse_h1\": 0.08687306602134803,\n \"rel_improvement_rmse_h3\": 0.20849675065004825,\n \"dm_test\": {\n \"h1\": {\n \"mean_loss_diff_model_minus_naive\": -0.11002038069122726,\n \"dm_stat_hln\": -1.3266201174612682,\n \"p_value_two_sided\": 0.191044366683287,\n \"nw_lags\": 2\n },\n \"h3\": {\n \"mean_loss_diff_model_minus_naive\": -0.485415259670029,\n \"dm_stat_hln\": -1.3657496075270925,\n \"p_value_two_sided\": 0.178518085003236,\n \"nw_lags\": 4\n }\n },\n \"n_training_last_origin_h3\": 306,\n \"sensitivity_no_covid_exclusion\": {\n \"rmse_h1\": 0.8040049585200156,\n \"rel_improvement_rmse_h1\": 0.011818718251932037,\n \"rmse_h3\": 0.7937029596656197,\n \"rel_improvement_rmse_h3\": 0.3037587776694858\n },\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"README states gdp_yoy is empty for the first 12 months, but the file contains yoy values for 1998 (both series).\",\n \"handling\": \"Used as given; yoy recomputed from levels agrees to rounding (<5e-5) where possible.\"\n },\n {\n \"issue\": \"gdp columns missing for 2026-08 and 2026-09 (not yet published).\",\n \"handling\": \"Not needed: latest target (2026-07) and latest GDP input (2026-02) are present.\"\n },\n {\n \"issue\": \"COVID-19 outliers (gdp_yoy from -16.2 to +18.5 in 2020-2021).\",\n \"handling\": \"Model training rows touching 2020-03..2021-12 excluded; naive unaffected; see out/exclusions.csv.\"\n },\n {\n \"issue\": \"Current-vintage data (revised), not first releases.\",\n \"handling\": \"Exercise simulates publication timing only; no real-time validity claimed.\"\n }\n ],\n \"n_input_rows\": {\n \"canada_gdp_employment.csv\": 345\n },\n \"n_analysed\": 310,\n \"random_seed\": null\n}[\n {\"id\":\"C1\",\"text\":\"The naive forecast gdp_yoy(t-2) has RMSE 0.814 pp at h=1 and 1.140 pp at h=3 over 48 origins (MAE 0.642 and 0.872).\",\"results_keys\":[\"rmse_naive_h1\",\"rmse_naive_h3\",\"mae_naive_h1\",\"mae_naive_h3\",\"n_origins\"],\"status\":\"supported\",\"caveat\":\"Current-vintage data; timing simulation only.\"},\n {\"id\":\"C2\",\"text\":\"The employment-augmented direct ADL model has lower RMSE and MAE than the naive forecast at both horizons (RMSE 0.743 and 0.902 pp; relative improvement 0.087 at h=1 and 0.208 at h=3).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_model_h3\",\"mae_model_h1\",\"mae_model_h3\",\"rel_improvement_rmse_h1\",\"rel_improvement_rmse_h3\"],\"status\":\"supported\",\"caveat\":\"Point estimates only; see C3.\"},\n {\"id\":\"C3\",\"text\":\"The improvements are not statistically significant: Diebold-Mariano (HLN-corrected) p-values are about 0.19 (h=1) and 0.18 (h=3).\",\"results_keys\":[\"dm_test\"],\"status\":\"supported\",\"caveat\":\"Low power with 48 overlapping errors.\"},\n {\"id\":\"C4\",\"text\":\"How large the gain is depends on the COVID-period training exclusion; without it the relative RMSE improvement is 0.012 at h=1 and 0.304 at h=3, but the model still beats naive at both horizons.\",\"results_keys\":[\"sensitivity_no_covid_exclusion\"],\"status\":\"supported\",\"caveat\":\"Sensitivity only, not the headline model.\"},\n {\"id\":\"C5\",\"text\":\"All forecasts use GDP only through t-2 and employment only through t-1; 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Model 'adl_direct_emp': direct OLS per horizon\n y(tau+h) = a + b*y(tau-2) + c*e(tau-1), training rows tau with tau+h <= t-2,\n excluding rows touching 2020-03..2021-12 (COVID); forecast plugs y(t-2), e(t-1).\nNo randomness is used.\n\"\"\"\nimport json, os\nimport numpy as np, pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDATA = os.path.join(ROOT, \"data\", \"canada_gdp_employment.csv\")\nOUT = os.path.join(ROOT, \"out\")\nMODEL = \"adl_direct_emp\"\nCOVID = (pd.Timestamp(\"2020-03-01\"), pd.Timestamp(\"2021-12-01\"))\n\nd = pd.read_csv(DATA, parse_dates=[\"month\"]).sort_values(\"month\").reset_index(drop=True)\nn_raw = len(d)\nd = d.set_index(\"month\")\nmonths = d.index\norigins = pd.date_range(\"2022-05-01\", \"2026-04-01\", freq=\"MS\")\nH = [1, 3]\nM = lambda m, k: m + pd.DateOffset(months=k)\nfmt = lambda x: x.strftime(\"%Y-%m-%d\")\nin_covid = lambda m: (m >= COVID[0]) & (m <= COVID[1])\n\n\ndef training_rows(t, h, return_ledger=False, exclude_covid=True):\n \"\"\"Training rows available at origin t for horizon h (vectorised).\"\"\"\n gdp_last = M(t, -2) # latest GDP month observed at origin t\n emp_last = M(t, -1) # latest employment month observed at origin t\n y = d[\"gdp_yoy\"].where(months <= gdp_last) # information truncation\n e = d[\"emp_yoy\"].where(months <= emp_last)\n df = pd.DataFrame({\"y_tgt\": y.shift(-h), \"y_lag\": y.shift(2), \"e_lag\": e.shift(1)}, index=months)\n ledger = []\n n0 = len(df)\n df1 = df.dropna()\n ledger.append((\"drop_unavailable\", f\"target month tau+{h} <= {fmt(gdp_last)}, y(tau-2) and e(tau-1) observed\",\n n0, len(df1), \"information-availability rule / series edges\"))\n tau = df1.index\n bad = in_covid(tau) | in_covid(tau + pd.DateOffset(months=h)) | in_covid(tau - pd.DateOffset(months=2)) | in_covid(tau - pd.DateOffset(months=1))\n df2 = df1[~np.asarray(bad)] if exclude_covid else df1\n ledger.append((\"exclude_covid\", \"drop rows whose target/predictor months fall in 2020-03..2021-12\",\n len(df1), len(df2), \"COVID outliers dominate OLS; decided with pre-2022 info\"))\n # sanity: every used month respects the rule\n assert (df2.index + pd.DateOffset(months=h)).max() <= gdp_last\n return (df2, ledger) if return_ledger else df2\n\n\nrows = []\nn_analysed = None\nfor t in origins:\n y_t2 = d.at[M(t, -2), \"gdp_yoy\"]\n e_t1 = d.at[M(t, -1), \"emp_yoy\"]\n for h in H:\n tgt = M(t, h)\n actual = d.at[tgt, \"gdp_yoy\"]\n rows.append(dict(origin_date=fmt(t), target_date=fmt(tgt), horizon=h, forecast=y_t2, actual=actual,\n model=\"naive\", last_target_date_used=fmt(M(t, -2)), last_predictor_date_used=\"\"))\n tr = training_rows(t, h)\n X = np.column_stack([np.ones(len(tr)), tr[\"y_lag\"], tr[\"e_lag\"]])\n beta, *_ = np.linalg.lstsq(X, tr[\"y_tgt\"].values, rcond=None)\n fc = float(beta @ np.array([1.0, y_t2, e_t1]))\n rows.append(dict(origin_date=fmt(t), target_date=fmt(tgt), horizon=h, forecast=fc, actual=actual,\n model=MODEL, last_target_date_used=fmt(M(t, -2)), last_predictor_date_used=fmt(M(t, -1))))\n\nfc = pd.DataFrame(rows)\nassert len(fc) == 192 and fc[\"actual\"].notna().all()\nfc.to_csv(os.path.join(OUT, \"forecasts.csv\"), index=False, float_format=\"%.6f\")\n\n# exclusion ledger for the last estimation sample (last origin, h=1); n_raw = all file rows\nt_last = origins[-1]\ntr_last, led = training_rows(t_last, 1, return_ledger=True)\nn_analysed = len(tr_last)\nassert led[0][2] == n_raw\nex = pd.DataFrame([dict(step=s, rule=r, n_before=a, n_after=b, n_removed=a - b, rationale=w) for s, r, a, b, w in led])\nex.to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\nn_last_h3 = len(training_rows(t_last, 3))\n\nres = {\"task_id\": \"F3-conf-01\", \"model_name\": MODEL,\n \"model_description\": (\"Direct (per-horizon) OLS regression of gdp_yoy(t+h) on a constant, gdp_yoy(t-2) and emp_yoy(t-1), \"\n \"re-estimated at each origin on an expanding window of training rows (from 1998-03) whose target month is <= t-2, \"\n \"excluding rows touching 2020-03..2021-12.\"),\n \"n_origins\": int(len(origins)), \"first_origin\": fmt(origins[0]), \"last_origin\": fmt(t_last),\n \"last_target_date_available\": fmt(M(t_last, -2)), \"last_predictor_date_available\": fmt(M(t_last, -1))}\nfor h in H:\n for m, lab in [(\"naive\", \"naive\"), (MODEL, \"model\")]:\n s = fc[(fc.horizon == h) & (fc.model == m)]\n err = s[\"forecast\"] - s[\"actual\"]\n res[f\"rmse_{lab}_h{h}\"] = float(np.sqrt(np.mean(err ** 2)))\n res[f\"mae_{lab}_h{h}\"] = float(np.mean(np.abs(err)))\nfor h in H:\n res[f\"rel_improvement_rmse_h{h}\"] = 1 - res[f\"rmse_model_h{h}\"] / res[f\"rmse_naive_h{h}\"]\n\n# Uncertainty: Diebold-Mariano test (squared loss), HAC variance with h-1 lags (Newey-West), HLN small-sample correction\nfrom scipy import stats\ndm = {}\nfor h in H:\n en = fc[(fc.horizon == h) & (fc.model == \"naive\")].sort_values(\"origin_date\")\n em = fc[(fc.horizon == h) & (fc.model == MODEL)].sort_values(\"origin_date\")\n dl = (em[\"forecast\"].values - em[\"actual\"].values) ** 2 - (en[\"forecast\"].values - en[\"actual\"].values) ** 2\n T = len(dl); dbar = dl.mean(); u = dl - dbar\n L = h + 1 # Newey-West lags h+1 since effective GDP horizon is h+2 months\n v = np.mean(u * u) + 2 * sum((1 - k / (L + 1)) * np.mean(u[k:] * u[:-k]) for k in range(1, L + 1))\n stat = dbar / np.sqrt(v / T)\n hk = h + 2\n stat *= np.sqrt((T + 1 - 2 * hk + hk * (hk - 1) / T) / T)\n p = 2 * stats.t.sf(abs(stat), df=T - 1)\n dm[f\"h{h}\"] = {\"mean_loss_diff_model_minus_naive\": float(dbar), \"dm_stat_hln\": float(stat), \"p_value_two_sided\": float(p), \"nw_lags\": L}\nres[\"dm_test\"] = dm\nres[\"n_training_last_origin_h3\"] = int(n_last_h3)\n# Sensitivity: same model without the COVID exclusion (not the headline model)\nsens = {}\nfor h in H:\n errs = []\n for t in origins:\n tr = training_rows(t, h, exclude_covid=False)\n X = np.column_stack([np.ones(len(tr)), tr[\"y_lag\"], tr[\"e_lag\"]])\n b, *_ = np.linalg.lstsq(X, tr[\"y_tgt\"].values, rcond=None)\n f_ = float(b @ np.array([1.0, d.at[M(t, -2), \"gdp_yoy\"], d.at[M(t, -1), \"emp_yoy\"]]))\n errs.append(f_ - d.at[M(t, h), \"gdp_yoy\"])\n errs = np.array(errs)\n sens[f\"rmse_h{h}\"] = float(np.sqrt(np.mean(errs ** 2)))\n sens[f\"rel_improvement_rmse_h{h}\"] = 1 - sens[f\"rmse_h{h}\"] / res[f\"rmse_naive_h{h}\"]\nres[\"sensitivity_no_covid_exclusion\"] = sens\nres.update({\"feasibility\": \"complete\", \"feasibility_reason\": None,\n \"data_issues\": [\n {\"issue\": \"README states gdp_yoy is empty for the first 12 months, but the file contains yoy values for 1998 (both series).\",\n \"handling\": \"Used as given; yoy recomputed from levels agrees to rounding (<5e-5) where possible.\"},\n {\"issue\": \"gdp columns missing for 2026-08 and 2026-09 (not yet published).\",\n \"handling\": \"Not needed: latest target (2026-07) and latest GDP input (2026-02) are present.\"},\n {\"issue\": \"COVID-19 outliers (gdp_yoy from -16.2 to +18.5 in 2020-2021).\",\n \"handling\": \"Model training rows touching 2020-03..2021-12 excluded; naive unaffected; see out/exclusions.csv.\"},\n {\"issue\": \"Current-vintage data (revised), not first releases.\",\n \"handling\": \"Exercise simulates publication timing only; no real-time validity claimed.\"}],\n \"n_input_rows\": {\"canada_gdp_employment.csv\": int(n_raw)},\n \"n_analysed\": int(n_analysed), \"random_seed\": None})\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps({k: v for k, v in res.items() if k.startswith((\"rmse\", \"mae\", \"rel\", \"n_\"))}, indent=2))\nprint(json.dumps(dm, indent=2))\n# F3-conf-01 — Forecasting Canadian monthly GDP y/y growth under publication lags\n\n## Question\nAt the end of each month t (48 origins, `first_origin` = 2022-05-01 to `last_origin` = 2026-04-01, `n_origins` = 48), how accurately can year-over-year growth of Canadian monthly real GDP for month t+1 and t+3 be forecast using only data published by then? And does a model that also uses the more timely LFS employment growth beat the naive forecast? Under the publication rules, GDP is observed only up to t−2 and employment up to t−1. At the last origin this means GDP through `last_target_date_available` = 2026-02-01 and employment through `last_predictor_date_available` = 2026-03-01. So the \"h=1\" GDP forecast is really three months beyond the last observed GDP month, and \"h=3\" is five months beyond it.\n\n## Data and exclusions\n- Input: `data/canada_gdp_employment.csv`, 345 rows (`n_input_rows`). Its SHA-256 matches the README. Months run without gaps from 1998-01 to 2026-09. GDP is missing only for 2026-08 and 2026-09, which were not yet published. Year-over-year growth recomputed from the levels matches the file to within rounding. The full audit is in `out/state/data_audit.md`, and the data issues are listed in `data_issues`.\n- Information truncation: at each origin, GDP data after t−2 and employment data after t−1 are removed before anything is computed. That covers the estimation sample, the training targets and the values plugged into the forecast. `out/forecasts.csv` records `last_target_date_used` and `last_predictor_date_used` for every row.\n- Exclusion: model training rows are dropped if their target or predictor months fall in 2020-03..2021-12. Year-over-year GDP growth swings from −16.2% to +18.5% in that window, and those points would dominate OLS. The decision relies only on information available before the first origin. The naive forecast is not affected.\n- Exclusion ledger (`out/exclusions.csv`) for the last estimation sample (origin 2026-04, h=1): 345 rows → 335 after the availability and series-edge rule → 310 after the COVID exclusion (`n_analysed` = 310). The h=3 sample at the last origin has 306 rows (`n_training_last_origin_h3`).\n\n## Method\n- **Naive:** the forecast for both horizons is gdp_yoy(t−2).\n- **Model `adl_direct_emp`** (`model_name`, `model_description`): a separate OLS regression for each horizon, gdp_yoy(τ+h) = a + b·gdp_yoy(τ−2) + c·emp_yoy(τ−1). It is re-estimated at every origin on an expanding window of rows τ ≥ 1998-03 with τ+h ≤ t−2, so every training target is already observed at the origin. The forecast plugs in gdp_yoy(t−2) and emp_yoy(t−1). The specification was fixed in advance; no model selection was done on the evaluation period. The model involves no randomness (`random_seed` = null).\n- **Evaluation:** RMSE and MAE of forecast − actual over the 48 origins, for each horizon, using the current-vintage values. Relative improvement = 1 − RMSE_model/RMSE_naive.\n\n## Results\nErrors are in percentage points of year-over-year growth.\n\n| | naive RMSE | naive MAE | model RMSE | model MAE | rel. improvement (RMSE) |\n|---|---|---|---|---|---|\n| h=1 | 0.814 (`rmse_naive_h1`) | 0.642 (`mae_naive_h1`) | 0.743 (`rmse_model_h1`) | 0.604 (`mae_model_h1`) | 0.087 (`rel_improvement_rmse_h1`) |\n| h=3 | 1.140 (`rmse_naive_h3`) | 0.872 (`mae_naive_h3`) | 0.902 (`rmse_model_h3`) | 0.753 (`mae_model_h3`) | 0.208 (`rel_improvement_rmse_h3`) |\n\nThe employment-augmented model has lower RMSE and lower MAE than the naive forecast at both horizons. The point gain is about 9% of RMSE at h=1 and about 21% at h=3.\n\n## Uncertainty\n- **Diebold–Mariano test** (`dm_test`): squared-error loss, Newey–West variance with h+1 lags, Harvey–Leybourne–Newbold small-sample correction applied with the effective horizon h+2, and a t(47) reference distribution. Model minus naive mean loss difference: h=1 −0.110, DM = −1.33, p = 0.19; h=3 −0.485, DM = −1.37, p = 0.18. **Neither improvement is statistically significant at conventional levels.** With 48 overlapping, autocorrelated forecast errors, the test has little power.\n- **Sensitivity to the COVID exclusion** (`sensitivity_no_covid_exclusion`, not the headline model): estimating the same model without the exclusion gives RMSE 0.804 at h=1 (relative improvement 0.012) and 0.794 at h=3 (relative improvement 0.304). So the size of the gain, especially at h=1, depends on how the 2020–21 observations are handled. The direction (model better than naive) is the same in both versions.\n\n## Limitations and open issues\n- The data are the current vintage. Monthly GDP and LFS figures are revised after first publication, so these results simulate only publication *timing*. They do not measure real-time accuracy, and no real-time validity is claimed.\n- The evaluation window, 2022-05 to 2026-07 targets, is short. It begins with the post-COVID disinflation and slowdown, when growth fell from about 6% toward 1–2%, which favours models that mean-revert relative to the random-walk-style naive forecast. The results may not carry over to other periods.\n- Only one model was evaluated, as the task requires. The COVID exclusion is a judgement call, and the sensitivity analysis above shows it materially changes the h=1 gain.\n- The README says gdp_yoy is empty for the first 12 months, but the file contains values for 1998. These values were used as given (see `data_issues`).\nstep,rule,n_before,n_after,n_removed,rationale\ndrop_unavailable,\"target month tau+1 <= 2026-02-01, y(tau-2) and e(tau-1) observed\",345,335,10,information-availability rule / series edges\nexclude_covid,drop rows whose target/predictor months fall in 2020-03..2021-12,335,310,25,COVID outliers dominate OLS; decided with pre-2022 info\norigin_date,target_date,horizon,forecast,actual,model,last_target_date_used,last_predictor_date_used\n2022-05-01,2022-06-01,1,4.933500,5.957100,naive,2022-03-01,\n2022-05-01,2022-06-01,1,4.713444,5.957100,adl_direct_emp,2022-03-01,2022-04-01\n2022-05-01,2022-08-01,3,4.933500,4.831700,naive,2022-03-01,\n2022-05-01,2022-08-01,3,4.392103,4.831700,adl_direct_emp,2022-03-01,2022-04-01\nchecks.md\ncontract.md\ndata_audit.md\ngate_receipts\nlog.md\nphases.json","is_error":false}]},"uuid":"9639e1c6-760b-430d-a33c-d6c92edcdc87","timestamp":"2026-10-30T05:03:10.254Z","toolUseResult":{"stdout":"\"\"\"F3-conf-01: GDP y/y growth forecasts under publication lags.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nNaive: y(t-2). Model 'adl_direct_emp': direct OLS per horizon\n y(tau+h) = a + b*y(tau-2) + c*e(tau-1), training rows tau with tau+h <= t-2,\n excluding rows touching 2020-03..2021-12 (COVID); forecast plugs y(t-2), e(t-1).\nNo randomness is used.\n\"\"\"\nimport json, os\nimport numpy as np, pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDATA = os.path.join(ROOT, \"data\", \"canada_gdp_employment.csv\")\nOUT = os.path.join(ROOT, \"out\")\nMODEL = \"adl_direct_emp\"\nCOVID = (pd.Timestamp(\"2020-03-01\"), pd.Timestamp(\"2021-12-01\"))\n\nd = pd.read_csv(DATA, parse_dates=[\"month\"]).sort_values(\"month\").reset_index(drop=True)\nn_raw = len(d)\nd = d.set_index(\"month\")\nmonths = d.index\norigins = pd.date_range(\"2022-05-01\", \"2026-04-01\", freq=\"MS\")\nH = [1, 3]\nM = lambda m, k: m + pd.DateOffset(months=k)\nfmt = lambda x: x.strftime(\"%Y-%m-%d\")\nin_covid = lambda m: (m >= COVID[0]) & (m <= COVID[1])\n\n\ndef training_rows(t, h, return_ledger=False, exclude_covid=True):\n \"\"\"Training rows available at origin t for horizon h (vectorised).\"\"\"\n gdp_last = M(t, -2) # latest GDP month observed at origin t\n emp_last = M(t, -1) # latest employment month observed at origin t\n y = d[\"gdp_yoy\"].where(months <= gdp_last) # information truncation\n e = d[\"emp_yoy\"].where(months <= emp_last)\n df = pd.DataFrame({\"y_tgt\": y.shift(-h), \"y_lag\": y.shift(2), \"e_lag\": e.shift(1)}, index=months)\n ledger = []\n n0 = len(df)\n df1 = df.dropna()\n ledger.append((\"drop_unavailable\", f\"target month tau+{h} <= {fmt(gdp_last)}, y(tau-2) and e(tau-1) observed\",\n n0, len(df1), \"information-availability rule / series edges\"))\n tau = df1.index\n bad = in_covid(tau) | in_covid(tau + pd.DateOffset(months=h)) | in_covid(tau - pd.DateOffset(months=2)) | in_covid(tau - pd.DateOffset(months=1))\n df2 = df1[~np.asarray(bad)] if exclude_covid else df1\n ledger.append((\"exclude_covid\", \"drop rows whose target/predictor months fall in 2020-03..2021-12\",\n len(df1), len(df2), \"COVID outliers dominate OLS; decided with pre-2022 info\"))\n # sanity: every used month respects the rule\n assert (df2.index + pd.DateOffset(months=h)).max() <= gdp_last\n return (df2, ledger) if return_ledger else df2\n\n\nrows = []\nn_analysed = None\nfor t in origins:\n y_t2 = d.at[M(t, -2), \"gdp_yoy\"]\n e_t1 = d.at[M(t, -1), \"emp_yoy\"]\n for h in H:\n tgt = M(t, h)\n actual = d.at[tgt, \"gdp_yoy\"]\n rows.append(dict(origin_date=fmt(t), target_date=fmt(tgt), horizon=h, forecast=y_t2, actual=actual,\n model=\"naive\", last_target_date_used=fmt(M(t, -2)), last_predictor_date_used=\"\"))\n tr = training_rows(t, h)\n X = np.column_stack([np.ones(len(tr)), tr[\"y_lag\"], tr[\"e_lag\"]])\n beta, *_ = np.linalg.lstsq(X, tr[\"y_tgt\"].values, rcond=None)\n fc = float(beta @ np.array([1.0, y_t2, e_t1]))\n rows.append(dict(origin_date=fmt(t), target_date=fmt(tgt), horizon=h, forecast=fc, actual=actual,\n model=MODEL, last_target_date_used=fmt(M(t, -2)), last_predictor_date_used=fmt(M(t, -1))))\n\nfc = pd.DataFrame(rows)\nassert len(fc) == 192 and fc[\"actual\"].notna().all()\nfc.to_csv(os.path.join(OUT, \"forecasts.csv\"), index=False, float_format=\"%.6f\")\n\n# exclusion ledger for the last estimation sample (last origin, h=1); n_raw = all file rows\nt_last = origins[-1]\ntr_last, led = training_rows(t_last, 1, return_ledger=True)\nn_analysed = len(tr_last)\nassert led[0][2] == n_raw\nex = pd.DataFrame([dict(step=s, rule=r, n_before=a, n_after=b, n_removed=a - b, rationale=w) for s, r, a, b, w in led])\nex.to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\nn_last_h3 = len(training_rows(t_last, 3))\n\nres = {\"task_id\": \"F3-conf-01\", \"model_name\": MODEL,\n \"model_description\": (\"Direct (per-horizon) OLS regression of gdp_yoy(t+h) on a constant, gdp_yoy(t-2) and emp_yoy(t-1), \"\n \"re-estimated at each origin on an expanding window of training rows (from 1998-03) whose target month is <= t-2, \"\n \"excluding rows touching 2020-03..2021-12.\"),\n \"n_origins\": int(len(origins)), \"first_origin\": fmt(origins[0]), \"last_origin\": fmt(t_last),\n \"last_target_date_available\": fmt(M(t_last, -2)), \"last_predictor_date_available\": fmt(M(t_last, -1))}\nfor h in H:\n for m, lab in [(\"naive\", \"naive\"), (MODEL, \"model\")]:\n s = fc[(fc.horizon == h) & (fc.model == m)]\n err = s[\"forecast\"] - s[\"actual\"]\n res[f\"rmse_{lab}_h{h}\"] = float(np.sqrt(np.mean(err ** 2)))\n res[f\"mae_{lab}_h{h}\"] = float(np.mean(np.abs(err)))\nfor h in H:\n res[f\"rel_improvement_rmse_h{h}\"] = 1 - res[f\"rmse_model_h{h}\"] / res[f\"rmse_naive_h{h}\"]\n\n# Uncertainty: Diebold-Mariano test (squared loss), HAC variance with h-1 lags (Newey-West), HLN small-sample correction\nfrom scipy import stats\ndm = {}\nfor h in H:\n en = fc[(fc.horizon == h) & (fc.model == \"naive\")].sort_values(\"origin_date\")\n em = fc[(fc.horizon == h) & (fc.model == MODEL)].sort_values(\"origin_date\")\n dl = (em[\"forecast\"].values - em[\"actual\"].values) ** 2 - (en[\"forecast\"].values - en[\"actual\"].values) ** 2\n T = len(dl); dbar = dl.mean(); u = dl - dbar\n L = h + 1 # Newey-West lags h+1 since effective GDP horizon is h+2 months\n v = np.mean(u * u) + 2 * sum((1 - k / (L + 1)) * np.mean(u[k:] * u[:-k]) for k in range(1, L + 1))\n stat = dbar / np.sqrt(v / T)\n hk = h + 2\n stat *= np.sqrt((T + 1 - 2 * hk + hk * (hk - 1) / T) / T)\n p = 2 * stats.t.sf(abs(stat), df=T - 1)\n dm[f\"h{h}\"] = {\"mean_loss_diff_model_minus_naive\": float(dbar), \"dm_stat_hln\": float(stat), \"p_value_two_sided\": float(p), \"nw_lags\": L}\nres[\"dm_test\"] = dm\nres[\"n_training_last_origin_h3\"] = int(n_last_h3)\n# Sensitivity: same model without the COVID exclusion (not the headline model)\nsens = {}\nfor h in H:\n errs = []\n for t in origins:\n tr = training_rows(t, h, exclude_covid=False)\n X = np.column_stack([np.ones(len(tr)), tr[\"y_lag\"], tr[\"e_lag\"]])\n b, *_ = np.linalg.lstsq(X, tr[\"y_tgt\"].values, rcond=None)\n f_ = float(b @ np.array([1.0, d.at[M(t, -2), \"gdp_yoy\"], d.at[M(t, -1), \"emp_yoy\"]]))\n errs.append(f_ - d.at[M(t, h), \"gdp_yoy\"])\n errs = np.array(errs)\n sens[f\"rmse_h{h}\"] = float(np.sqrt(np.mean(errs ** 2)))\n sens[f\"rel_improvement_rmse_h{h}\"] = 1 - sens[f\"rmse_h{h}\"] / res[f\"rmse_naive_h{h}\"]\nres[\"sensitivity_no_covid_exclusion\"] = sens\nres.update({\"feasibility\": \"complete\", \"feasibility_reason\": None,\n \"data_issues\": [\n {\"issue\": \"README states gdp_yoy is empty for the first 12 months, but the file contains yoy values for 1998 (both series).\",\n \"handling\": \"Used as given; yoy recomputed from levels agrees to rounding (<5e-5) where possible.\"},\n {\"issue\": \"gdp columns missing for 2026-08 and 2026-09 (not yet published).\",\n \"handling\": \"Not needed: latest target (2026-07) and latest GDP input (2026-02) are present.\"},\n {\"issue\": \"COVID-19 outliers (gdp_yoy from -16.2 to +18.5 in 2020-2021).\",\n \"handling\": \"Model training rows touching 2020-03..2021-12 excluded; naive unaffected; see out/exclusions.csv.\"},\n {\"issue\": \"Current-vintage data (revised), not first releases.\",\n \"handling\": \"Exercise simulates publication timing only; no real-time validity claimed.\"}],\n \"n_input_rows\": {\"canada_gdp_employment.csv\": int(n_raw)},\n \"n_analysed\": int(n_analysed), \"random_seed\": None})\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps({k: v for k, v in res.items() if k.startswith((\"rmse\", \"mae\", \"rel\", \"n_\"))}, indent=2))\nprint(json.dumps(dm, indent=2))\n# F3-conf-01 — Forecasting Canadian monthly GDP y/y growth under publication lags\n\n## Question\nAt the end of each month t (48 origins, `first_origin` = 2022-05-01 to `last_origin` = 2026-04-01, `n_origins` = 48), how accurately can year-over-year growth of Canadian monthly real GDP for month t+1 and t+3 be forecast using only data published by then? And does a model that also uses the more timely LFS employment growth beat the naive forecast? Under the publication rules, GDP is observed only up to t−2 and employment up to t−1. At the last origin this means GDP through `last_target_date_available` = 2026-02-01 and employment through `last_predictor_date_available` = 2026-03-01. So the \"h=1\" GDP forecast is really three months beyond the last observed GDP month, and \"h=3\" is five months beyond it.\n\n## Data and exclusions\n- Input: `data/canada_gdp_employment.csv`, 345 rows (`n_input_rows`). Its SHA-256 matches the README. Months run without gaps from 1998-01 to 2026-09. GDP is missing only for 2026-08 and 2026-09, which were not yet published. Year-over-year growth recomputed from the levels matches the file to within rounding. The full audit is in `out/state/data_audit.md`, and the data issues are listed in `data_issues`.\n- Information truncation: at each origin, GDP data after t−2 and employment data after t−1 are removed before anything is computed. That covers the estimation sample, the training targets and the values plugged into the forecast. `out/forecasts.csv` records `last_target_date_used` and `last_predictor_date_used` for every row.\n- Exclusion: model training rows are dropped if their target or predictor months fall in 2020-03..2021-12. Year-over-year GDP growth swings from −16.2% to +18.5% in that window, and those points would dominate OLS. The decision relies only on information available before the first origin. The naive forecast is not affected.\n- Exclusion ledger (`out/exclusions.csv`) for the last estimation sample (origin 2026-04, h=1): 345 rows → 335 after the availability and series-edge rule → 310 after the COVID exclusion (`n_analysed` = 310). The h=3 sample at the last origin has 306 rows (`n_training_last_origin_h3`).\n\n## Method\n- **Naive:** the forecast for both horizons is gdp_yoy(t−2).\n- **Model `adl_direct_emp`** (`model_name`, `model_description`): a separate OLS regression for each horizon, gdp_yoy(τ+h) = a + b·gdp_yoy(τ−2) + c·emp_yoy(τ−1). It is re-estimated at every origin on an expanding window of rows τ ≥ 1998-03 with τ+h ≤ t−2, so every training target is already observed at the origin. The forecast plugs in gdp_yoy(t−2) and emp_yoy(t−1). The specification was fixed in advance; no model selection was done on the evaluation period. The model involves no randomness (`random_seed` = null).\n- **Evaluation:** RMSE and MAE of forecast − actual over the 48 origins, for each horizon, using the current-vintage values. Relative improvement = 1 − RMSE_model/RMSE_naive.\n\n## Results\nErrors are in percentage points of year-over-year growth.\n\n| | naive RMSE | naive MAE | model RMSE | model MAE | rel. improvement (RMSE) |\n|---|---|---|---|---|---|\n| h=1 | 0.814 (`rmse_naive_h1`) | 0.642 (`mae_naive_h1`) | 0.743 (`rmse_model_h1`) | 0.604 (`mae_model_h1`) | 0.087 (`rel_improvement_rmse_h1`) |\n| h=3 | 1.140 (`rmse_naive_h3`) | 0.872 (`mae_naive_h3`) | 0.902 (`rmse_model_h3`) | 0.753 (`mae_model_h3`) | 0.208 (`rel_improvement_rmse_h3`) |\n\nThe employment-augmented model has lower RMSE and lower MAE than the naive forecast at both horizons. The point gain is about 9% of RMSE at h=1 and about 21% at h=3.\n\n## Uncertainty\n- **Diebold–Mariano test** (`dm_test`): squared-error loss, Newey–West variance with h+1 lags, Harvey–Leybourne–Newbold small-sample correction applied with the effective horizon h+2, and a t(47) reference distribution. Model minus naive mean loss difference: h=1 −0.110, DM = −1.33, p = 0.19; h=3 −0.485, DM = −1.37, p = 0.18. **Neither improvement is statistically significant at conventional levels.** With 48 overlapping, autocorrelated forecast errors, the test has little power.\n- **Sensitivity to the COVID exclusion** (`sensitivity_no_covid_exclusion`, not the headline model): estimating the same model without the exclusion gives RMSE 0.804 at h=1 (relative improvement 0.012) and 0.794 at h=3 (relative improvement 0.304). So the size of the gain, especially at h=1, depends on how the 2020–21 observations are handled. The direction (model better than naive) is the same in both versions.\n\n## Limitations and open issues\n- The data are the current vintage. Monthly GDP and LFS figures are revised after first publication, so these results simulate only publication *timing*. They do not measure real-time accuracy, and no real-time validity is claimed.\n- The evaluation window, 2022-05 to 2026-07 targets, is short. It begins with the post-COVID disinflation and slowdown, when growth fell from about 6% toward 1–2%, which favours models that mean-revert relative to the random-walk-style naive forecast. The results may not carry over to other periods.\n- Only one model was evaluated, as the task requires. The COVID exclusion is a judgement call, and the sensitivity analysis above shows it materially changes the h=1 gain.\n- The README says gdp_yoy is empty for the first 12 months, but the file contains values for 1998. These values were used as given (see `data_issues`).\nstep,rule,n_before,n_after,n_removed,rationale\ndrop_unavailable,\"target month tau+1 <= 2026-02-01, y(tau-2) and e(tau-1) observed\",345,335,10,information-availability rule / series edges\nexclude_covid,drop rows whose target/predictor months fall in 2020-03..2021-12,335,310,25,COVID outliers dominate OLS; decided with pre-2022 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/tmp && rm -rf rc && mkdir rc && cp -r ~/wp29/runs/RC0210/data rc/ && mkdir rc/out && cp ~/wp29/runs/RC0210/out/analysis.py rc/out/ && cd rc && ~/wp29/venv/bin/python out/analysis.py >/dev/null && diff out/forecasts.csv ~/wp29/runs/RC0210/out/forecasts.csv && echo FC_SAME; ~/wp29/venv/bin/python -c \"\nimport json;a=json.load(open('out/results.json'));b=json.load(open('$HOME/wp29/runs/RC0210/out/results.json'));print([k for k in a if a[k]!=b.get(k)])\"\n~/wp29/venv/bin/python - <<'E'\nimport pandas as pd, numpy as np\nd=pd.read_csv('data/canada_gdp_employment.csv',parse_dates=['month']).set_index('month')\nf=pd.read_csv('out/forecasts.csv',parse_dates=['origin_date','target_date'])\nprint((f.actual-d.loc[f.target_date,'gdp_yoy'].values).abs().max())\nn=f[f.model=='naive']; print((n.forecast-d.loc[n.origin_date-pd.DateOffset(months=2),'gdp_yoy'].values).abs().max())\nprint(d.isna().sum()); print(d.head(14)); print(d.tail(4))\n# independent model check at one 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2\ngdp_yoy 2\nemp_level 0\nemp_yoy 0\ndtype: int64\n gdp_level gdp_yoy emp_level emp_yoy\nmonth \n1998-01-01 1251276.0 4.2359 13864.8 2.4298\n1998-02-01 1263285.0 4.5780 13914.5 2.7803\n1998-03-01 1267784.0 4.9633 13949.4 2.7974\n1998-04-01 1268479.0 4.3134 13977.6 2.9946\n1998-05-01 1266172.0 3.7544 13993.3 2.6112\n1998-06-01 1265876.0 3.5354 14005.8 2.3068\n1998-07-01 1265509.0 2.4034 14063.8 2.4200\n1998-08-01 1277712.0 3.2611 14101.7 2.1944\n1998-09-01 1281876.0 3.4198 14140.7 2.3509\n1998-10-01 1287736.0 3.4908 14159.4 2.3588\n1998-11-01 1291195.0 3.6872 14198.9 2.4489\n1998-12-01 1303212.0 3.7097 14200.0 2.3431\n1999-01-01 1307658.0 4.5060 14273.3 2.9463\n1999-02-01 1313944.0 4.0101 14263.3 2.5067\n gdp_level gdp_yoy emp_level emp_yoy\nmonth \n2026-06-01 2371886.0 2.0909 21139.7 0.4705\n2026-07-01 2371771.0 1.4203 21214.8 0.9349\n2026-08-01 NaN NaN 21173.1 1.0331\n2026-09-01 NaN NaN 21104.8 0.4517\n1.9306427376431914 [1.930643]\n# data/README.md — F3-conf-01\n\n## canada_gdp_employment.csv\nOne row per month (`month`, YYYY-MM-01), 1998-01 to 2026-09-01 (345 data rows), built from two Statistics Canada vectors retrieved through the Web Data Service:\n\n- **Endpoint**: `POST https://www150.statcan.gc.ca/t1/wds/rest/getDataFromVectorsAndLatestNPeriods` with body `[{\"vectorId\":65201210,\"latestN\":400},{\"vectorId\":2062811,\"latestN\":400}]`\n- **Retrieved (UTC)**: 2026-10-30T03:25:10Z\n- **SHA-256 of this file**: f4c8e4976fb5f5f0c326e40bcb4f85b8b22963e5be89e2729e1a430c198f2bed\n- **License**: Statistics Canada Open Licence (https://www.statcan.gc.ca/en/reference/licence).\n\nColumns:\n- `gdp_level` — vector v65201210, table 36-10-0434-01: Gross domestic product at basic prices, all industries, chained (2017) dollars, seasonally adjusted at annual rates, millions of dollars, monthly. Last available month: 2026-07 (the value for a reference month is published by Statistics Canada about two months after the end of that month — e.g. July 2026 GDP was published on 2026-09-30).\n- `gdp_yoy` — target series: year-over-year growth of `gdp_level`, 100 × (level_m / level_{m-12} − 1), rounded to 4 decimals (percent). Empty for the first 12 months.\n- `emp_level` — vector v2062811, table 14-10-0287-01: Employment, both sexes, 15 years and over, seasonally adjusted, thousands of persons, Labour Force Survey, monthly. Last available month: 2026-09 (published in the first or second week of the following month).\n- `emp_yoy` — predictor series: year-over-year growth of `emp_level`, same formula, percent, 4 decimals.\n\n**Publication lags (information rule used in TASK.md)**: at the end of month t, `gdp_*` is known for months ≤ t − 2 and `emp_*` for months ≤ t − 1. Both series are the current vintage as of retrieval (monthly GDP and LFS employment are revised after first publication); the file is therefore a final-vintage dataset and the exercise simulates only the publication *timing*, not the historical first-release values. No real-time (vintage) validity is claimed.\nShell cwd was reset to /Users/simon-pierreboucher/wp29/runs/RC0210","is_error":false}]},"uuid":"858d84d0-8fbd-47f4-870a-cc9e3a1be805","timestamp":"2026-10-30T05:03:27.437Z","toolUseResult":{"stdout":"FC_SAME\n[]\n0.0\n0.0\ngdp_level 2\ngdp_yoy 2\nemp_level 0\nemp_yoy 0\ndtype: int64\n gdp_level gdp_yoy emp_level emp_yoy\nmonth \n1998-01-01 1251276.0 4.2359 13864.8 2.4298\n1998-02-01 1263285.0 4.5780 13914.5 2.7803\n1998-03-01 1267784.0 4.9633 13949.4 2.7974\n1998-04-01 1268479.0 4.3134 13977.6 2.9946\n1998-05-01 1266172.0 3.7544 13993.3 2.6112\n1998-06-01 1265876.0 3.5354 14005.8 2.3068\n1998-07-01 1265509.0 2.4034 14063.8 2.4200\n1998-08-01 1277712.0 3.2611 14101.7 2.1944\n1998-09-01 1281876.0 3.4198 14140.7 2.3509\n1998-10-01 1287736.0 3.4908 14159.4 2.3588\n1998-11-01 1291195.0 3.6872 14198.9 2.4489\n1998-12-01 1303212.0 3.7097 14200.0 2.3431\n1999-01-01 1307658.0 4.5060 14273.3 2.9463\n1999-02-01 1313944.0 4.0101 14263.3 2.5067\n gdp_level gdp_yoy emp_level emp_yoy\nmonth \n2026-06-01 2371886.0 2.0909 21139.7 0.4705\n2026-07-01 2371771.0 1.4203 21214.8 0.9349\n2026-08-01 NaN NaN 21173.1 1.0331\n2026-09-01 NaN NaN 21104.8 0.4517\n1.9306427376431914 [1.930643]\n# data/README.md — F3-conf-01\n\n## canada_gdp_employment.csv\nOne row per month (`month`, YYYY-MM-01), 1998-01 to 2026-09-01 (345 data rows), built from two Statistics Canada vectors retrieved through the Web Data Service:\n\n- **Endpoint**: `POST https://www150.statcan.gc.ca/t1/wds/rest/getDataFromVectorsAndLatestNPeriods` with body `[{\"vectorId\":65201210,\"latestN\":400},{\"vectorId\":2062811,\"latestN\":400}]`\n- **Retrieved (UTC)**: 2026-10-30T03:25:10Z\n- **SHA-256 of this file**: f4c8e4976fb5f5f0c326e40bcb4f85b8b22963e5be89e2729e1a430c198f2bed\n- **License**: Statistics Canada Open Licence (https://www.statcan.gc.ca/en/reference/licence).\n\nColumns:\n- `gdp_level` — vector v65201210, table 36-10-0434-01: Gross domestic product at basic prices, all industries, chained (2017) dollars, seasonally adjusted at annual rates, millions of dollars, monthly. Last available month: 2026-07 (the value for a reference month is published by Statistics Canada about two months after the end of that month — e.g. July 2026 GDP was published on 2026-09-30).\n- `gdp_yoy` — target series: year-over-year growth of `gdp_level`, 100 × (level_m / level_{m-12} − 1), rounded to 4 decimals (percent). Empty for the first 12 months.\n- `emp_level` — vector v2062811, table 14-10-0287-01: Employment, both sexes, 15 years and over, seasonally adjusted, thousands of persons, Labour Force Survey, monthly. Last available month: 2026-09 (published in the first or second week of the following month).\n- `emp_yoy` — predictor series: year-over-year growth of `emp_level`, same formula, percent, 4 decimals.\n\n**Publication lags (information rule used in TASK.md)**: at the end of month t, `gdp_*` is known for months ≤ t − 2 and `emp_*` for months ≤ t − 1. Both series are the current vintage as of retrieval (monthly GDP and LFS employment are revised after first publication); the file is therefore a final-vintage dataset and the exercise simulates only the publication *timing*, not the historical first-release values. No real-time (vintage) validity is claimed.","stderr":"\nShell cwd was reset to 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These cannot be recomputed from the levels in the file, and they enter the training sample (from 1998-03). The report says 'agrees to rounding where possible', which correctly implies the 1998 values were not verified, but whether they are valid is still unknown.\",\n \"suggested_fix\": \"Add a sensitivity run that starts training in 1999-01 (the first month whose yoy can be checked against the levels), or say explicitly that the 1998 yoy values are unverified.\"\n },\n {\n \"id\": \"R2\",\n \"severity\": \"minor\",\n \"location\": \"report.md Method/Data ('decided with pre-2022 info', 'specification fixed in advance')\",\n \"issue\": \"Nothing in the files can confirm that the COVID-exclusion window and the specification were chosen before looking at the evaluation results. Without the exclusion, h=1 RMSE is worse (rel. improvement 0.012) and h=3 RMSE is better (0.304). So the headline choice is not obviously cherry-picked, but the h=1 gain depends on it.\",\n \"suggested_fix\": \"Describe the claim as a design statement, and in the claims and summary keep the h=1 point gain clearly tied to the exclusion choice (C4 already does this in part).\"\n },\n {\n \"id\": \"R3\",\n \"severity\": \"minor\",\n \"location\": \"results.json n_analysed\",\n \"issue\": \"n_analysed (310) is the h=1 sample at the last origin. The h=3 sample is 306, reported separately under an extra key. This is consistent and disclosed, but the meaning of n_analysed depends on the horizon.\",\n \"suggested_fix\": \"State in model_description or the report that n_analysed refers to h=1.\"\n }\n ],\n \"summary\": \"A fresh copy of analysis.py reproduces results.json and forecasts.csv exactly (192 rows, deterministic). Separate checks confirm that actuals match gdp_yoy of the target month, that the naive forecast equals gdp_yoy(t-2), and that a hand-built direct OLS gives the same model forecast at a sample origin. The code follows the information rules: GDP is truncated at t-2 and employment at t-1 before the lagged rows are built, training targets satisfy tau+h <= t-2, and the plug-in values are y(t-2) and e(t-1). All required keys are present and internally consistent. The point improvements (0.087 at h=1, 0.208 at h=3) come with DM p-values of about 0.18-0.19, which the report correctly calls not significant. It also reports sensitivity to the COVID exclusion and states the current-vintage, short-window and mean-reversion caveats honestly. 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The review is saved in `out/review/review.json`.\n\nI re-ran `out/analysis.py` in a scratch copy and it reproduced `results.json` and `forecasts.csv` exactly: 192 forecast rows, deterministic, every required key present. Independent checks matched:\n- **Actuals:** each one equals `gdp_yoy` for its target month.\n- **Naive forecast:** always `gdp_yoy` of month t−2.\n- **Model forecast:** a regression I rebuilt by hand gave the same value at a sample origin.\n\n**Publication-lag rules:** the code follows them. At each origin it cuts GDP off at t−2 and employment at t−1 before building any lagged inputs. Every training target is from month t−2 or earlier. The values plugged into the forecast are GDP growth at t−2 and employment growth at t−1. Nothing uses future data.\n\n**Claims:** they match the numbers.\n- The model has lower RMSE and MAE than the naive forecast at both horizons. The RMSE improvement is 0.087 at h=1 and 0.208 at h=3.\n- The report correctly says neither gain is statistically significant: a Diebold–Mariano test (an extra the task did not ask for) gives p ≈ 0.19 and 0.18.\n- It shows how much the result depends on dropping the 2020–21 COVID rows from training. Without that exclusion the h=1 gain shrinks to 0.012 and the h=3 gain grows to 0.304.\n- It states the limitations honestly: revised current-vintage data rather than first releases, a short evaluation window, and a post-COVID slowdown that favours a mean-reverting model over the naive one.\n\n**Minor issues:**\n1. **Unverified 1998 values:** the README says GDP growth is empty for the first 12 months, but the file has 1998 values. They can't be checked against the levels in the file, yet they are used in training.\n2. **Ex-ante choices:** the report says the COVID exclusion and the model specification were fixed in advance. That can't be confirmed from the files, and the h=1 gain depends on that exclusion.\n3. **`n_analysed` (310):** this is the h=1 training sample at the last origin; the h=3 sample is 306. Both are disclosed, but the key's meaning depends on the horizon."}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1499,"cache_read_input_tokens":16636,"output_tokens":792,"output_tokens_details":{"thinking_tokens":5},"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":1499},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXqVv6vGNUqxWJkf1jeo","requestRef":"fd5463a0-734a-4573-bc00-59506c0e1fdc","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f78c9bcd-3c73-4260-bfcd-b8bf5edc6637","timestamp":"2026-10-30T05:03:51.547Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0210","sessionId":"85786b51-cfce-46d2-8490-f3b68612238d","version":"2.1.314","gitBranch":"HEAD"}38{"type":"last-prompt","lastPrompt":"Review","leafUuid":"f78c9bcd-3c73-4260-bfcd-b8bf5edc6637","sessionId":"85786b51-cfce-46d2-8490-f3b68612238d"}39{"type":"cost-state","sessionId":"85786b51-cfce-46d2-8490-f3b68612238d","totalCostUSD":0.1782656,"totalAPIDuration":43982,"totalAPIDurationWithoutRetries":43978,"totalToolDuration":1254,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":45423,"startTime":1793336586136,"modelUsage":{"claude-opus-5-5":{"inputTokens":12,"outputTokens":4349,"thinkingTokens":1200,"cacheReadInputTokens":40413,"cacheCreationInputTokens":16631,"cacheCreationEphemeral5mInputTokens":16631,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.1782656}},"hasUnknownModelCost":false}40