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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 96\ndrwxr-xr-x 10 simon-pierreboucher staff 320 oct. 30 01:05 .\ndrwxr-xr-x 7 simon-pierreboucher staff 224 oct. 30 01:04 ..\n-rw-r--r-- 1 simon-pierreboucher staff 8238 oct. 30 01:04 analysis.py\n-rw-r--r-- 1 simon-pierreboucher staff 1684 oct. 30 01:05 claims.json\n-rw-r--r-- 1 simon-pierreboucher staff 673 oct. 30 01:04 exclusions.csv\n-rw-r--r-- 1 simon-pierreboucher staff 12929 oct. 30 01:04 forecasts.csv\n-rw-r--r-- 1 simon-pierreboucher staff 5974 oct. 30 01:05 report.md\n-rw-r--r-- 1 simon-pierreboucher staff 2865 oct. 30 01:04 results.json\ndrwxr-xr-x 2 simon-pierreboucher staff 64 oct. 30 01:05 review\ndrwxr-xr-x 9 simon-pierreboucher staff 288 oct. 30 01:05 state\n{\n \"task_id\": \"F3-conf-01\",\n \"model_name\": \"ardl_direct_emp\",\n \"model_description\": \"Direct OLS regression per horizon h of gdp_yoy[s+h] on a constant, gdp_yoy[s-2] and emp_yoy[s-1], estimated at each origin on an expanding window from 1998 using only pairs whose target is published (<= t-2), excluding rows touching the pre-specified COVID window 2020-03..2021-12; forecast plugs in gdp_yoy[t-2] and emp_yoy[t-1].\",\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_stat_h1\": 1.3944544671156984,\n \"dm_pvalue_two_sided_h1\": 0.16973721446272597,\n \"dm_hac_lags_h1\": 2,\n \"dm_stat_h3\": 1.4447840259739004,\n \"dm_pvalue_two_sided_h3\": 0.1551529243590485,\n \"dm_hac_lags_h3\": 4,\n \"diag_rmse_ar_only_h1\": 0.7153894841379895,\n \"diag_mae_ar_only_h1\": 0.5809934710095334,\n \"diag_rmse_ar_only_h3\": 0.8640294076084106,\n \"diag_mae_ar_only_h3\": 0.716270971598207,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"gdp_yoy is populated for 1998-01..1998-12 although data/README.md says it is empty for the first 12 months and the file has no 1997 levels to verify it.\",\n \"handling\": \"Values kept as given (they are the official target column); all gdp_yoy values computable from gdp_level in the file match to 4 decimals.\"\n },\n {\n \"issue\": \"gdp_level/gdp_yoy missing for 2026-08 and 2026-09 (not yet published).\",\n \"handling\": \"Expected; never needed (latest target 2026-07).\"\n },\n {\n \"issue\": \"COVID-19 swings (gdp_yoy -16.2% in 2020-04, +18.5% in 2021-04) would dominate OLS estimates.\",\n \"handling\": \"Pre-specified exclusion of training rows whose target or regressor month lies in 2020-03..2021-12; naive forecast unaffected.\"\n },\n {\n \"issue\": \"Current-vintage data, not real-time vintages.\",\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 \"n_analysed_last_h3\": 306,\n \"last_coefficients_h1\": {\n \"const\": 0.2984584285466793,\n \"gdp_yoy_lag2\": 0.8160660347393057,\n \"emp_yoy_lag1\": 0.058054549122923786\n },\n \"last_coefficients_h3\": {\n \"const\": 0.6858809168481204,\n \"gdp_yoy_lag2\": 0.6596629835912409,\n \"emp_yoy_lag1\": 0.03216114193552756\n },\n \"random_seed\": null\n}[\n {\"id\":\"C1\",\"text\":\"Over 48 origins the employment-augmented direct regression has lower RMSE than the naive forecast at h=1 (0.743 vs 0.814; relative improvement 0.087).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_naive_h1\",\"rel_improvement_rmse_h1\"],\"status\":\"supported\",\"caveat\":\"Point estimate only; DM p=0.17; current-vintage data.\"},\n {\"id\":\"C2\",\"text\":\"At h=3 the model RMSE is 0.902 vs naive 1.140 (relative improvement 0.208).\",\"results_keys\":[\"rmse_model_h3\",\"rmse_naive_h3\",\"rel_improvement_rmse_h3\"],\"status\":\"supported\",\"caveat\":\"Point estimate only; DM p=0.16.\"},\n {\"id\":\"C3\",\"text\":\"Neither improvement over the naive forecast is statistically significant at conventional levels (Diebold-Mariano).\",\"results_keys\":[\"dm_pvalue_two_sided_h1\",\"dm_pvalue_two_sided_h3\",\"dm_stat_h1\",\"dm_stat_h3\"],\"status\":\"supported\",\"caveat\":\"HAC lag choice is a judgement call; 48 overlapping origins.\"},\n {\"id\":\"C4\",\"text\":\"The gain over naive is not attributable to employment growth: the same regression without employment has lower RMSE at both horizons, and the employment coefficient is small.\",\"results_keys\":[\"diag_rmse_ar_only_h1\",\"diag_rmse_ar_only_h3\",\"rmse_model_h1\",\"rmse_model_h3\",\"last_coefficients_h1\",\"last_coefficients_h3\"],\"status\":\"supported\",\"caveat\":\"Diagnostic added after inspecting coefficients; no significance test of model vs AR-only.\"},\n {\"id\":\"C5\",\"text\":\"All forecasts respect the publication-lag rules (GDP <= t-2, employment <= t-1), confirmed by assertions and an independent masked re-estimation.\",\"results_keys\":[\"last_target_date_available\",\"last_predictor_date_available\"],\"status\":\"supported\",\"caveat\":\"Timing only; not real-time vintage validity.\"}\n]","is_error":false}]},"uuid":"fc076e21-8137-48ad-9599-1ddb758d975c","timestamp":"2026-10-30T05:05:47.282Z","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 96\ndrwxr-xr-x 10 simon-pierreboucher staff 320 oct. 30 01:05 .\ndrwxr-xr-x 7 simon-pierreboucher staff 224 oct. 30 01:04 ..\n-rw-r--r-- 1 simon-pierreboucher staff 8238 oct. 30 01:04 analysis.py\n-rw-r--r-- 1 simon-pierreboucher staff 1684 oct. 30 01:05 claims.json\n-rw-r--r-- 1 simon-pierreboucher staff 673 oct. 30 01:04 exclusions.csv\n-rw-r--r-- 1 simon-pierreboucher staff 12929 oct. 30 01:04 forecasts.csv\n-rw-r--r-- 1 simon-pierreboucher staff 5974 oct. 30 01:05 report.md\n-rw-r--r-- 1 simon-pierreboucher staff 2865 oct. 30 01:04 results.json\ndrwxr-xr-x 2 simon-pierreboucher staff 64 oct. 30 01:05 review\ndrwxr-xr-x 9 simon-pierreboucher staff 288 oct. 30 01:05 state\n{\n \"task_id\": \"F3-conf-01\",\n \"model_name\": \"ardl_direct_emp\",\n \"model_description\": \"Direct OLS regression per horizon h of gdp_yoy[s+h] on a constant, gdp_yoy[s-2] and emp_yoy[s-1], estimated at each origin on an expanding window from 1998 using only pairs whose target is published (<= t-2), excluding rows touching the pre-specified COVID window 2020-03..2021-12; forecast plugs in gdp_yoy[t-2] and emp_yoy[t-1].\",\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_stat_h1\": 1.3944544671156984,\n \"dm_pvalue_two_sided_h1\": 0.16973721446272597,\n \"dm_hac_lags_h1\": 2,\n \"dm_stat_h3\": 1.4447840259739004,\n \"dm_pvalue_two_sided_h3\": 0.1551529243590485,\n \"dm_hac_lags_h3\": 4,\n \"diag_rmse_ar_only_h1\": 0.7153894841379895,\n \"diag_mae_ar_only_h1\": 0.5809934710095334,\n \"diag_rmse_ar_only_h3\": 0.8640294076084106,\n \"diag_mae_ar_only_h3\": 0.716270971598207,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"gdp_yoy is populated for 1998-01..1998-12 although data/README.md says it is empty for the first 12 months and the file has no 1997 levels to verify it.\",\n \"handling\": \"Values kept as given (they are the official target column); all gdp_yoy values computable from gdp_level in the file match to 4 decimals.\"\n },\n {\n \"issue\": \"gdp_level/gdp_yoy missing for 2026-08 and 2026-09 (not yet published).\",\n \"handling\": \"Expected; never needed (latest target 2026-07).\"\n },\n {\n \"issue\": \"COVID-19 swings (gdp_yoy -16.2% in 2020-04, +18.5% in 2021-04) would dominate OLS estimates.\",\n \"handling\": \"Pre-specified exclusion of training rows whose target or regressor month lies in 2020-03..2021-12; naive forecast unaffected.\"\n },\n {\n \"issue\": \"Current-vintage data, not real-time vintages.\",\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 \"n_analysed_last_h3\": 306,\n \"last_coefficients_h1\": {\n \"const\": 0.2984584285466793,\n \"gdp_yoy_lag2\": 0.8160660347393057,\n \"emp_yoy_lag1\": 0.058054549122923786\n },\n \"last_coefficients_h3\": {\n \"const\": 0.6858809168481204,\n \"gdp_yoy_lag2\": 0.6596629835912409,\n \"emp_yoy_lag1\": 0.03216114193552756\n },\n \"random_seed\": null\n}[\n {\"id\":\"C1\",\"text\":\"Over 48 origins the employment-augmented direct regression has lower RMSE than the naive forecast at h=1 (0.743 vs 0.814; relative improvement 0.087).\",\"results_keys\":[\"rmse_model_h1\",\"rmse_naive_h1\",\"rel_improvement_rmse_h1\"],\"status\":\"supported\",\"caveat\":\"Point estimate only; DM p=0.17; current-vintage data.\"},\n {\"id\":\"C2\",\"text\":\"At h=3 the model RMSE is 0.902 vs naive 1.140 (relative improvement 0.208).\",\"results_keys\":[\"rmse_model_h3\",\"rmse_naive_h3\",\"rel_improvement_rmse_h3\"],\"status\":\"supported\",\"caveat\":\"Point estimate only; DM p=0.16.\"},\n {\"id\":\"C3\",\"text\":\"Neither improvement over the naive forecast is statistically significant at conventional levels (Diebold-Mariano).\",\"results_keys\":[\"dm_pvalue_two_sided_h1\",\"dm_pvalue_two_sided_h3\",\"dm_stat_h1\",\"dm_stat_h3\"],\"status\":\"supported\",\"caveat\":\"HAC lag choice is a judgement call; 48 overlapping origins.\"},\n {\"id\":\"C4\",\"text\":\"The gain over naive is not attributable to employment growth: the same regression without employment has lower RMSE at both horizons, and the employment coefficient is small.\",\"results_keys\":[\"diag_rmse_ar_only_h1\",\"diag_rmse_ar_only_h3\",\"rmse_model_h1\",\"rmse_model_h3\",\"last_coefficients_h1\",\"last_coefficients_h3\"],\"status\":\"supported\",\"caveat\":\"Diagnostic added after inspecting coefficients; 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writes out/results.json, out/forecasts.csv, out/exclusions.csv. Deterministic (no randomness).\"\"\"\nimport json, os\nimport numpy as np, pandas as pd\n\nDATA = \"data/canada_gdp_employment.csv\"\nOUT = \"out\"\nH = [1, 3]\nMODEL = \"ardl_direct_emp\"\nCOVID = (pd.Timestamp(\"2020-03-01\"), pd.Timestamp(\"2021-12-01\")) # pre-specified exclusion window\n\nraw = pd.read_csv(DATA, parse_dates=[\"month\"])\nn_raw = len(raw)\nd = raw.set_index(\"month\").sort_index()\nmonths = d.index\ny = d[\"gdp_yoy\"]; e = d[\"emp_yoy\"]\n\ndef shift(m, k):\n return m + pd.DateOffset(months=k)\n\ndef in_covid(m):\n return (m >= COVID[0]) & (m <= COVID[1])\n\ndef design(t, h):\n \"\"\"Training rows for origin t, horizon h (direct regression).\n Pseudo-origin s: target y[s+h], regressors const, y[s-2], e[s-1].\n Availability at origin t: y months <= t-2, e months <= t-1.\"\"\"\n s = months\n tgt_m = s + pd.DateOffset(months=h)\n ym = s - pd.DateOffset(months=2); em = s - pd.DateOffset(months=1)\n steps = []\n n0 = len(s)\n keep = np.ones(n0, bool)\n k1 = keep & (tgt_m <= shift(t, -2)) & (ym <= shift(t, -2)) & (em <= shift(t, -1))\n steps.append((\"availability\", f\"target month s+{h} <= t-2 and regressors observed at origin t\", keep.sum(), k1.sum()))\n yt = y.reindex(tgt_m).values; yl = y.reindex(ym).values; el = e.reindex(em).values\n k2 = k1 & ~np.isnan(yt) & ~np.isnan(yl) & ~np.isnan(el)\n steps.append((\"lags_in_sample\", \"target and lagged regressors present in file (drops first months lacking y[s-2]/e[s-1] and GDP-empty months)\", k1.sum(), k2.sum()))\n cov = in_covid(tgt_m) | in_covid(ym) | in_covid(em)\n k3 = k2 & ~np.asarray(cov)\n steps.append((\"covid_window\", \"drop rows whose target or regressor month lies in 2020-03..2021-12\", k2.sum(), k3.sum()))\n X = np.column_stack([np.ones(k3.sum()), yl[k3], el[k3]])\n return X, yt[k3], tgt_m[k3], steps\n\nrows = []\norigins = pd.date_range(\"2022-05-01\", \"2026-04-01\", freq=\"MS\")\nassert len(origins) == 48\nlast_info = {}\nar_rows = []\nfor t in origins:\n yl_t = y.loc[shift(t, -2)]; el_t = e.loc[shift(t, -1)]\n for h in H:\n tm = shift(t, h)\n actual = y.loc[tm]\n rows.append(dict(origin_date=t, target_date=tm, horizon=h, forecast=yl_t, actual=actual, model=\"naive\",\n last_target_date_used=shift(t, -2), last_predictor_date_used=None))\n X, Y, tms, steps = design(t, h)\n beta, *_ = np.linalg.lstsq(X, Y, rcond=None)\n f = float(beta @ np.array([1.0, yl_t, el_t]))\n rows.append(dict(origin_date=t, target_date=tm, horizon=h, forecast=f, actual=actual, model=MODEL,\n last_target_date_used=max(tms.max(), shift(t, -2)), last_predictor_date_used=shift(t, -1)))\n b_ar, *_ = np.linalg.lstsq(X[:, :2], Y, rcond=None) # diagnostic: same sample, no employment\n ar_rows.append(dict(origin_date=t, horizon=h, forecast=float(b_ar @ np.array([1.0, yl_t])), actual=actual))\n last_info[h] = dict(n=len(Y), steps=steps, beta=beta.tolist(), last_target=str(tms.max().date()))\n\nfc = pd.DataFrame(rows)\n# information-rule checks\nassert (fc.last_target_date_used <= fc.origin_date - pd.DateOffset(months=2)).all()\nm = fc.model == MODEL\nassert (fc.loc[m, \"last_predictor_date_used\"] <= fc.loc[m, \"origin_date\"] - pd.DateOffset(months=1)).all()\nassert fc.actual.notna().all() and len(fc) == 192\n\nout = fc.copy()\nfor c in [\"origin_date\", \"target_date\", \"last_target_date_used\", \"last_predictor_date_used\"]:\n out[c] = out[c].apply(lambda v: \"\" if v is None or pd.isna(v) else pd.Timestamp(v).strftime(\"%Y-%m-%d\"))\nout[\"forecast\"] = out[\"forecast\"].round(6)\nout.to_csv(os.path.join(OUT, \"forecasts.csv\"), index=False)\n\ndef err(model, h):\n s = fc[(fc.model == model) & (fc.horizon == h)]\n u = (s.actual - s.forecast).values\n return float(np.sqrt(np.mean(u ** 2))), float(np.mean(np.abs(u)))\n\nres = {\"task_id\": \"F3-conf-01\", \"model_name\": MODEL,\n \"model_description\": (\"Direct OLS regression per horizon h of gdp_yoy[s+h] on a constant, gdp_yoy[s-2] and emp_yoy[s-1], \"\n \"estimated at each origin on an expanding window from 1998 using only pairs whose target is published (<= t-2), \"\n \"excluding rows touching the pre-specified COVID window 2020-03..2021-12; forecast plugs in gdp_yoy[t-2] and emp_yoy[t-1].\"),\n \"n_origins\": 48, \"first_origin\": \"2022-05-01\", \"last_origin\": \"2026-04-01\",\n \"last_target_date_available\": shift(origins[-1], -2).strftime(\"%Y-%m-%d\"),\n \"last_predictor_date_available\": shift(origins[-1], -1).strftime(\"%Y-%m-%d\")}\nfor h in H:\n rn, mn = err(\"naive\", h); rm, mm = err(MODEL, h)\n res[f\"rmse_naive_h{h}\"] = rn; res[f\"mae_naive_h{h}\"] = mn\n res[f\"rmse_model_h{h}\"] = rm; res[f\"mae_model_h{h}\"] = mm\norder = [\"rmse_naive_h1\", \"mae_naive_h1\", \"rmse_naive_h3\", \"mae_naive_h3\", \"rmse_model_h1\", \"mae_model_h1\", \"rmse_model_h3\", \"mae_model_h3\"]\nres = {**res, **{k: res[k] for k in order}}\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# Diebold-Mariano (squared loss, HAC with h-1 lags, Harvey-Leybourne-Newbold correction) for uncertainty\nfrom scipy import stats\nfor h in H:\n a = fc[(fc.model == \"naive\") & (fc.horizon == h)].sort_values(\"origin_date\")\n b = fc[(fc.model == MODEL) & (fc.horizon == h)].sort_values(\"origin_date\")\n dlt = (a.actual.values - a.forecast.values) ** 2 - (b.actual.values - b.forecast.values) ** 2\n T = len(dlt); dm = dlt - dlt.mean()\n L = max(h - 1, 0) + 2 # a few extra lags given overlapping y/y targets\n v = dm @ dm / T + 2 * sum((1 - l / (L + 1)) * (dm[l:] @ dm[:-l]) / T for l in range(1, L + 1))\n stat = dlt.mean() / np.sqrt(v / T)\n stat *= np.sqrt((T + 1 - 2 * h + h * (h - 1) / T) / T)\n res[f\"dm_stat_h{h}\"] = float(stat); res[f\"dm_pvalue_two_sided_h{h}\"] = float(2 * stats.t.sf(abs(stat), T - 1))\n res[f\"dm_hac_lags_h{h}\"] = L\n\nar = pd.DataFrame(ar_rows)\nfor h in H:\n a = ar[ar.horizon == h]; u = (a.actual - a.forecast).values\n res[f\"diag_rmse_ar_only_h{h}\"] = float(np.sqrt(np.mean(u ** 2)))\n res[f\"diag_mae_ar_only_h{h}\"] = float(np.mean(np.abs(u)))\nres[\"feasibility\"] = \"complete\"; res[\"feasibility_reason\"] = None\nres[\"data_issues\"] = [\n {\"issue\": \"gdp_yoy is populated for 1998-01..1998-12 although data/README.md says it is empty for the first 12 months and the file has no 1997 levels to verify it.\",\n \"handling\": \"Values kept as given (they are the official target column); all gdp_yoy values computable from gdp_level in the file match to 4 decimals.\"},\n {\"issue\": \"gdp_level/gdp_yoy missing for 2026-08 and 2026-09 (not yet published).\", \"handling\": \"Expected; never needed (latest target 2026-07).\"},\n {\"issue\": \"COVID-19 swings (gdp_yoy -16.2% in 2020-04, +18.5% in 2021-04) would dominate OLS estimates.\",\n \"handling\": \"Pre-specified exclusion of training rows whose target or regressor month lies in 2020-03..2021-12; naive forecast unaffected.\"},\n {\"issue\": \"Current-vintage data, not real-time vintages.\", \"handling\": \"Exercise simulates publication timing only; no real-time validity claimed.\"}]\nres[\"n_input_rows\"] = {\"canada_gdp_employment.csv\": int(n_raw)}\nres[\"n_analysed\"] = int(last_info[1][\"n\"])\nres[\"n_analysed_last_h3\"] = int(last_info[3][\"n\"])\nres[\"last_coefficients_h1\"] = dict(zip([\"const\", \"gdp_yoy_lag2\", \"emp_yoy_lag1\"], last_info[1][\"beta\"]))\nres[\"last_coefficients_h3\"] = dict(zip([\"const\", \"gdp_yoy_lag2\", \"emp_yoy_lag1\"], last_info[3][\"beta\"]))\nres[\"random_seed\"] = None\n\npd.DataFrame([dict(step=s, rule=r, n_before=int(a), n_after=int(b), n_removed=int(a - b),\n rationale=\"last estimation sample (origin 2026-04-01, h=1); rows = candidate pseudo-origins s, one per input month\")\n for s, r, a, b in last_info[1][\"steps\"]]).to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\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\", \"dm_\", \"n_\"))}, 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), how accurately can the year-over-year growth of Canadian monthly real GDP for months t+1 and t+3 be forecast using only data published by then? And does a model that also uses Labour Force Survey employment growth beat the naive forecast? At origin t, GDP is known only up to t−2 and employment only up to t−1. At the last origin this gives `last_target_date_available` = 2026-02-01 and `last_predictor_date_available` = 2026-03-01.\n\n## Data and exclusions\n- Input: `data/canada_gdp_employment.csv`, 345 rows (`n_input_rows`). The SHA-256 matches the README. Full audit in `out/state/data_audit.md`.\n- Every year-over-year value that can be recomputed from the levels in the file matches exactly. GDP is missing for 2026-08 and 2026-09 (not yet published). 1998 `gdp_yoy` values are present even though the README says they should be empty. They are kept as given (`data_issues`).\n- The file contains data published after each origin. The code removes it at each origin: training pairs need a target month ≤ t−2, a GDP regressor month ≤ t−2 and an employment month ≤ t−1. An independent check that blanks out these later data and re-estimates gives the same forecasts (`out/state/checks.md`, check 5).\n- Exclusions for the last estimation sample (origin 2026-04-01, h=1), from `out/exclusions.csv`:\n - 345 candidate rows.\n - Minus 8 rows not available at the origin.\n - Minus 2 rows missing a lag or target.\n - Minus 25 rows that touch the COVID window 2020-03..2021-12.\n - Leaves 310 rows (`n_analysed`). The h=3 sample has 306 rows (`n_analysed_last_h3`).\n- I fixed the COVID exclusion before computing any out-of-sample error. It affects only model training, not the naive forecast.\n\n## Method\n- **Naive forecast**: `gdp_yoy[t−2]` for both horizons.\n- **Model `ardl_direct_emp`** (`model_name`, `model_description`): a separate OLS regression for each horizon h, `gdp_yoy[s+h] = a + b·gdp_yoy[s−2] + c·emp_yoy[s−1]`.\n - It is re-estimated at every origin on an expanding window starting in 1998, using only pairs that were observable at that origin.\n - The forecast plugs in `gdp_yoy[t−2]` and `emp_yoy[t−1]`.\n - No model selection was done and nothing is random (`random_seed` = null).\n- **Errors**: actual minus forecast on the current-vintage data, summarised as RMSE and MAE over the 48 origins. The full forecast ledger is `out/forecasts.csv` (192 rows).\n- **Diagnostic (not the submitted model)**: the same regression without employment, estimated on the same sample (`diag_rmse_ar_only_h*`, `diag_mae_ar_only_h*`). It tells us whether any gain comes from employment.\n\n## Results\n| horizon | RMSE naive | MAE naive | RMSE model | MAE model | 1 − RMSE ratio | RMSE AR-only (diagnostic) |\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`) | 0.715 (`diag_rmse_ar_only_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`) | 0.864 (`diag_rmse_ar_only_h3`) |\n\n- In this sample the employment model has a lower RMSE and MAE than the naive forecast at both horizons: about 9% lower RMSE at h=1 and 21% at h=3.\n- **The gain does not come from employment.** Without employment, the regression is more accurate still: RMSE 0.715 vs 0.743 at h=1 and 0.864 vs 0.902 at h=3.\n- In the final estimation the employment coefficient is small: 0.058 at h=1 and 0.032 at h=3 (`last_coefficients_h1`, `last_coefficients_h3`). The GDP coefficient is below one (0.82 and 0.66), with a positive constant.\n- So the improvement over the naive forecast comes from the GDP growth series drifting back towards its average, which the naive forecast ignores. Adding employment growth does not help out of sample.\n- The answer to \"does the model with employment beat the naive forecast?\" is yes on point estimates, but not significantly (see Uncertainty), and not because of employment.\n\n## Uncertainty\n- I used Diebold–Mariano tests of equal squared-error loss, model vs naive, with HAC variance and the Harvey–Leybourne–Newbold small-sample correction:\n - h=1: statistic 1.39, two-sided p = 0.17 (`dm_stat_h1`, `dm_pvalue_two_sided_h1`).\n - h=3: statistic 1.44, p = 0.16 (`dm_stat_h3`, `dm_pvalue_two_sided_h3`).\n- HAC lags were 2 at h=1 and 4 at h=3 (`dm_hac_lags_h1`, `dm_hac_lags_h3`). I chose these myself because year-over-year targets overlap. This choice is a judgement call.\n- With only 48 overlapping origins, neither improvement is statistically significant at conventional levels.\n- I did not run a significance test for the model vs the AR-only diagnostic.\n\n## Limitations and open issues\n- **Not real-time.** The data are the current vintage. The exercise reproduces publication timing only, not the first-release values forecasters actually saw. Revisions to GDP and LFS data are ignored, so the errors are not real-time errors.\n- **One evaluation window.** The 48 origins (2022–2026) cover the post-COVID slowdown. With a different window the ranking could change.\n- **COVID exclusion.** Training rows touching 2020-03..2021-12 were excluded; this was decided in advance, not tuned. I did not report a variant that keeps those rows.\n- **Diagnostic after the fact.** The AR-only comparison was added after seeing the employment coefficients. It is reported as a diagnostic and does not replace the submitted model.\n- **Unverifiable 1998 values.** The 1998 `gdp_yoy` values cannot be checked against levels in the file.\n- **Workflow incident.** The analysis script was first written by mistake to `data/out/`. It was moved to `out/` and the stray folder removed. The data file's SHA-256 was re-checked and is unchanged.\nstep,rule,n_before,n_after,n_removed,rationale\navailability,target month s+1 <= t-2 and regressors observed at origin t,345,337,8,\"last estimation sample (origin 2026-04-01, h=1); rows = candidate pseudo-origins s, one per input month\"\nlags_in_sample,target and lagged regressors present in file (drops first months lacking y[s-2]/e[s-1] and GDP-empty months),337,335,2,\"last estimation sample (origin 2026-04-01, h=1); rows = candidate pseudo-origins s, one per input month\"\ncovid_window,drop rows whose target or regressor month lies in 2020-03..2021-12,335,310,25,\"last estimation sample (origin 2026-04-01, h=1); rows = candidate pseudo-origins s, one per input month\"\norigin_date,target_date,horizon,forecast,actual,model,last_target_date_used,last_predictor_date_used\n2022-05-01,2022-06-01,1,4.9335,5.9571,naive,2022-03-01,\n2022-05-01,2022-06-01,1,4.713444,5.9571,ardl_direct_emp,2022-03-01,2022-04-01\n2022-05-01,2022-08-01,3,4.9335,4.8317,naive,2022-03-01,\n2022-05-01,2022-08-01,3,4.392103,4.8317,ardl_direct_emp,2022-03-01,2022-04-01\nchecks.md\ncontract.md\ndata_audit.md\ngate_receipts\nleakage_check.py\nlog.md\nphases.json\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.","is_error":false}]},"uuid":"1e0d342b-bf62-4006-9784-2472af7e0627","timestamp":"2026-10-30T05:05:48.932Z","toolUseResult":{"stdout":"\"\"\"F3-conf-01: forecasting Canadian monthly GDP y/y growth under publication lags.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nReads data/ only; writes out/results.json, out/forecasts.csv, out/exclusions.csv. Deterministic (no randomness).\"\"\"\nimport json, os\nimport numpy as np, pandas as pd\n\nDATA = \"data/canada_gdp_employment.csv\"\nOUT = \"out\"\nH = [1, 3]\nMODEL = \"ardl_direct_emp\"\nCOVID = (pd.Timestamp(\"2020-03-01\"), pd.Timestamp(\"2021-12-01\")) # pre-specified exclusion window\n\nraw = pd.read_csv(DATA, parse_dates=[\"month\"])\nn_raw = len(raw)\nd = raw.set_index(\"month\").sort_index()\nmonths = d.index\ny = d[\"gdp_yoy\"]; e = d[\"emp_yoy\"]\n\ndef shift(m, k):\n return m + pd.DateOffset(months=k)\n\ndef in_covid(m):\n return (m >= COVID[0]) & (m <= COVID[1])\n\ndef design(t, h):\n \"\"\"Training rows for origin t, horizon h (direct regression).\n Pseudo-origin s: target y[s+h], regressors const, y[s-2], e[s-1].\n Availability at origin t: y months <= t-2, e months <= t-1.\"\"\"\n s = months\n tgt_m = s + pd.DateOffset(months=h)\n ym = s - pd.DateOffset(months=2); em = s - pd.DateOffset(months=1)\n steps = []\n n0 = len(s)\n keep = np.ones(n0, bool)\n k1 = keep & (tgt_m <= shift(t, -2)) & (ym <= shift(t, -2)) & (em <= shift(t, -1))\n steps.append((\"availability\", f\"target month s+{h} <= t-2 and regressors observed at origin t\", keep.sum(), k1.sum()))\n yt = y.reindex(tgt_m).values; yl = y.reindex(ym).values; el = e.reindex(em).values\n k2 = k1 & ~np.isnan(yt) & ~np.isnan(yl) & ~np.isnan(el)\n steps.append((\"lags_in_sample\", \"target and lagged regressors present in file (drops first months lacking y[s-2]/e[s-1] and GDP-empty months)\", k1.sum(), k2.sum()))\n cov = in_covid(tgt_m) | in_covid(ym) | in_covid(em)\n k3 = k2 & ~np.asarray(cov)\n steps.append((\"covid_window\", \"drop rows whose target or regressor month lies in 2020-03..2021-12\", k2.sum(), k3.sum()))\n X = np.column_stack([np.ones(k3.sum()), yl[k3], el[k3]])\n return X, yt[k3], tgt_m[k3], steps\n\nrows = []\norigins = pd.date_range(\"2022-05-01\", \"2026-04-01\", freq=\"MS\")\nassert len(origins) == 48\nlast_info = {}\nar_rows = []\nfor t in origins:\n yl_t = y.loc[shift(t, -2)]; el_t = e.loc[shift(t, -1)]\n for h in H:\n tm = shift(t, h)\n actual = y.loc[tm]\n rows.append(dict(origin_date=t, target_date=tm, horizon=h, forecast=yl_t, actual=actual, model=\"naive\",\n last_target_date_used=shift(t, -2), last_predictor_date_used=None))\n X, Y, tms, steps = design(t, h)\n beta, *_ = np.linalg.lstsq(X, Y, rcond=None)\n f = float(beta @ np.array([1.0, yl_t, el_t]))\n rows.append(dict(origin_date=t, target_date=tm, horizon=h, forecast=f, actual=actual, model=MODEL,\n last_target_date_used=max(tms.max(), shift(t, -2)), last_predictor_date_used=shift(t, -1)))\n b_ar, *_ = np.linalg.lstsq(X[:, :2], Y, rcond=None) # diagnostic: same sample, no employment\n ar_rows.append(dict(origin_date=t, horizon=h, forecast=float(b_ar @ np.array([1.0, yl_t])), actual=actual))\n last_info[h] = dict(n=len(Y), steps=steps, beta=beta.tolist(), last_target=str(tms.max().date()))\n\nfc = pd.DataFrame(rows)\n# information-rule checks\nassert (fc.last_target_date_used <= fc.origin_date - pd.DateOffset(months=2)).all()\nm = fc.model == MODEL\nassert (fc.loc[m, \"last_predictor_date_used\"] <= fc.loc[m, \"origin_date\"] - pd.DateOffset(months=1)).all()\nassert fc.actual.notna().all() and len(fc) == 192\n\nout = fc.copy()\nfor c in [\"origin_date\", \"target_date\", \"last_target_date_used\", \"last_predictor_date_used\"]:\n out[c] = out[c].apply(lambda v: \"\" if v is None or pd.isna(v) else pd.Timestamp(v).strftime(\"%Y-%m-%d\"))\nout[\"forecast\"] = out[\"forecast\"].round(6)\nout.to_csv(os.path.join(OUT, \"forecasts.csv\"), index=False)\n\ndef err(model, h):\n s = fc[(fc.model == model) & (fc.horizon == h)]\n u = (s.actual - s.forecast).values\n return float(np.sqrt(np.mean(u ** 2))), float(np.mean(np.abs(u)))\n\nres = {\"task_id\": \"F3-conf-01\", \"model_name\": MODEL,\n \"model_description\": (\"Direct OLS regression per horizon h of gdp_yoy[s+h] on a constant, gdp_yoy[s-2] and emp_yoy[s-1], \"\n \"estimated at each origin on an expanding window from 1998 using only pairs whose target is published (<= t-2), \"\n \"excluding rows touching the pre-specified COVID window 2020-03..2021-12; forecast plugs in gdp_yoy[t-2] and emp_yoy[t-1].\"),\n \"n_origins\": 48, \"first_origin\": \"2022-05-01\", \"last_origin\": \"2026-04-01\",\n \"last_target_date_available\": shift(origins[-1], -2).strftime(\"%Y-%m-%d\"),\n \"last_predictor_date_available\": shift(origins[-1], -1).strftime(\"%Y-%m-%d\")}\nfor h in H:\n rn, mn = err(\"naive\", h); rm, mm = err(MODEL, h)\n res[f\"rmse_naive_h{h}\"] = rn; res[f\"mae_naive_h{h}\"] = mn\n res[f\"rmse_model_h{h}\"] = rm; res[f\"mae_model_h{h}\"] = mm\norder = [\"rmse_naive_h1\", \"mae_naive_h1\", \"rmse_naive_h3\", \"mae_naive_h3\", \"rmse_model_h1\", \"mae_model_h1\", \"rmse_model_h3\", \"mae_model_h3\"]\nres = {**res, **{k: res[k] for k in order}}\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# Diebold-Mariano (squared loss, HAC with h-1 lags, Harvey-Leybourne-Newbold correction) for uncertainty\nfrom scipy import stats\nfor h in H:\n a = fc[(fc.model == \"naive\") & (fc.horizon == h)].sort_values(\"origin_date\")\n b = fc[(fc.model == MODEL) & (fc.horizon == h)].sort_values(\"origin_date\")\n dlt = (a.actual.values - a.forecast.values) ** 2 - (b.actual.values - b.forecast.values) ** 2\n T = len(dlt); dm = dlt - dlt.mean()\n L = max(h - 1, 0) + 2 # a few extra lags given overlapping y/y targets\n v = dm @ dm / T + 2 * sum((1 - l / (L + 1)) * (dm[l:] @ dm[:-l]) / T for l in range(1, L + 1))\n stat = dlt.mean() / np.sqrt(v / T)\n stat *= np.sqrt((T + 1 - 2 * h + h * (h - 1) / T) / T)\n res[f\"dm_stat_h{h}\"] = float(stat); res[f\"dm_pvalue_two_sided_h{h}\"] = float(2 * stats.t.sf(abs(stat), T - 1))\n res[f\"dm_hac_lags_h{h}\"] = L\n\nar = pd.DataFrame(ar_rows)\nfor h in H:\n a = ar[ar.horizon == h]; u = (a.actual - a.forecast).values\n res[f\"diag_rmse_ar_only_h{h}\"] = float(np.sqrt(np.mean(u ** 2)))\n res[f\"diag_mae_ar_only_h{h}\"] = float(np.mean(np.abs(u)))\nres[\"feasibility\"] = \"complete\"; res[\"feasibility_reason\"] = None\nres[\"data_issues\"] = [\n {\"issue\": \"gdp_yoy is populated for 1998-01..1998-12 although data/README.md says it is empty for the first 12 months and the file has no 1997 levels to verify it.\",\n \"handling\": \"Values kept as given (they are the official target column); all gdp_yoy values computable from gdp_level in the file match to 4 decimals.\"},\n {\"issue\": \"gdp_level/gdp_yoy missing for 2026-08 and 2026-09 (not yet published).\", \"handling\": \"Expected; never needed (latest target 2026-07).\"},\n {\"issue\": \"COVID-19 swings (gdp_yoy -16.2% in 2020-04, +18.5% in 2021-04) would dominate OLS estimates.\",\n \"handling\": \"Pre-specified exclusion of training rows whose target or regressor month lies in 2020-03..2021-12; naive forecast unaffected.\"},\n {\"issue\": \"Current-vintage data, not real-time vintages.\", \"handling\": \"Exercise simulates publication timing only; no real-time validity claimed.\"}]\nres[\"n_input_rows\"] = {\"canada_gdp_employment.csv\": int(n_raw)}\nres[\"n_analysed\"] = int(last_info[1][\"n\"])\nres[\"n_analysed_last_h3\"] = int(last_info[3][\"n\"])\nres[\"last_coefficients_h1\"] = dict(zip([\"const\", \"gdp_yoy_lag2\", \"emp_yoy_lag1\"], last_info[1][\"beta\"]))\nres[\"last_coefficients_h3\"] = dict(zip([\"const\", \"gdp_yoy_lag2\", \"emp_yoy_lag1\"], last_info[3][\"beta\"]))\nres[\"random_seed\"] = None\n\npd.DataFrame([dict(step=s, rule=r, n_before=int(a), n_after=int(b), n_removed=int(a - b),\n rationale=\"last estimation sample (origin 2026-04-01, h=1); rows = candidate pseudo-origins s, one per input month\")\n for s, r, a, b in last_info[1][\"steps\"]]).to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\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\", \"dm_\", \"n_\"))}, 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), how accurately can the year-over-year growth of Canadian monthly real GDP for months t+1 and t+3 be forecast using only data published by then? And does a model that also uses Labour Force Survey employment growth beat the naive forecast? At origin t, GDP is known only up to t−2 and employment only up to t−1. At the last origin this gives `last_target_date_available` = 2026-02-01 and `last_predictor_date_available` = 2026-03-01.\n\n## Data and exclusions\n- Input: `data/canada_gdp_employment.csv`, 345 rows (`n_input_rows`). The SHA-256 matches the README. Full audit in `out/state/data_audit.md`.\n- Every year-over-year value that can be recomputed from the levels in the file matches exactly. GDP is missing for 2026-08 and 2026-09 (not yet published). 1998 `gdp_yoy` values are present even though the README says they should be empty. They are kept as given (`data_issues`).\n- The file contains data published after each origin. The code removes it at each origin: training pairs need a target month ≤ t−2, a GDP regressor month ≤ t−2 and an employment month ≤ t−1. An independent check that blanks out these later data and re-estimates gives the same forecasts (`out/state/checks.md`, check 5).\n- Exclusions for the last estimation sample (origin 2026-04-01, h=1), from `out/exclusions.csv`:\n - 345 candidate rows.\n - Minus 8 rows not available at the origin.\n - Minus 2 rows missing a lag or target.\n - Minus 25 rows that touch the COVID window 2020-03..2021-12.\n - Leaves 310 rows (`n_analysed`). The h=3 sample has 306 rows (`n_analysed_last_h3`).\n- I fixed the COVID exclusion before computing any out-of-sample error. It affects only model training, not the naive forecast.\n\n## Method\n- **Naive forecast**: `gdp_yoy[t−2]` for both horizons.\n- **Model `ardl_direct_emp`** (`model_name`, `model_description`): a separate OLS regression for each horizon h, `gdp_yoy[s+h] = a + b·gdp_yoy[s−2] + c·emp_yoy[s−1]`.\n - It is re-estimated at every origin on an expanding window starting in 1998, using only pairs that were observable at that origin.\n - The forecast plugs in `gdp_yoy[t−2]` and `emp_yoy[t−1]`.\n - No model selection was done and nothing is random (`random_seed` = null).\n- **Errors**: actual minus forecast on the current-vintage data, summarised as RMSE and MAE over the 48 origins. The full forecast ledger is `out/forecasts.csv` (192 rows).\n- **Diagnostic (not the submitted model)**: the same regression without employment, estimated on the same sample (`diag_rmse_ar_only_h*`, `diag_mae_ar_only_h*`). It tells us whether any gain comes from employment.\n\n## Results\n| horizon | RMSE naive | MAE naive | RMSE model | MAE model | 1 − RMSE ratio | RMSE AR-only (diagnostic) |\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`) | 0.715 (`diag_rmse_ar_only_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`) | 0.864 (`diag_rmse_ar_only_h3`) |\n\n- In this sample the employment model has a lower RMSE and MAE than the naive forecast at both horizons: about 9% lower RMSE at h=1 and 21% at h=3.\n- **The gain does not come from employment.** Without employment, the regression is more accurate still: RMSE 0.715 vs 0.743 at h=1 and 0.864 vs 0.902 at h=3.\n- In the final estimation the employment coefficient is small: 0.058 at h=1 and 0.032 at h=3 (`last_coefficients_h1`, `last_coefficients_h3`). The GDP coefficient is below one (0.82 and 0.66), with a positive constant.\n- So the improvement over the naive forecast comes from the GDP growth series drifting back towards its average, which the naive forecast ignores. Adding employment growth does not help out of sample.\n- The answer to \"does the model with employment beat the naive forecast?\" is yes on point estimates, but not significantly (see Uncertainty), and not because of employment.\n\n## Uncertainty\n- I used Diebold–Mariano tests of equal squared-error loss, model vs naive, with HAC variance and the Harvey–Leybourne–Newbold small-sample correction:\n - h=1: statistic 1.39, two-sided p = 0.17 (`dm_stat_h1`, `dm_pvalue_two_sided_h1`).\n - h=3: statistic 1.44, p = 0.16 (`dm_stat_h3`, `dm_pvalue_two_sided_h3`).\n- HAC lags were 2 at h=1 and 4 at h=3 (`dm_hac_lags_h1`, `dm_hac_lags_h3`). I chose these myself because year-over-year targets overlap. This choice is a judgement call.\n- With only 48 overlapping origins, neither improvement is statistically significant at conventional levels.\n- I did not run a significance test for the model vs the AR-only diagnostic.\n\n## Limitations and open issues\n- **Not real-time.** The data are the current vintage. The exercise reproduces publication timing only, not the first-release values forecasters actually saw. Revisions to GDP and LFS data are ignored, so the errors are not real-time errors.\n- **One evaluation window.** The 48 origins (2022–2026) cover the post-COVID slowdown. With a different window the ranking could change.\n- **COVID exclusion.** Training rows touching 2020-03..2021-12 were excluded; this was decided in advance, not tuned. I did not report a variant that keeps those rows.\n- **Diagnostic after the fact.** The AR-only comparison was added after seeing the employment coefficients. It is reported as a diagnostic and does not replace the submitted model.\n- **Unverifiable 1998 values.** The 1998 `gdp_yoy` values cannot be checked against levels in the file.\n- **Workflow incident.** The analysis script was first written by mistake to `data/out/`. It was moved to `out/` and the stray folder removed. The data file's SHA-256 was re-checked and is unchanged.\nstep,rule,n_before,n_after,n_removed,rationale\navailability,target month s+1 <= t-2 and regressors observed at origin t,345,337,8,\"last estimation sample (origin 2026-04-01, h=1); rows = candidate pseudo-origins s, one per input month\"\nlags_in_sample,target and lagged regressors present in file (drops first months lacking y[s-2]/e[s-1] and GDP-empty months),337,335,2,\"last estimation sample (origin 2026-04-01, h=1); rows = candidate pseudo-origins s, one per input month\"\ncovid_window,drop rows whose target or regressor month lies in 2020-03..2021-12,335,310,25,\"last estimation sample (origin 2026-04-01, h=1); rows = candidate pseudo-origins s, one per input month\"\norigin_date,target_date,horizon,forecast,actual,model,last_target_date_used,last_predictor_date_used\n2022-05-01,2022-06-01,1,4.9335,5.9571,naive,2022-03-01,\n2022-05-01,2022-06-01,1,4.713444,5.9571,ardl_direct_emp,2022-03-01,2022-04-01\n2022-05-01,2022-08-01,3,4.9335,4.8317,naive,2022-03-01,\n2022-05-01,2022-08-01,3,4.392103,4.8317,ardl_direct_emp,2022-03-01,2022-04-01\nchecks.md\ncontract.md\ndata_audit.md\ngate_receipts\nleakage_check.py\nlog.md\nphases.json\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. 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data/canada_gdp_employment.csv\nmonth,gdp_level,gdp_yoy,emp_level,emp_yoy\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\n1999-03-01,1314242.0,3.6645,14278.7,2.3607\ngdp maxdiff 4.985325298356713e-05\nemp maxdiff 4.968314845221755e-05\ngdp_level 2\ngdp_yoy 2\nemp_level 0\nemp_yoy 0\ndtype: int64\nmodel horizon\nardl_direct_emp 1 48\n 3 48\nnaive 1 48\n 3 48\ndtype: int64\nShell cwd was reset to 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> out/review/review.json <<'EOF'\n{\n \"verdict\": \"accept\",\n \"issues\": [\n {\n \"id\": \"R1\",\n \"severity\": \"minor\",\n \"location\": \"out/claims.json C4; out/report.md Results\",\n \"issue\": \"C4 and the report say the gain 'is not attributable to employment' and that employment 'does not help out of sample', and C4 is marked 'supported'. This rests only on point RMSE differences (0.743 vs 0.715 at h=1, 0.902 vs 0.864 at h=3) with no test. The report also states as fact that the gain comes from mean reversion, which is an interpretation.\",\n \"suggested_fix\": \"Rephrase as 'in this sample the AR-only diagnostic had lower RMSE than the employment model; no evidence that employment adds accuracy (untested)'. Mark the mean-reversion explanation as an interpretation.\"\n },\n {\n \"id\": \"R2\",\n \"severity\": \"minor\",\n \"location\": \"out/analysis.py COVID window; out/report.md Data and exclusions\",\n \"issue\": \"Training rows touching 2020-03..2021-12 are excluded (25 rows in the last sample). Nothing in the files can confirm the claim that this was 'pre-specified'. The window boundaries are a judgement call (they use data that is available at every origin, so there is no leakage), and no sensitivity variant is reported.\",\n \"suggested_fix\": \"Report the model RMSE/MAE with no exclusion (or with a dummy variable) as a sensitivity check, or soften the 'pre-specified' wording.\"\n },\n {\n \"id\": \"R3\",\n \"severity\": \"minor\",\n \"location\": \"out/results.json dm_*\",\n \"issue\": \"The DM HAC lag count (h+1) is chosen ad hoc. The test ignores parameter-estimation uncertainty in the expanding-window regression, and the HLN correction is applied together with a nonstandard lag choice. The p-values are therefore approximate. The report already says the lag choice is a judgement call.\",\n \"suggested_fix\": \"Note that the DM p-values are approximate. Optionally report how sensitive they are to the lag choice.\"\n }\n ],\n \"summary\": \"Re-running analysis.py in a scratch copy reproduces results.json and forecasts.csv exactly. 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This rests only on point RMSE differences (0.743 vs 0.715 at h=1, 0.902 vs 0.864 at h=3) with no test. The report also states as fact that the gain comes from mean reversion, which is an interpretation.\",\n \"suggested_fix\": \"Rephrase as 'in this sample the AR-only diagnostic had lower RMSE than the employment model; no evidence that employment adds accuracy (untested)'. Mark the mean-reversion explanation as an interpretation.\"\n },\n {\n \"id\": \"R2\",\n \"severity\": \"minor\",\n \"location\": \"out/analysis.py COVID window; out/report.md Data and exclusions\",\n \"issue\": \"Training rows touching 2020-03..2021-12 are excluded (25 rows in the last sample). Nothing in the files can confirm the claim that this was 'pre-specified'. 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I found three minor issues and nothing critical or major. The review is saved at `out/review/review.json`.\n\n**What I checked:**\n- **Reproducibility:** I re-ran `out/analysis.py` in a scratch copy. It reproduced `results.json` and `forecasts.csv` exactly. The data file's SHA-256 matches `data/README.md`, and the ledger has 192 rows, 48 for each model and horizon.\n- **Publication-lag rules:** I wrote my own version of the model that hides any data published after each origin date before fitting. It matched every submitted forecast to within 5e-7, so the code respects the lag rules. The naive forecast is GDP growth from two months earlier (t−2), as `TASK.md` requires.\n- **Required outputs:** every required key in `results.json` is present.\n- **Counts and dates:** the exclusion steps (345 → 337 → 335 → 310 rows) and the last available dates (GDP 2026-02-01, employment 2026-03-01) are consistent with the rules.\n- **Claims and limitations:** the headline claims match the numbers. RMSE improves by 8.7% at one month ahead and 20.8% at three months, and neither gain is statistically significant (p ≈ 0.17 and 0.16). The stated limitations are honest: current-vintage data, a single evaluation window, the COVID exclusion, and a diagnostic added after seeing the results.\n\n**Minor issues:**\n1. **R1 – wording too strong:** the report says the gain \"is not attributable to employment\" and that employment \"does not help out of sample\". That rests only on untested differences: the same model without employment has slightly lower RMSE (0.715 vs 0.743, 0.864 vs 0.902). The report also states as fact that the gain comes from GDP growth drifting back to its average, which is an interpretation.\n2. **R2 – COVID exclusion:** training rows touching 2020-03 to 2021-12 were dropped (25 rows in the last sample). It is not possible to confirm from the files that this was decided in advance, as claimed. 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