# F3-conf-01 — Forecasting Canadian monthly GDP y/y growth under publication lags

# Question

At the end of each month t (48 origins, first_origin = 2022-05-01 to last_origin = 2026-04-01; n_origins), how accurately can year-over-year growth of Canadian monthly real GDP be forecast for months t+1 and t+3 using only data published by then, and does a model that also uses the timelier LFS employment growth beat the naive forecast (latest published GDP growth, month t−2)?

# Data and exclusions

• One file, data/canada_gdp_employment.csv, 345 data rows (n_input_rows), 1998-01 to 2026-09; SHA-256 matches data/README.md. Audit details are in out/state/data_audit.md.
• Publication-lag rule: at origin t, GDP is used only up to t−2 and employment only up to t−1. At the last origin, that means GDP up to 2026-02-01 (last_target_date_available) and employment up to 2026-03-01 (last_predictor_date_available). Every row of out/forecasts.csv records the latest dates it actually used, and all of them satisfy the rule (out/state/checks.md).
• No data row was deleted. When estimating the model, I dropped regression rows whose target or regressor month falls in the COVID window 2020-03..2021-12, where y/y values swing between −16 % and +19 %. I made this choice before computing any out-of-sample error. Exclusion ledger for the last estimation sample (origin 2026-04, h=1), in out/exclusions.csv: 345 rows → 338 known at the origin → 335 with lagged regressors available → 310 after the COVID exclusion (n_analysed).
• Data issues and how I handled them are listed in data_issues. The main ones: GDP for 2026-08/09 is not yet published (not needed); the 1998 y/y values cannot be checked against levels (all later values match the levels exactly); the data are the current vintage.

# Method

• Naive: forecast = gdp_yoy(t−2) for both horizons.
• Model dir_ols_emp (model_name, model_description): a direct h-step OLS of gdp_yoy(s) on a constant, gdp_yoy(s−h−2) and emp_yoy(s−h−1). This mirrors the information gaps at the origin (GDP lags the origin by 2 months, employment by 1). It is re-estimated at every origin on an expanding window starting in 1998, using only training targets ≤ t−2. The forecast plugs in gdp_yoy(t−2) and emp_yoy(t−1).
• Evaluation: RMSE and MAE in percentage points over the 48 origins per horizon, against gdp_yoy of month t+h as given in the file.
• Diagnostics beyond the required outputs:
  • A Diebold–Mariano test on squared-error loss, with an HAC variance (h−1 lags) and the Harvey–Leybourne–Newbold correction (dm_stat_h*, dm_pvalue_two_sided_h*).
  • An ablation: the same regression without employment (rmse_ablation_no_emp_h*).
• Nothing is random (random_seed = null). out/analysis.py regenerates every output.

# Results

• On both RMSE and MAE, the model beats the naive forecast at both horizons. The RMSE reduction is about 9 % at h=1 and 21 % at h=3.
• Employment is not what drives the gain. The same regression without employment does slightly better: RMSE 0.715 at h=1 (rmse_ablation_no_emp_h1) and 0.864 at h=3 (rmse_ablation_no_emp_h3). The improvement over naive comes from the autoregressive mean reversion (constant plus a lag coefficient below 1), not from LFS employment growth.

# Uncertainty

• The Diebold–Mariano test of equal squared-error accuracy (model vs naive) gives:
  • h=1: statistic 2.03, p = 0.048 (dm_stat_h1, dm_pvalue_two_sided_h1)
  • h=3: statistic 1.64, p = 0.108 (dm_stat_h3, dm_pvalue_two_sided_h3)
• The evidence that the model beats naive is therefore borderline at h=1 and not significant at the 5 % level at h=3.
• With only 48 overlapping, serially correlated errors over a single disinflation and slowdown episode (2022–2026), the RMSE estimates are imprecise. I computed no confidence intervals for the RMSEs themselves.
• I did not test whether the employment-augmented model differs significantly from the no-employment ablation.

# Limitations and open issues

• Timing only, not real-time: the data are the current vintage (revised). The exercise simulates publication timing but not the historical first-release values, so no real-time validity is claimed. Errors against first releases would probably be larger.
• COVID exclusion: dropping 2020-03..2021-12 from estimation is a modelling choice. Other ways of handling that period (dummies, robust estimation) were not tried.
• Short evaluation window: the 48 origins cover one macro episode, and the ranking of methods may not generalise.
• One specification: only one model specification was evaluated, beyond the diagnostic ablation, and no model selection was done.
• All parts of the task were completed (feasibility = "complete").