# F3-conf-02 — Real-time forecasts of US real GDP growth from data vintages

# Question

How accurately could US quarterly real GDP growth (A191RL1Q225SBEA, % q/q SAAR) have been forecast 1 and 2 quarters ahead in real time, using only the ALFRED vintage published at each of 8 origins (2024-01-31 … 2025-12-31), and does a simple AR model beat the naive (last value) forecast? Errors are measured against the first-release value of each target quarter.

# Data and exclusions

• 8 ALFRED vintage files (307–314 rows each, 1947Q2 to the last published quarter); first_release.csv (13 rows, 2023Q3–2026Q3); current_vintage.csv (318 rows), used only for the revision statistic.
• No missing values, duplicate dates or quarterly gaps were found in any file.
• At each origin only that origin's vintage file was used (all historical values as published at that date). Targets are the 1st and 2nd quarters after the last quarter in the file; all 16 targets (2024Q1–2026Q1) have first releases.
• The origin grid has no 2025-10-31 vintage (2025Q3 advance estimate delayed by the 2025 federal shutdown), so the 8th origin is 2025-12-31; horizons are defined relative to the last published quarter, so this does not change the target definition.
• Model estimation sample: 1985Q1 onward; regression pairs in which either the dependent or the lagged value is 2020Q2 or 2020Q3 (the COVID collapse/rebound, ≈ −28% and +35% SAAR) were excluded. This rule was fixed before looking at forecast errors.

# Method

• Naive: forecast for h = 1, 2 = last value in the origin's vintage file.
• Model ar1_1985_excovid: AR(1) with intercept, y_t = c + φ y_{t−1} + e_t, OLS on the origin's vintage (1985Q1 – last quarter, excluding COVID pairs; 153–160 regression observations); h = 2 forecast iterated (c + φ·ŷ_{T+1}). Estimates were very stable across origins (c ≈ 1.73–1.78, φ ≈ 0.335–0.343; see out/ar_coefficients.csv).
• Metrics: RMSE and MAE over 8 origins per horizon; relative improvement = 1 − RMSE_model/RMSE_naive. Revision statistic = mean |current-vintage value − first release| over the 8 h = 1 target quarters.
• n_train in forecasts.csv: for the naive rows, the number of rows in the vintage file; for model rows, the number of OLS regression observations. n_analysed (160) = model regression observations at the last origin.
• Fully deterministic; no random numbers used.

# Results

(percentage points of annualised growth). The AR(1) had a smaller absolute error than the naive forecast at 5/8 origins for h = 1 and at 8/8 for h = 2. The AR(1) mostly pulls forecasts towards the post-1985 mean (≈ 2.6%), which helped most after the outlying 2025Q1 (−0.3%) and 2025Q3 (+4.3%) releases.

Mean absolute revision between first release and the 2026-10-30 vintage for the 8 h = 1 targets: 0.56 pp (individual revisions 0.1–1.2 pp), i.e. a non-trivial fraction of the forecast errors themselves.

# Uncertainty

• With only 8 origins, the results are very imprecise. Diebold–Mariano tests (squared loss, Harvey–Leybourne–Newbold small-sample correction, t(7) reference) give p = 0.18 for h = 1 and p = 0.12 for h = 2: the AR(1) advantage is not statistically significant at conventional levels (see out/supplementary.json).
• Sensitivity: an AR(1) estimated on the same sample including the COVID quarters gave RMSE 1.35 (h = 1) and 1.34 (h = 2), slightly better than the main specification; the qualitative conclusion (AR beats naive) is unchanged. This variant is reported only as sensitivity; the main specification was not switched after seeing results.
• The evaluation period (2024–2025) included unusual swings (tariff-related import surge in 2025Q1), so the numbers are specific to this short window.

# Limitations and open issues

• 8 origins × 2 horizons is a tiny evaluation sample; h = 2 errors at consecutive origins overlap (MA(1) structure), reducing effective sample size further.
• Only one simple univariate model was evaluated; no claims about richer models (nowcasts, factor models, SPF) are made.
• Actuals are first releases (advance estimates as of month-end); evaluating against later vintages would give different numbers given revisions averaging 0.56 pp.
• current_vintage.csv was used only for the revision statistic, never for estimation or forecasting.