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

## Question
How accurately could US quarterly real GDP growth (A191RL1Q225SBEA, % change q/q at a seasonally adjusted annual rate) have been forecast 1 and 2 quarters ahead *at the time*? The forecasts use only the ALFRED vintage published at each of 8 origins (`first_origin` = 2024-01-31 … `last_origin` = 2025-12-31, `n_origins` = 8). They are scored against first-release values. The question is also whether a simple AR model beats the naive last-value forecast.

## Data and exclusions
- Inputs: 8 vintage files (307–314 rows each), `current_vintage.csv` (318 rows) and `first_release.csv` (13 rows). Row counts are in `n_input_rows`. All SHA-256 hashes match `data/README.md`. No missing values, no duplicate dates, no gaps (see `out/state/data_audit.md`).
- Real-time rule: at each origin only the vintage file dated at that origin is read for estimation and forecast input. `current_vintage.csv` is used only for `mean_abs_revision_h1_targets`. The script asserts that each target's first-release date falls after its origin.
- Exclusions (model only; the naive forecast uses all rows): keep quarters from 1985Q1 onward; form lag pairs; drop pairs that involve the pandemic quarters 2020Q2–2020Q3. At the last origin this gives 314 rows → 163 → 162 → 159 regression pairs (`n_analysed` = 314 rows in the last origin's training vintage; `n_model_estimation_pairs_last_origin` = 159). The full ledger for every origin is in `out/exclusions.csv`.
- Data issues are listed in `data_issues`. Origins are unevenly spaced because the 2025 shutdown delayed the advance estimate of 2025Q3. As a result, 2025Q4 is the h=2 target of origin 7 and also the h=1 target of origin 8.
- Process note: a working-directory slip briefly created a folder of my own state files under `data/out/`. I moved it to `out/state/`. The data files themselves were never written, and their hashes were re-verified afterwards.

## Method
- Naive: the forecast for both horizons is the last value in the origin vintage.
- Model `ar1_1985` (`model_name`, `model_description`): an AR(1) with intercept, estimated by OLS at each origin on that vintage only. The sample runs from 1985Q1 to the last published quarter, minus the pandemic pairs. The h=2 forecast is iterated from the h=1 forecast. I chose this specification before computing any forecast and did not tune it on the evaluation results. Across origins the estimates are stable: φ ≈ 0.34 and intercept ≈ 1.75 (printed by the script).
- Evaluation: errors are forecast − first release, summarised by RMSE and MAE over 8 origins per horizon. No randomness is used (`random_seed` = null).

## Results
| | h=1 | h=2 |
|---|---|---|
| Naive RMSE / MAE (pp) | 2.010 (`rmse_naive_h1`) / 1.688 (`mae_naive_h1`) | 2.265 (`rmse_naive_h2`) / 1.813 (`mae_naive_h2`) |
| AR(1) RMSE / MAE (pp) | 1.484 (`rmse_model_h1`) / 1.233 (`mae_model_h1`) | 1.398 (`rmse_model_h2`) / 1.030 (`mae_model_h2`) |
| 1 − RMSE_model/RMSE_naive | 0.262 (`rel_improvement_rmse_h1`) | 0.383 (`rel_improvement_rmse_h2`) |

- In this sample the AR(1) has lower RMSE and MAE than the naive forecast at both horizons. It does better because it pulls forecasts toward the post-1985 mean, which helps around volatile quarters such as the 2025Q1 contraction (−0.3) and the following rebound.
- The mean absolute revision between the first release and the 2026-10-30 value of the 8 h=1 target quarters is 0.5625 pp (`mean_abs_revision_h1_targets`). That is about a third of the AR(1) h=1 MAE, so the choice of "truth" vintage matters at the margin.

## Uncertainty
Each horizon has only 8 forecast errors, and the h=1 and h=2 samples overlap in their target quarters, so these estimates are very imprecise. Two descriptive tests of the squared-error loss differential (naive² − model²):
- h=1: the model is better at 5 of 8 origins (`n_origins_model_better_sqerr_h1`); t = 1.49, two-sided p = 0.18 (`dm_tstat_sqerr_h1`, `dm_pvalue_two_sided_h1`).
- h=2: the model is better at 8 of 8 origins (`n_origins_model_better_sqerr_h2`); t = 1.55, p = 0.17 (`dm_tstat_sqerr_h2`, `dm_pvalue_two_sided_h2`).

These tests use simple t-statistics without HAC correction and assume approximate normality, which n = 8 cannot support well. The model's advantage is therefore not statistically significant at conventional levels. Parameter-estimation uncertainty is not propagated into the forecasts.

## Limitations and open issues
- The evaluation window is short (2024–2025, 8 origins), so the results may not generalise to other periods, such as recessions.
- Excluding the pandemic quarters and starting the sample in 1985 are judgement calls (made a priori). Other choices would change the AR estimates somewhat.
- Advance estimates are noisy (see the revision statistic). Scoring against later vintages could change the ranking; this was not evaluated.
- The task is complete (`feasibility` = "complete"). No required value is null.