# Real-time forecasting of US retail-sales YoY growth from ALFRED vintages

# Question

Could the year-over-year growth of US retail and food services sales (RSAFS, g_m = 100·ln(L_m/L_{m−12})) have been forecast in real time, 1 and 3 months beyond the last published month, better than the no-change (naive) forecast, when forecast errors are measured against the first published value of each target month? We evaluate 10 month-end origins from 2025-10-31 (first_origin) to 2026-07-31 (last_origin), n_origins = 10.

# Data and exclusions

• Inputs (row counts in n_input_rows): 10 RSAFS and 10 PAYEMS ALFRED vintages, the current UMCSENT and RSAFS files, and first_release.csv. All SHA-256 hashes match data/README.md (see out/state/data_audit.md).
• Real-time design. The forecast made at origin V uses only RSAFS_vintage_V (vintage_used = origin_date in every row of out/forecasts.csv). The target is last(V)+h, where last(V) is the last month in that vintage. Observed publication delays: last(V) = 2025-08 at V = 2025-10-31 and 2026-01 at V = 2026-03-31 (two months before the vintage date); the 2026-04-30 vintage adds two months (2026-02 and 2026-03) at once. For every other origin last(V) is the month before V. As a result, the h=1 targets are 2025-09, 2025-10, 2025-11, 2025-12, 2026-01, 2026-02, 2026-04, 2026-05, 2026-06 and 2026-07, and the h=3 targets run from 2025-11 to 2026-09. 2026-03 is not an h=1 target, and 2026-05 is not an h=3 target.
• Actuals are yoy_first_release from first_release.csv. The h=3 actuals for 2026-08 and 2026-09 come after a large level revision of RSAFS (current levels are about 4–5% below the vintage levels). YoY is always computed within a single vintage, so the actuals stay internally consistent.
• PAYEMS and UMCSENT were audited but are not used by any forecast. RSAFS_current.csv is used only for the revision estimand.
• Exclusions (out/exclusions.csv): 80 forecast–actual pairs were planned and 80 were analysed, with 0 removed. n_analysed = 20 pairs for my model (10 per horizon).
• Data problems and how each was handled are listed in data_issues.

# Method

• Baselines (computed from the vintage dated V): naive (g_last for both horizons); seasonal naive (g_{T−12} from the vintage); AR(1) (OLS of g_m on a constant and g_{m−1} over 1993-02 ≤ m ≤ last(V), with iterated forecasts; φ̂ ≈ 0.84 at every origin, see out/supplementary.json).
• My model (model_name, model_description): a base-effect random walk with drift in the log level. The forecast is ln L̂_T = ln L_last + h·g_last/1200, and the YoY forecast is 100·(ln L̂_T − ln L_{T−12}), with L_{T−12} taken from the same vintage. In words, it is the naive forecast corrected for the known change in the year-earlier comparison level (base effects) plus a drift. The model has no estimated parameters. I fixed the specification before seeing any evaluation result and tried no alternatives on the evaluation sample, so there is no specification search to correct for.
• Evaluation: RMSE and MAE over the 10 origins for each horizon; 1 − RMSE_model/RMSE_naive; and a Diebold–Mariano test on d_t = e²_naive − e²_model. The DM test uses a Bartlett (Newey–West) long-run variance with truncation lag h−1, no HLN correction, and a two-sided normal p-value.
• Supplementary uncertainty measure: a moving-block bootstrap (block length max(h,2), B = 5000, seed random_seed) of RMSE_naive − RMSE_model.
• Revision estimand: the mean over the 10 h=1 targets of |g_current − yoy_first_release|.

# Results

Table 1 (out/table1.csv; RMSE / MAE in percentage points; n = 10 per cell):

• h = 1: my model lowers RMSE by 44.8% relative to naive (rel_improvement_rmse_h1 = 0.448). The DM statistic is 2.43 (dm_stat_h1), with p = 0.015 (dm_pvalue_h1), giving conclusion_code_h1 = model_better_significant.
• h = 3: the improvement is 19.6% (rel_improvement_rmse_h3 = 0.196). The DM statistic is 1.55 (dm_stat_h3), with p = 0.122 (dm_pvalue_h3), giving conclusion_code_h3 = model_better_not_significant.
• At h = 3 every alternative has a lower RMSE than naive, but my model's edge over AR(1) is small: 1.142 against 1.187.
• Revisions: first-release YoY of the h=1 targets differs from today's published YoY by 0.548 pp on average (mean_abs_revision_h1_targets). That is the same order as the model's h=1 RMSE. All 10 revisions are negative (out/supplementary.json), consistent with the large level revision after mid-2026.
• Figure 1 (out/figure1.png) plots the first-release actuals and the naive, AR(1) and model forecasts for each horizon.

# Uncertainty

• Small sample. With only 10 origins, the DM statistic relies on a normal approximation that is unreliable at this sample size. The long-run variance is estimated from 10 loss differentials, and at h=3 from overlapping errors with only two lags. With n = 10 the omitted HLN correction would shrink the statistic and Student-t critical values would be wider. The h=1 p-value of 0.015 (dm_pvalue_h1) should therefore be read as suggestive evidence, not a firm rejection.
• h = 1 evidence. Two other measures point the same way. The model has the smaller squared error at 8 of 10 origins (share_origins_model_smaller_sq_error_h1 = 0.8). The block-bootstrap 95% interval for RMSE_naive − RMSE_model is [0.26, 0.70] pp (boot_rmse_diff_ci95_lo_h1, boot_rmse_diff_ci95_hi_h1) and excludes zero. Even so, a bootstrap on 10 points is itself fragile.
• h = 3 evidence. The bootstrap interval is [−0.14, 0.63] pp (boot_rmse_diff_ci95_lo_h3, boot_rmse_diff_ci95_hi_h3) and includes zero. The model wins at 6 of 10 origins (share_origins_model_smaller_sq_error_h3). The data cannot distinguish the model from naive at this horizon.
• Why the h=1 gain is plausible. It has a mechanical explanation that should carry over to other periods: the year-earlier comparison level is already known at the origin, and the naive forecast ignores it.

# Limitations and open issues

• Short, unusual sample. There are only 10 origins, the period covers irregular publication timing and a large benchmark revision, and the h=3 errors overlap. Results may not generalise.
• Mixed-vintage actuals. First-release actuals for targets 2026-08 and 2026-09 (h=3, last two origins) come from vintages after a big level revision. Forecasts made from pre-revision vintages are compared with actuals from post-revision vintages; because the comparison is in YoY terms the effect is muted but not removed.
• Predictors not used. PAYEMS and UMCSENT were not used. I made no attempt to show whether they add information, and nothing is claimed about them.
• Unresolved conflict with the gate. The provided gate checks origin_date < target_date in out/forecasts.csv. TASK.md requires target_date to be the first day of the target month (YYYY-MM-01). Because a month-end vintage contains at most the month before V, every h=1 target month begins before its month-end origin date (e.g. origin 2026-05-31, target 2026-05-01), so 40 of 80 rows fail that literal rule. The substantive availability rule — the target month is not yet published in the vintage used — holds for all 80 rows, and this is asserted in out/analysis.py. I kept the format TASK.md specifies instead of relabelling dates to pass the gate. Phase P4 is therefore recorded as "blocked" by this rule only (see out/state/checks.md). All required estimands were produced (feasibility = complete).