# F3-conf-03 — Rolling-origin ridge forecasts of US industrial production growth

# Question

Does a fixed-penalty ridge regression (λ = 50, key lambda) on 8 standardised monthly predictors (key n_features) forecast next month's US industrial production growth (100×Δln INDPRO) better than the naive last-value forecast and the expanding historical mean? Evaluation uses n_origins = 60 rolling origins from first_origin (2021-09-01) to last_origin (2026-08-01), horizon h = 1.

# Data and exclusions

• data/ip_predictors.csv (n_input_rows: 417 rows, 1992-01 to 2026-09; SHA-256 matches data/README.md). Full audit in out/state/data_audit.md.
• Missing values: only neworder_chg for 1992-01/02; those months are never ridge feature rows. The README says every change series is empty in 1992-01, but ip_growth, oil_chg and permit_chg do have 1992-01 values. I used them as given. Extreme 2020 (COVID) and 2008 values were kept. All of this is listed under data_issues.
• Exclusion ledger (out/exclusions.csv): 417 raw rows, minus 2 (before the 1992-03 training start), minus 2 (rows whose target falls after the last origin) = 413 training rows at the last origin (n_analysed).

# Method

• Naive forecast: ip_growth of month t. Expanding mean: mean of ip_growth from 1992-04 to t.
• Ridge: at each origin t, the training rows are s = 1992-03 … t−1, with target ip_growth_{s+1}. The features are ip_growth_s, its lags 1 and 2, oil_chg_s, fedfunds_s, permit_chg_s, neworder_chg_s and tcu_s. Each feature is standardised with the mean and sample SD (ddof = 1) of that origin's training rows, recomputed at every origin (normalisation_window = "expanding"). The target is centred on its training mean ȳ. Then b = (Z′Z + 50 I)⁻¹ Z′(y − ȳ), and the forecast is ȳ + z̃_t·b. No values dated after t are used. A test in which all data after a given origin were corrupted left the forecasts at that origin unchanged (out/state/checks.md).
• Metrics: RMSE and MAE of actual − forecast over the 60 origins. Relative improvement = 1 − RMSE_ridge/RMSE_baseline.
• Uncertainty: two-sided Diebold–Mariano test on squared-error loss differentials (h = 1, Harvey–Leybourne–Newbold small-sample correction, t₅₉ reference). There is no randomness (random_seed = null).
• Replication: ~/wp29/venv/bin/python out/analysis.py. It writes out/results.json, out/forecasts.csv (180 rows) and out/exclusions.csv.

# Results

• Ridge vs naive: relative RMSE improvement +0.365 (rel_improvement_vs_naive). Ridge's RMSE is about 36% lower.
• Ridge vs expanding mean: relative RMSE improvement −0.031 (rel_improvement_vs_mean). Ridge's RMSE is about 3% higher than the mean's, and its MAE is also higher (mae_ridge > mae_mean).
• Answer: ridge beats the naive forecast but not the expanding historical mean over 2021-09 to 2026-08.

# Uncertainty

• Ridge vs naive: DM statistic −3.36 (dm_stat_ridge_vs_naive), p = 0.0014 (dm_pvalue_ridge_vs_naive). The ridge advantage over naive is statistically significant at conventional levels.
• Ridge vs mean: DM statistic +0.54 (dm_stat_ridge_vs_mean), p = 0.59 (dm_pvalue_ridge_vs_mean). The two forecasts are statistically indistinguishable. The small ridge disadvantage is well within sampling noise.
• With 60 evaluation points, RMSE differences of a few percent are not reliably detectable.

# Limitations and open issues

• The data are the current (revised) vintage and publication lags are ignored. These results describe revised-data predictability under a stylised timing assumption, not real-time forecasting performance.
• λ = 50 is fixed by the task and was not tuned. Other penalties or feature sets could give different results; none were explored, by design.
• The training windows include the extreme 2020 observations. Under ridge's squared loss these may distort the coefficients. Following the task, no outlier treatment was applied.
• The DM test assumes a covariance-stationary loss differential. The evaluation window is a single, partly post-COVID regime.
• The README/data discrepancy about 1992-01 values is noted but unresolved. It affects only the earliest training row's lag-2 feature.
• feasibility = "complete".