# 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 (n_features) forecast next-month US industrial production growth (100 × Δln INDPRO, percent per month) better than the naive (last value) and expanding-mean forecasts? The test uses n_origins = 60 rolling origins from first_origin = 2021-09-01 to last_origin = 2026-08-01, at horizon h = 1. Estimands: out-of-sample RMSE and MAE of each forecast, and 1 − RMSE_ridge/RMSE_baseline.

# Data and exclusions

• Input: data/ip_predictors.csv, with 417 data rows (n_input_rows) covering 1992-01 to 2026-09. Its SHA-256 matches the README. The full audit is in out/state/data_audit.md.
• Missing values: only neworder_chg for 1992-01 and 1992-02. Neither month is used.
• Data issues (data_issues):
  • The README says the first month of every change series is empty, but three of these columns are filled for 1992-01. These values were used as given.
  • Extreme COVID-era observations (ip_growth −14.1 in 2020-04) fall inside every training window. They were kept, because the specification fixes the training rows.
  • The data are the current vintage, not real-time.
• Exclusion ledger (out/exclusions.csv), for the ridge training set at the last origin: 417 rows → minus 2 months before 1992-03 → minus 2 months whose target lies after the origin → 413 training rows (n_analysed).

# Method

• Naive forecast: ip_growth_t.
• Expanding-mean forecast: the mean of ip_growth over 1992-04..t.
• Ridge forecast:
  • Training rows are s = 1992-03 … t−1, with target ip_growth_{s+1}.
  • The features are ip_growth_s, ip_growth_{s−1}, ip_growth_{s−2}, oil_chg_s, fedfunds_s, permit_chg_s, neworder_chg_s and tcu_s.
  • Each feature is z-scored with the mean and the ddof=1 standard deviation of that origin's training rows. These statistics are recomputed at every origin (normalisation_window = "expanding").
  • The target is centred on its training mean ȳ, which serves as the unpenalised intercept.
  • The coefficients are b = (Z′Z + 50 I)⁻¹ Z′(y − ȳ), and the forecast is ȳ + z̃_t·b.
• The method has no randomness (random_seed = null).
• Code: out/analysis.py. It writes out/results.json, out/forecasts.csv (180 rows) and out/exclusions.csv.

# Results

• Compared with the naive forecast, ridge improves RMSE by 0.365 (rel_improvement_vs_naive), i.e. ~36% (C1).
• Compared with the expanding mean, ridge is slightly worse: the relative improvement is −0.031 (rel_improvement_vs_mean), and its MAE is also higher (C3).
• So ridge beats the naive forecast but not the expanding mean over this window.

# Uncertainty

I ran Diebold–Mariano tests on the squared-error loss differential (ridge minus baseline), with the Harvey–Leybourne–Newbold small-sample correction and t(59) reference.

• Ridge vs naive: DM = −3.36 (dm_stat_ridge_vs_naive), p = 0.0014 (dm_pvalue_ridge_vs_naive). Ridge is significantly better (C2).
• Ridge vs mean: DM = 0.54 (dm_stat_ridge_vs_mean), p = 0.59 (dm_pvalue_ridge_vs_mean). There is no significant difference (C4).

Only 60 errors are evaluated, so the relative-improvement figures carry sizeable sampling error. The ~3% gap to the mean is well within noise.

# Limitations and open issues

• The data are the current vintage and publication lags are ignored. The results describe how predictable the revised series is under stylised timing, not real-time forecast accuracy.
• λ is fixed at 50 by the specification and was not tuned. Other penalties or feature sets could rank differently; this was not evaluated.
• COVID outliers stay in every training window and can distort the scaling statistics and the coefficients.
• The evaluation window (2021-10 to 2026-09 targets) is a single, fairly calm post-pandemic period.
• The DM test is applied to forecasts from estimated models (with the mean nested in ridge as λ→∞), so its p-values are approximate.
• Feasibility: complete.