# F3-conf-03 — Ridge vs naive / expanding-mean forecasts of US IP growth (h = 1)

# Question

Does a ridge regression with a fixed penalty (λ = 50, lambda) on 8 standardised monthly predictors (n_features) forecast next month's US industrial production growth (100·Δln INDPRO, percent per month) better than the naive last-value forecast and the expanding historical mean? There are 60 rolling origins (n_origins), from first_origin = 2021-09-01 to last_origin = 2026-08-01, so the targets run from 2021-10 to 2026-09.

# Data and exclusions

• The input is data/ip_predictors.csv (n_input_rows = 417 rows, 1992-01 to 2026-09). Its SHA-256 matches the README. The months are contiguous and there are no duplicates. Details are in out/state/data_audit.md.
• The only missing values are neworder_chg for 1992-01 and 1992-02. Both months fall before the training start specified in the task (1992-03), so no imputation was needed.
• The README says the 1992-01 value of every change series is empty, but ip_growth, oil_chg and permit_chg do have 1992-01 values. I used them as given, and only ip_growth 1992-01 enters the model (as the second lag of the first training row). This and the vintage caveat are recorded in data_issues.
• Exclusion ledger (out/exclusions.csv): 417 raw rows, minus 2 months before 1992-03, minus 2 months whose target falls after the last origin, gives 413 training rows at the last origin (n_analysed).

# Method

• Naive forecast: ip_growth at origin t.
• Expanding-mean forecast: the mean of ip_growth over 1992-04 to t.
• Ridge regression:
  • At each origin, the training rows are s ∈ [1992-03, t−1], with target ip_growth at s+1. The features are ip_growth at s, s−1 and s−2, plus oil_chg, fedfunds, permit_chg, neworder_chg and tcu at s.
  • Each feature is standardised with the mean and the sample SD (ddof = 1) of that origin's training rows (normalisation_window = "expanding"). The target is centred on its training mean ȳ.
  • Coefficients: b = (Z′Z + 50·I)⁻¹Z′(y−ȳ). Forecast: ȳ + z̃_t·b, where z̃_t is the origin's feature vector standardised with the same mean and SD.
• Errors: RMSE and MAE over the 60 one-step errors, computed on the current-vintage data.
• Determinism: the procedure is deterministic and uses no randomness (random_seed = null). out/analysis.py regenerates results.json, forecasts.csv and exclusions.csv.

# Results

• Compared with the naive forecast, ridge cuts RMSE by 36.5% (rel_improvement_vs_naive = 0.3649).
• Compared with the expanding mean, ridge is worse: RMSE is 3.1% higher (rel_improvement_vs_mean = −0.0310), and its MAE is also higher (mae_ridge > mae_mean).
• Answer: the ridge model beats the naive baseline but not the expanding-mean baseline over this evaluation window.

# Uncertainty

• The evaluation uses only 60 monthly errors. As a supplementary check that the task did not require, I ran Diebold–Mariano-type tests on squared-error loss differentials (h = 1, simple variance, t-reference).
  • Ridge vs naive: the gain is clearly distinguishable from zero (supplementary.dm_stat_ridge_vs_naive = 3.36, p = 0.0014, supplementary.dm_pvalue_ridge_vs_naive).
  • Ridge vs expanding mean: the difference is not distinguishable from zero (supplementary.dm_stat_ridge_vs_mean = −0.54, p = 0.59, supplementary.dm_pvalue_ridge_vs_mean). The small loss relative to the mean should therefore be read as "no evidence of improvement", not as evidence that ridge is genuinely worse.
• No confidence intervals for the RMSEs were requested or computed.

# Limitations and open issues

• Not real-time: the data are the current vintage, and publication lags are ignored by design. INDPRO, TCU and NEWORDER are heavily revised, so these results do not measure real-time forecast performance.
• Fixed specification: λ = 50 is fixed by the task and not tuned. Performance against the mean baseline may depend on this choice and on the 2020 COVID observations in the training windows (ip_growth minimum −14.14 in 2020-04), which were not treated in any special way.
• Single evaluation window: results cover 2021-10 to 2026-09 only and may not generalise to other periods.
• Small discrepancy: forecasts in forecasts.csv are rounded to 8 decimals, so metrics recomputed from that file differ from results.json by less than 1e-9.