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

## Question
Does a fixed-penalty ridge regression (λ = 50) on eight standardised monthly predictors forecast next month's US industrial production growth (100 × Δln INDPRO, % per month) better than (a) the naive last-value forecast and (b) the expanding historical mean, over 60 rolling origins from 2021-09 to 2026-08 (horizon h = 1)?

## Data and exclusions
- `data/ip_predictors.csv`: 417 monthly rows, 1992-01 to 2026-09, current-vintage FRED data (see `data/README.md`). No rows were dropped.
- Missing values: only `neworder_chg` for 1992-01 and 1992-02. Neither falls in any training window (training rows start at 1992-03), so no imputation was needed.
- Minor discrepancy: the README says the first month of every change series is empty, but `ip_growth`, `oil_chg` and `permit_chg` are populated for 1992-01. I kept the values as given. `ip_growth` 1992-01 enters only as the second lag in the 1992-03 training row, which is what the task specification implies.
- The extreme COVID-19 months of 2020 (ip_growth from −14.14 to +6.35 %) stay in every training window, as the specification requires. They inflate the standardisation statistics and affect the coefficients.

## Method
- Origins t = 2021-09-01 … 2026-08-01 (60). Each origin's target is `ip_growth` at t+1.
- Naive forecast: `ip_growth` at t.
- Expanding-mean forecast: the mean of `ip_growth` from 1992-04 to t.
- Ridge: the training rows are s = 1992-03 … t−1, with target y_{s+1}. The features are ip_growth_s, ip_growth_{s−1} and ip_growth_{s−2}, plus oil_chg_s, fedfunds_s, permit_chg_s, neworder_chg_s and tcu_s.
  - At every origin I recompute the feature means and sample SDs (ddof = 1) and the target mean from that origin's training rows only. `normalisation_window = "expanding"`.
  - b = (Z′Z + 50 I)⁻¹ Z′(y − ȳ), with no penalised intercept. Forecast = ȳ + ((z_t − μ)/σ)·b.
  - The code asserts that no training target is dated after t.
- I scored errors against current-vintage actuals and computed RMSE and MAE over the 60 origins.
- `out/analysis.py` regenerates `results.json`, `forecasts.csv` (180 rows) and `uncertainty.json`.

## Results
| model | RMSE (%/month) | MAE (%/month) |
|---|---|---|
| naive | 0.8831 | 0.6990 |
| expanding mean | 0.5439 | 0.4293 |
| ridge (λ=50) | 0.5608 | 0.4514 |

- Relative RMSE improvement of ridge over naive: 1 − 0.5608/0.8831 = **+0.365** (36.5 % lower RMSE).
- Relative RMSE improvement of ridge over the expanding mean: **−0.031**. Ridge's RMSE is 3.1 % *higher* than the mean's, and its MAE is also higher.

So the ridge model clearly beats the naive forecast but does **not** beat the expanding historical mean over this evaluation window. At the one-month horizon, the eight predictors add no out-of-sample value over the unconditional mean.

## Uncertainty
These diagnostics are in `out/uncertainty.json`, produced by the same script.
- **Diebold–Mariano tests** (squared loss, with the Harvey–Leybourne–Newbold small-sample correction and a t(59) reference):
  - ridge vs naive: statistic −3.36, p = 0.0014. Ridge is significantly better.
  - ridge vs mean: statistic +0.54, p = 0.59. There is no significant difference.
- **Moving-block bootstrap** (block 6, B = 5000, seed 12345), 95 % intervals for the relative RMSE improvement:
  - vs naive: [0.248, 0.426].
  - vs mean: [−0.158, 0.056].
- With only 60 evaluation months, a small loss to the mean cannot be told apart from a small gain.

## Limitations and open issues
- **Data vintage.** I used current-vintage, revised data and ignored publication lags (INDPRO, TCU and NEWORDER are revised substantially). These results are **not** real-time forecast performance.
- **Model choices.** λ = 50 is fixed by the task, not tuned. The level variables (fedfunds, tcu) enter untransformed. The COVID outliers are untreated. Each of these could change the ridge results.
- **Evaluation window.** It is one short window (2021-09 to 2026-08) and includes the post-pandemic recovery. The relative ranking may not generalise to other periods.
- **Uncertainty method.** The DM test and the bootstrap both assume approximate stationarity of loss differentials. The bootstrap seed does not affect any value in `results.json`.