# Model card — rm_rw (realized-measure random walk)

# 1. Identity

• model_id: rm_rw · family: realized (Tier B) · tier: B · status: implemented · impl: ols (parameter-free, src/wp46/models/baselines.py::RMRandomWalk)
• Label: Realized-measure random walk · distributions: empirical
• Seminal citation: none (registry ref: null); the "last realized variance" benchmark appears in andersen2003modeling, corsi2009simple and the realized-volatility benchmarks (liu2015does, brini2026forecasting).

# 2. Definition

Let $x_t$ be the Tier B input (full-day variance proxy rv5ss_on = subsampled 5-min RV + squared overnight return, percent², observed at the close of day t; invalid days imputed by $r_t^2$ in the driver, D-07). Then $$\hat\sigma^2_{t+k|t} = x_t,\qquad k = 1..22 .$$ No mean equation (reported mu = mean of the last 250 returns); no innovation law (empirical standardised returns for VaR).

# 3. Parameter space and admissibility

None. fit is a no-op (loglik = nan, converged = True, admissible = True). Requires $x_t > 0$ (driver floors the input at 1e-8).

# 4. Nesting and relations

Martingale forecast of the realized measure: HAR-RV with $\beta_d = 1$ and all other coefficients zero; HEAVY with $\alpha = 1$, $\omega = \beta = 0$ (return equation). The Tier B floor, analogous to histvar22/ewma094 in Tier A.

# 5. Estimation

None (time_s ≈ 0). filter returns $x_{t-1}$ for day t (first value $x_0$).

# 6. Forecasting

Flat at $x_t$ for all horizons; cumulative $h$-day variance $= h,x_t$. Method: direct.

# 7. Implementation

• src/wp46/models/baselines.py::RMRandomWalk (needs_rm = True); input built by src/wp46/scoring/proxies.py::proxy_series("rv5ss_on") and imputed in src/wp46/estimation/rolling.py.
• Cross-check: none needed (identity map). Tests: none dedicated (not in the pilot, not in the integration tests).

# 8. Known limitations / failure modes

Transmits the full measurement noise of a single day's realized measure; no mean reversion → poor at h = 22; invalid-session imputation by $r_t^2$ (flagged) enters the forecast directly on those days; crypto realized measures are invalid before 2022 (D-06).

# 9. Computational footprint

Negligible.

# 10. Literature expectations

corsi2009simple and andersen2003modeling show that even simple RV-based forecasts beat daily GARCH at h = 1 when intraday data are available; liu2015does and brini2026forecasting use the random walk as the baseline that all HAR-type models beat. Expectation: better than Tier A models at h = 1 on liquid equities (H3), clearly worse than HAR at h = 5, 22.