# 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.