spb/wp46_uqo

1# Model card — `har_rv` (HAR-RV, direct projections per horizon, levels)23## 1. Identity4- **model_id:** `har_rv` · **family:** realized (Tier B) · **tier:** B · **status:** implemented · **impl:** ols (`src/wp46/models/baselines.py::HARRV(log=False)`)5- **Label:** HAR-RV (direct, levels) · **distributions:** empirical6- **Seminal citation:** `corsi2009simple`7- **Other references:** `andersen2007roughing` (HAR-CJ), `patton2015good` (HAR-RS), `bollerslev2016exploiting` (HARQ), `clements2021practical`, `branco2024forecasting`, `lyocsa2021stock`, `christensen2023machine`, `brini2026forecasting` (HAR as the realized benchmark); direct vs iterated multi-step: reference to be added (see `_missing_references.md`).89## 2. Definition10With $y_t$ the full-day variance proxy (`rv5ss_on`, percent², observed at the close of t) and regressors at origin t11$$\mathbf x_t = \big[1,\ y_t,\ \tfrac15\textstyle\sum_{i=0}^{4}y_{t-i},\ \tfrac1{22}\sum_{i=0}^{21}y_{t-i}\big]$$12(daily, weekly, monthly averages ending at t; undefined for t < 21), one **direct** OLS projection per horizon $h \in \{1, 5, 22\}$ of the average daily variance over the next h days:13$$\frac1h\sum_{k=1}^{h} y_{t+k} = \mathbf x_t'\boldsymbol\beta^{(h)} + e^{(h)}_{t+h} .$$14No innovation law (empirical standardised returns for VaR); `mu` = mean of the last 250 returns.1516## 3. Parameter space and admissibility17- Parameters: `b{h}_{c,d,w,m}` for h = 1, 5, 22 (12 coefficients). Unconstrained OLS (`np.linalg.lstsq`); no positivity constraint on coefficients; forecasts floored at 1e-8 percent².18- `converged = admissible = True` iff every horizon has ≥ 50 complete rows in the 1,000-day window; otherwise the fit is recorded as failed (`ok = False`, NaN coefficients).1920## 4. Nesting and relations21Restricted ARCH-type regression on realized measures (22 lags with step weights); nests `rm_rw` ($\beta_d = 1$, others 0). `loghar_rv` is the log version with smearing. HEAVY and Realized GARCH are the likelihood-based Tier B relatives.2223## 5. Estimation24OLS by `np.linalg.lstsq` on the rows of the 1,000-day window where the regressors and the h-step target are complete (the last h rows have no target). No optimizer, no starting values, no retries, no initial variance. Standard errors are not computed; point estimates only. Re-estimated every 5 days like every model; `filter` uses the h = 1 coefficients.2526## 6. Forecasting27`HARRV.forecast` computes the direct forecasts $\hat f_h = \mathbf x_t'\hat{\boldsymbol\beta}^{(h)}$ for h = 1, 5, 22, converts them to cumulative variances $C_h = \max(\hat f_h, 10^{-8})\,h$ and distributes the increments evenly across per-step variances:28$$\hat\sigma^2_{t+1|t} = C_1,\quad \hat\sigma^2_{t+k|t} = \frac{\max(C_5 - C_1,\ 4\cdot10^{-8})}{4}\ (k = 2..5),\quad \hat\sigma^2_{t+k|t} = \frac{\max(C_{22} - C_5,\ 17\cdot10^{-8})}{17}\ (k = 6..22),$$29so that the sums over k ≤ 1, 5, 22 equal the direct forecasts (monotonicity of the cumulative variance enforced by the floors). Method: `direct`.3031## 7. Implementation32- `src/wp46/models/baselines.py::HARRV`, `_har_X` (cumulative sums); dispatched by `make_model("har_rv")`.33- Cross-check: none against a library (`highfrequency::HARmodel` not run); OLS is deterministic.34- Tests: `tests/integration/test_rolling_driver.py::test_driver_tier_b_and_failure_flags` (`har_rv` with Tier B input); pilot `har_rv__empirical`: 207/207 refits `ok`, 1,032/1,032 forecasts `ok` on CL. No unit test of `_har_X`.3536## 8. Known limitations / failure modes37Negative or explosive forecasts are possible in levels (floored at 1e-8); OLS in levels is sensitive to outliers in the realized measure (COVID days); the direct h = 22 regression uses only T − 22 rows with overlapping targets; imputed $r_t^2$ on invalid sessions enters both regressors and targets (flagged); crypto Tier B only from 2022 (D-06).3839## 9. Computational footprint40Three least-squares fits of 1,000 × 4 per refit: pilot median fit time 0.0008 s (CL) / 0.0009 s (EURUSD) — the cheapest Tier B model.4142## 10. Literature expectations43`corsi2009simple`, `kourtis2016international`, `lyocsa2021stock`, `branco2024forecasting` ("nothing beats linear models"), `brini2026forecasting`: HAR is the realized-measure benchmark that is hard to beat at h = 1, 5, 22; `christensen2023machine` find ML gains only with extra predictors. Pre-registered H3: Tier B models beat the best Tier A model at h = 1 with a shrinking advantage at h = 22.44