spb/wp46_uqo

1# Model card — `avgarch11` (AVGARCH(1,1), Taylor–Schwert absolute-value GARCH)23## 1. Identity4- **model_id:** `avgarch11` · **family:** power · **tier:** A · **status:** implemented · **impl:** arch 8.0.0 (`GARCH(p=1, o=0, q=1, power=1.0)`, arch name "AVGARCH")5- **Label:** AVGARCH(1,1) (Taylor-Schwert) · **distributions:** normal, t, ged, skewt6- **Seminal citation:** `taylor2008modelling` (2nd ed. of Taylor 1986; the 1986 first edition has no verified record — see `docs/literature_matrix.md`, Unverified) and `schwert1989why`.7- **Other references:** `ding1993long` (APARCH nests it, δ = 1, γ = 0), `zakoian1994threshold`.89## 2. Definition (arch, power = 1)10$$r_t = \mu + \varepsilon_t,\ \varepsilon_t = \sigma_t z_t,\qquad \sigma_t = \omega + \alpha\,|\varepsilon_{t-1}| + \beta\,\sigma_{t-1} ,$$11pre-sample $|\varepsilon|$ and $\sigma$ replaced by the power-1 backcast ($\sum_{i<75} w_i|\varepsilon_i|$, $w_i \propto 0.94^i$). Innovations: normal, t, GED, Hansen skew-t.1213## 3. Parameter space and admissibility14- Parameters: `mu, omega, alpha[1], beta[1]` (+ distribution).15- arch bounds/constraints: $\omega \in [10^{-8}v_1, 10v_1]$ ($v_1 = \overline{|\varepsilon|}$), $\alpha, \beta \in [0,1]$, $\omega > 0$, $\alpha, \beta \ge 0$, $\alpha + \beta < 1$ (arch's generic constraint; the stationarity of $\sigma_t$ requires $\alpha E|z| + \beta < 1$, which is implied).16- Admissibility flag: **always `True`** (no check in `ArchModel.fit` for `avgarch11`).1718## 4. Nesting and relations19`aparch11` with δ = 1, γ = 0; `tarch11` with γ = 0. Not nested in `garch11` (power 1 vs 2). Symmetric; the only symmetric power-1 model of the registry.2021## 5. Estimation22arch SLSQP (`maxiter` 1000), grid starting values, power-1 backcast, ≤ 2 restarts (`ArchModel.fit`). Point estimates only.2324## 6. Forecasting25h = 1 analytic ($\hat\sigma_{t+1|t}^2 = (\omega + \alpha|\varepsilon_t| + \beta\sigma_t)^2$); h > 1 by **simulation** (2,000 paths of $\sigma_{t+k}$ via `GARCH._simulate_paths`, power 1; variance forecast = path mean of $\sigma_{t+k}^2$; note $E[\sigma_{t+k}^2] \ne (E\sigma_{t+k})^2$, which is why no analytic rule is used). Normal: seeded (46 + origin); t/GED/skew-t: arch's unseeded distribution simulator (`_discrepancies.md`). Cumulative = sum over k ≤ h. Method: `simulation` for h > 1.2627## 7. Implementation28- `src/wp46/models/arch_models.py` (`SPECS["avgarch11"]`), arch 8.0.0.29- Cross-check: none (not in the rugarch fixture script; rugarch `fGARCH(AVGARCH)` was not run).30- Tests: none dedicated.3132## 8. Known limitations / failure modes33No admissibility flag beyond optimizer constraints; simulation forecasts (Monte-Carlo error, unseeded for non-normal laws); boundary optima as for GARCH(1,1).3435## 9. Computational footprint36Estimation like `garch11`; simulation forecasts (22 × 2,000 draws per origin). No pilot timing.3738## 10. Literature expectations39`taylor2008modelling`/`schwert1989why` introduced absolute-value dynamics as more robust to outliers; `ding1993long` found δ ≈ 1.4 for S&P 500 (between AVGARCH and GARCH); `hansen2005forecast` include TS-GARCH variants without finding them superior to GARCH(1,1). Expectation: similar to GARCH(1,1), possibly more robust in stressed regimes (H6), at a higher forecasting cost (H5).40