L1 ⚛ L1-445 ⊙ Testnet

GARCH Volatility Estimation

Computational Finance · Time series volatility

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-445.md

# ⚛ L1 Principle — GARCH Volatility Estimation **ID:** `L1-445` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Finance — *Time series volatility* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** conditional vol series > **📡 Carrier:** N/A · **🌫 Noise:** gaussian student t > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555260 --- ## 🧠 1. Introduction **GARCH Volatility Estimation** is a **parameter-estimation problem** whose unknown lives in **conditional vol series** space, within the **Time series volatility** sub-domain of **Computational Finance**. Measurements consist of N/A via a **mle garch estimation** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; O · mle · log likelihood operator; S · recursion · garch update operator. Observations are corrupted by gaussian student t. Existence of the recovered conditional_vol_series is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); structural_break_in_vol_regime dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian student t sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Pointwise nonlinearity → O · mle · log likelihood → S · recursion · garch update → **y** (detector). ``` y = `S.recursion.garch_update` `O.mle.log_likelihood` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `O.mle.log_likelihood` | O · mle · log likelihood operator | | `S.recursion.garch_update` | S · recursion · garch update operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Finance | | Sub domain | Time series volatility | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | conditional_vol_series | | Noise model | gaussian_student_t | | Integration axis | temporal_financial | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered conditional_vol_series is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); structural_break_in_vol_regime dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian student t sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | volatility_forecast_QLIKE | | Secondary | log_likelihood_per_obs | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `mle_garch_estimation` **Center point:** | Parameter | Unit | Value | |---|---|---| | Beta true | — | 0.85 | | Alpha true | — | 0.1 | | T observations | — | 2000 | | Structural break prob | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Beta true | — | 0.5 – 0.99 | | Alpha true | — | 0.01 – 0.3 | | T observations | — | 100 – 10000 | | Structural break prob | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.08 volatility_forecast_QLIKE | Metric | Range | |---|---| | Volatility forecast qlike | 0.01 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **volatility_forecast_QLIKE**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x63e4a670d4c960d88f4f1b72e68b06c602a82438ce4019dd857bae8c6e2a3066` - **Chain tx hash:** `0xe8d9657c4300310590ddb58876216d6cc0e310ba01a7f34ecd24ebb96ac10a74` - **Chain block:** `41555260` --- ## File Mapping This bundle consists of: `L1-445.md`, `L1-445.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-445.md` | Source of truth — edit this | Human or LLM | | `L1-445.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-445`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-445.md).
Regenerate L1-445.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-445-001 GARCH Volatility Estimation — Nominal + Mismatch Specs

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-445",
  "chain_block": 41555260,
  "chain_hash": "0x63e4a670d4c960d88f4f1b72e68b06c602a82438ce4019dd857bae8c6e2a3066",
  "chain_tx_hash": "0xe8d9657c4300310590ddb58876216d6cc0e310ba01a7f34ecd24ebb96ac10a74",
  "domain": "Computational Finance",
  "hardness_fn": {
    "delta": 3,
    "kappa": 500,
    "metric": "volatility_forecast_QLIKE",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "volatility_forecast_QLIKE",
    "regime": "Existence of the recovered conditional_vol_series is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); structural_break_in_vol_regime dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian student t sets the irreducible data-fidelity floor.",
    "secondary": "log_likelihood_per_obs"
  },
  "physics_fingerprint": {
    "L_DAG": 2.5,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Computational Finance",
    "integration_axis": "temporal_financial",
    "noise_model": "gaussian_student_t",
    "primitives": [
      "N.pointwise",
      "O.mle.log_likelihood",
      "S.recursion.garch_update"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "mle_garch_estimation",
    "solution_space": "conditional_vol_series",
    "sub_domain": "Time series volatility",
    "title": "GARCH Volatility Estimation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "mle_garch_estimation"
    ],
    "allowed_omega_dimensions": [
      "T_observations",
      "alpha_true",
      "beta_true",
      "structural_break_prob"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.08 volatility_forecast_QLIKE",
      "forward_operator": "mle_garch_estimation",
      "input_format": "measurement_only",
      "omega": {
        "T_observations": 2000,
        "alpha_true": 0.1,
        "beta_true": 0.85,
        "structural_break_prob": 0.0
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "volatility_forecast_QLIKE": [
        0.01,
        0.5
      ]
    },
    "omega_bounds": {
      "T_observations": [
        100,
        10000
      ],
      "alpha_true": [
        0.01,
        0.3
      ],
      "beta_true": [
        0.5,
        0.99
      ],
      "structural_break_prob": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Time series volatility",
  "title": "GARCH Volatility Estimation"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.