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Oracle Approximating Shrinkage

Install and import#

bash
npm install fintech-algorithms
ts
import { calculate } from "fintech-algorithms/volatility-and-covariance/covariance-estimation/oracle-approximating-shrinkage";

Signature#

calculate(data)

Trace the finite-dimensional coefficient rather than assuming library equivalence. Supplied-parameter educational reference; no fitted performance claim.

Parameters#

NameTypeNotes
dataTopicInputSee data-contract/CONTRACT.md.

Returns#

TopicResult

Structured result with readiness, values, parameters, and diagnostics.

Warm-up#

The first depends on window or model order positions are null prefix until minimum history exists.

Errors#

  • When required data is missing, non-finite, malformed, or out of range — raises ContractError / Error

Complexity: time O(np²), space Full diagnostic trace retained for teaching; see implementation for observation/window/matrix dimensions.

Worked example#

executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

Input#

data
{
  "returns": [
    [1, 1.3660254037844386],
    [1, -0.3660254037844386],
    [-1, 0.3660254037844386]
  ],
  "parameters": {}
}

Call#

calculate(data)

Returns#

object with 8 fields: topic_id, title, parameters, matrix, latest, ready, ready_at, diagnostics

{
  "topic_id": "D10-F04-A04",
  "title": "Oracle Approximating Shrinkage",
  "parameters": {},
  "matrix": [
    [1, 0],
    [0, 1]
  ],
  "latest": [
    [1, 0],
    [0, 1]
  ],
  "ready": true,
  "ready_at": 0,
  "diagnostics": {
    "observations": 4,
    "assets": 2,
    "means": [0, 0],
    "causal": true,
    "ml_covariance": [
      [1, 0.5],
      [0.5, 1]
    ],
    "numerator": 4,
    "denominator": 2,
    "variant": "original finite-p OAS",
    "shrinkage": 1,
    "target": 1
  }
}

Diagrams#

Oracle Approximating Shrinkage — article hero
Oracle Approximating Shrinkage — concept map
Oracle Approximating Shrinkage — decision comparison
Oracle Approximating Shrinkage — worked example

Calculation flow#

Oracle Approximating Shrinkage — calculation-flow 
flowchart TD
    N0["Compute ML empirical covariance"]
    N1["Trace C and trace C²"]
    N2["Retain original 2/p coefficient terms"]
    N3["Handle isotropy and blend target"]
    N0 --> N1 --> N2 --> N3
Oracle Approximating Shrinkage — decision-boundary 
flowchart TD
    A["Supplied observations and parameters"] --> B{"Contract valid?"}
    B -->|No| E["Reject with explicit error"]
    B -->|Yes| C{"Required history available?"}
    C -->|No| W["Withhold; never insert zero"]
    C -->|Yes| D["Oracle Approximating Shrinkage calculation"]
    D --> F["Inspect diagnostics and stated limits"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

  • Scope of evidence

The rest of the Covariance Estimation family#