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Sample Covariance

Install and import#

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

Signature#

calculate(data)

Add complete rows and audit sample means, denominator and cells. 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-A01",
  "title": "Sample Covariance",
  "parameters": {},
  "matrix": [
    [1.3333333333333333, 0.6666666666666666],
    [0.6666666666666666, 1.3333333333333333]
  ],
  "latest": [
    [1.3333333333333333, 0.6666666666666666],
    [0.6666666666666666, 1.3333333333333333]
  ],
  "ready": true,
  "ready_at": 0,
  "diagnostics": {
    "observations": 4,
    "assets": 2,
    "means": [0, 0],
    "causal": true,
    "ml_covariance": [
      [1, 0.5],
      [0.5, 1]
    ],
    "denominator": 3
  }
}

Diagrams#

Sample Covariance — article hero
Sample Covariance — concept map
Sample Covariance — decision comparison
Sample Covariance — worked example

Calculation flow#

Sample Covariance — calculation-flow 
flowchart TD
    N0["Align complete asset vectors"]
    N1["Estimate endpoint column means"]
    N2["Sum centered outer products"]
    N3["Divide by n−1; singular PSD allowed"]
    N0 --> N1 --> N2 --> N3
Sample Covariance — 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["Sample Covariance 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#