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Realized Covariance

Install and import#

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

Signature#

calculate(data)

Pair exact intervals, then inspect positive and negative products. 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(nw), 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_x": [0.01, -0.02, 0.03, -0.01],
  "returns_y": [0.02, 0.01, -0.01, -0.02],
  "timestamps_x": [
    "2026-01-01T09:00:00Z",
    "2026-01-01T09:05:00Z",
    "2026-01-01T09:10:00Z",
    "2026-01-01T09:15:00Z"
  ],
  "timestamps_y": [
    "2026-01-01T09:00:00Z",
    "2026-01-01T09:05:00Z",
    "2026-01-01T09:10:00Z",
    "2026-01-01T09:15:00Z"
  ],
  "parameters": {
    "window": 4,
    "annualization_factor": 1
  }
}

Call#

calculate(data)

Returns#

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

{
  "topic_id": "D10-F02-A02",
  "title": "Realized Covariance",
  "parameters": {
    "window": 4,
    "annualization_factor": 1
  },
  "series": [
    null,
    null,
    null,
    {
      "covariance": -0.00009999999999999996,
      "contributions": [0.0002, -0.0002, -0.0003, 0.0002],
      "window_start": 0,
      "window_end": 3
    }
  ],
  "latest": {
    "covariance": -0.00009999999999999996,
    "contributions": [0.0002, -0.0002, -0.0003, 0.0002],
    "window_start": 0,
    "window_end": 3
  },
  "ready": true,
  "ready_at": 3,
  "diagnostics": {
    "causal": true,
    "input_count": 4,
    "annualization_factor": 1
  }
}

Diagrams#

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

Calculation flow#

Realized Covariance — calculation-flow 
flowchart TD
    N0["Validate identical regular clocks"]
    N1["Pair x and y on each interval"]
    N2["Retain signed products"]
    N3["Sum co-movement, not correlation"]
    N0 --> N1 --> N2 --> N3
Realized 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["Realized 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 Realized Measures family#