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EWMA Covariance

Install and import#

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

Signature#

calculate(data)

Watch the same new vector compete with the existing matrix. 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": [
    [0.01, 0.02],
    [-0.02, 0.01]
  ],
  "parameters": {
    "decay": 0.5
  }
}

Call#

calculate(data)

Returns#

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

{
  "topic_id": "D10-F04-A02",
  "title": "EWMA Covariance",
  "parameters": {
    "decay": 0.5
  },
  "matrix": [
    [0.00022500000000000002, -0.00005],
    [-0.00005, 0.00015000000000000001]
  ],
  "latest": [
    [0.00022500000000000002, -0.00005],
    [-0.00005, 0.00015000000000000001]
  ],
  "ready": true,
  "ready_at": 0,
  "diagnostics": {
    "observations": 2,
    "assets": 2,
    "means": [-0.005, 0.015],
    "causal": true,
    "ml_covariance": [
      [0.000225, 0.000075],
      [0.000075, 0.000025]
    ],
    "states": [
      [
        [0.00005, 0.0001],
        [0.0001, 0.0002]
      ],
      [
        [0.00022500000000000002, -0.00005],
        [-0.00005, 0.00015000000000000001]
      ]
    ],
    "mean_convention": "supplied zero-mean residuals",
    "weight_mass": 0.75,
    "seed_weight": 0.25
  }
}

Diagrams#

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

Calculation flow#

EWMA Covariance — calculation-flow 
flowchart TD
    N0["Declare zero-mean residuals and seed"]
    N1["Compute current outer product"]
    N2["Blend λ old + (1−λ) new"]
    N3["Report remaining seed weight"]
    N0 --> N1 --> N2 --> N3
EWMA 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["EWMA 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#