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Quadratic-Weighted Moving Average

Install and import#

bash
npm install fintech-algorithms
ts
import { quadraticWeightedMovingAverage } from "fintech-algorithms/technical-indicators/trend-smoothing/quadratic-weighted-moving-average";

Signature#

quadraticWeightedMovingAverage(input)

Averages close over a rolling period-bar window with weights that grow as the square of a bar's position, 1, 4, 9 and so on, front-loading recency harder than the linear weights of a WMA.

Parameters#

NameTypeNotes
inputTopicInputbars is a non-empty array of OHLCV records with strictly increasing timestamp, finite open, high, low, close and non-negative volume, all sharing one adjustment basis. From parameters this topic reads only period, an integer of at least 2, default 14, which sets both the window length and the number of squared weights.

Returns#

TopicResult

series and latest carry a single key, value, the weight-normalised average. The first period - 1 entries are null while the window fills, so with the default period ready_at is 13.

Warm-up#

The first period - 1 bars (13 at the default period of 14) positions are null. The average prints only from a complete period-bar window, so ready_at is period - 1. Weights are divided by their own sum, so the output stays in price units.

Errors#

  • When parameters.period is not an integer of at least 2 — throws Error
  • When bars is empty or a bar violates the OHLCV contract — throws Error

Complexity: time O(n * period), space O(n).

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#

input
{
  "bars": [
    {
      "timestamp": "2024-01-02",
      "basis": "synthetic-unadjusted",
      "open": 100,
      "high": 101.45,
      "low": 98.695,
      "close": 100,
      "volume": 750000,
      "benchmark": 200
    },
    {
      "timestamp": "2024-01-03",
      "basis": "synthetic-unadjusted",
      "open": 101.49111452,
      "high": 103.38381693,
      "low": 100.05480022,
      "close": 101.78791214,
      "volume": 795117,
      "benchmark": 200.56326135
    },
    {
      "timestamp": "2024-01-04",
      "basis": "synthetic-unadjusted",
      "open": 102.45519048,
      "high": 104.6701838,
      "low": 100.91147007,
      "close": 102.9549389,
      "volume": 840234,
      "benchmark": 201.11020913
    }
  ],
  "parameters": {}
}

Call#

quadraticWeightedMovingAverage(input)

Returns#

object with 9 fields: topic_id, title, state, ready, ready_at, series, latest, parameters, …

{
  "topic_id": "D07-F01-A21",
  "title": "Quadratic-Weighted Moving Average",
  "state": "calculated",
  "ready": true,
  "ready_at": 13,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 103.03978017722167
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}

Diagrams#

Quadratic-Weighted Moving Average — article hero
Quadratic-Weighted Moving Average — concept map
Quadratic-Weighted Moving Average — decision comparison
Quadratic-Weighted Moving Average — worked example

Calculation flow#

Quadratic-Weighted Moving Average calculation flow 
flowchart LR
    A["an oldest-to-newest finite price series, declared price so"] --> B["Validate order, basis, and finite values"]
    B --> C["Apply the selected Quadratic-Weighted Moving Average convention"]
    C --> D["Emit value, readiness, and diagnostics"]
    D --> E["Interpret descriptively; test outcomes separately"]
    B -->|invalid or insufficient| X["Withhold output with a reason"]
Quadratic-Weighted Moving Average readiness and evidence states 
stateDiagram-v2
    [*] --> Waiting
    Waiting --> Ready: enough valid causal observations
    Waiting --> Rejected: malformed or unsupported input
    Ready --> Calculated: selected formula applied
    Calculated --> Interpreted: diagnostic and limitation retained
    Interpreted --> Ready: next observation arrives
    Rejected --> Waiting: corrected input and deterministic reset

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#

  • TA-Lib function groups — see linked primary or authoritative record
  • TA-Lib C/C++ API — see linked primary or authoritative record
  • TA-Lib maintained source — see linked primary or authoritative record
  • Evidence decision
  • Level 1 evidence map

The rest of the Trend Smoothing family#