# Quadratic-Weighted Moving Average

`D07-F01-A21` · Technical Indicators → Trend Smoothing · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/trend-smoothing/quadratic-weighted-moving-average/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

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

## Signature

```ts
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

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` 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

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`:

```json
{
  "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

```ts
quadraticWeightedMovingAverage(input)
```

### Returns

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

```json
{
  "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
  }
}
```

## Verification and provenance

Tier: **verified** (via E).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/technical-indicators/trend-smoothing/quadratic-weighted-moving-average/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-smoothing/quadratic-weighted-moving-average/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt