# Gaussian Moving Average

`D07-F01-A22` · Technical Indicators → Trend Smoothing · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/trend-smoothing/gaussian-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 { gaussianMovingAverage } from "fintech-algorithms/technical-indicators/trend-smoothing/gaussian-moving-average";
```

## Signature

```ts
gaussianMovingAverage(input)
```

Averages close under a Gaussian weight curve centred at `offset * (period - 1)` with width `period / sigma`. The default offset of 0.5 puts the peak in the middle of the window, which is what separates this from ALMA's recency-shifted variant of the same kernel.

## 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 `period`, an integer of at least 2, default 14; `offset`, a finite number between 0 and 1, default 0.5; and `sigma`, a finite number of at least 0.000001, default 6. |

## 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 kernel is applied only to complete `period`-bar windows, so `ready_at` is `period - 1`. Centring the peak makes the filter symmetric in weighting but the output is still computed only from bars up to and including the current one.

## Errors

- When `parameters.offset` is not a finite number between 0 and 1 — throws Error
- When `parameters.sigma` is not a finite number of at least 0.000001 — throws Error
- When `parameters.period` is not an integer of at least 2 — 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
gaussianMovingAverage(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F01-A22",
  "title": "Gaussian Moving Average",
  "state": "calculated",
  "ready": true,
  "ready_at": 13,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 105.48707931937686
  },
  "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/gaussian-moving-average/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-smoothing/gaussian-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