# Fractal Adaptive Moving Average (FRAMA)

`D07-F01-A14` · Technical Indicators → Trend Smoothing · archetype `series-transform` · difficulty 2/5 · verification **verified**

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

## Signature

```ts
fractalAdaptiveMovingAverageFrama(input)
```

Estimates the fractal dimension of each `period`-bar close window by comparing the ranges of its two halves against the range of the whole, then smooths close with `exp(-4.6 * (dimension - 1))` as the adaptive constant.

## 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 that must also be even, default 14, and `minimum_alpha`, a finite number between 0 and 1 that floors the smoothing constant, default 0.01. |

## Returns

`TopicResult`

`series` and `latest` carry a single key, `value`. The first `period - 1` entries are null, the bar at that index is seeded with close, and the recursion runs from there, 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 dimension estimate needs a full `period`-bar window split into two halves, so the first output lands at index `period - 1` and is seeded with the close itself. `ready_at` is that index. A degenerate window with no range is treated as dimension 1, which gives the fastest constant.

## Errors

- When `parameters.period` is odd — the half-window split requires an even period — throws Error
- When `parameters.minimum_alpha` is not a finite number between 0 and 1 — 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
fractalAdaptiveMovingAverageFrama(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F01-A14",
  "title": "Fractal Adaptive Moving Average (FRAMA)",
  "state": "calculated",
  "ready": true,
  "ready_at": 13,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 101.14724461464692
  },
  "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/fractal-adaptive-moving-average-frama/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-smoothing/fractal-adaptive-moving-average-frama/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt