# Following Adaptive Moving Average (FAMA)

`D07-F01-A12` · Technical Indicators → Trend Smoothing · archetype `series-transform` · difficulty 2/5 · verification **verified**

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

## Signature

```ts
followingAdaptiveMovingAverageFama(input)
```

Runs an efficiency-ratio adaptive average over close and its slower follower: net movement across `period` bars divided by the summed absolute bar-to-bar movement sets the smoothing constant, and FAMA tracks MAMA at half that 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, default 14, plus `fast_alpha`, default 0.5, and `slow_alpha`, default 0.05, both finite numbers between 0 and 1. |

## Returns

`TopicResult`

`series` and `latest` carry two keys, `mama` and `fama`. Both are null for the first `period` bars, are seeded with the close at index `period`, and thereafter recurse, so with the default period `ready_at` is 14.

## Warm-up

The first `period bars (14 at the default period of 14)` positions are `null`. The efficiency ratio needs a `period`-bar lookback, so the loop starts at index `period` and both series are seeded there with the close. `ready_at` is that index. A window with zero total movement is treated as an efficiency ratio of 0 rather than dividing by zero.

## Errors

- When `parameters.fast_alpha` or `parameters.slow_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
- 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
followingAdaptiveMovingAverageFama(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F01-A12",
  "title": "Following Adaptive Moving Average (FAMA)",
  "state": "calculated",
  "ready": true,
  "ready_at": 14,
  "series": {
    "mama": [null, null, null, null, null, null],
    "fama": [null, null, null, null, null, null]
  },
  "latest": {
    "mama": 103.83007356524162,
    "fama": 104.7546779146645
  },
  "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/following-adaptive-moving-average-fama/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-smoothing/following-adaptive-moving-average-fama/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt