# Relative Momentum Index

`D07-F03-A18` · Technical Indicators → Momentum · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/momentum/relative-momentum-index/
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 { relativeMomentumIndex } from "fintech-algorithms/technical-indicators/momentum/relative-momentum-index";
```

## Signature

```ts
relativeMomentumIndex(input)
```

An RSI-shaped 0..100 reading built on the change over `momentum_lag` bars instead of the one-bar change, Wilder-smoothed over `period`.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is a chronological array of OHLCV rows, each with a non-empty `timestamp` plus finite `open`, `high`, `low`, `close` and `volume`. From `parameters` this topic reads `period` (integer >= 2, default 14) for the Wilder smoothing and `momentum_lag` (integer >= 1, default 5) for the change interval. The preamble also validates `fast_period` (default 5) and `slow_period` (default 34) before branching, so a bad value for either throws even though this topic does not use them. |

## Returns

`TopicResult`

`series` and `latest` carry one key, `value`, equal to 100 times the smoothed up-move divided by the sum of the smoothed up- and down-moves. The warm-up prefix stacks the momentum lag on top of the Wilder seed.

## Warm-up

The first `momentum_lag + period - 1 bars (18 with the defaults 5 and 14)` positions are `null`. The lagged change is null for the first `momentum_lag` bars and the Wilder average then needs `period` consecutive values to seed, so `ready_at` is 18 on the canonical fixture. Smoothed up- and down-moves that sum to exactly 0 also yield a null.

## Errors

- When `momentum_lag` is not an integer >= 1 — throws Error
- When `bars` are not strictly increasing by `timestamp` — throws Error

## Complexity

Time `O(n)`, 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
relativeMomentumIndex(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F03-A18",
  "title": "Relative Momentum Index",
  "state": "calculated",
  "ready": true,
  "ready_at": 18,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 36.68238933579245
  },
  "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/momentum/relative-momentum-index/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/momentum/relative-momentum-index/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt