# Mass Index

`D07-F02-A14` · Technical Indicators → Trend Systems · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/trend-systems/mass-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 { massIndex } from "fintech-algorithms/technical-indicators/trend-systems/mass-index";
```

## Signature

```ts
massIndex(input)
```

Takes the ratio of a 9-period EMA of the high-low range to the 9-period EMA of that EMA, then sums the ratio over a longer window, so range expansion after a contraction pushes the total up.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is the OHLCV series, validated for finite prices, strictly increasing `timestamp`, a single adjustment `basis`, non-negative `volume`, and a high and low that bracket the other prices. From `parameters` this topic reads `sum_period` (integer, minimum 2, default 25), the length of the final sum; the two EMA lengths are fixed at 9 and are not configurable. `period` is still validated by the family, with the same integer-minimum-2 rule, but no branch of this calculation uses it. |

## Returns

`TopicResult`

`series` and `latest` carry a single `value` key. The chained EMAs make the warm-up much longer than `sum_period` alone suggests.

## Warm-up

The first `sum_period + 15 bars (40 by default)` positions are `null`. The first EMA resolves at index 8, the EMA of that EMA at index 16, and the sum then needs `sum_period` consecutive ratios. With the default `sum_period` of 25 the first value lands at index 40, so `ready_at` is 40.

## Errors

- When `parameters.sum_period` or `parameters.period` is present but is not an integer of at least 2 — throws Error
- When `bars` is empty, or a bar has a non-finite price, a negative volume, a timestamp not greater than the previous one, or a high below its open, low, or close — throws Error

## Complexity

Time `O(n * sum_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
massIndex(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F02-A14",
  "title": "Mass Index",
  "state": "calculated",
  "ready": true,
  "ready_at": 40,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 25.15692329607823
  },
  "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-systems/mass-index/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-systems/mass-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