# Random Walk Index (High/Low)

`D07-F02-A16` · Technical Indicators → Trend Systems · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/trend-systems/random-walk-index-high-low/
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 { randomWalkIndexHighLow } from "fintech-algorithms/technical-indicators/trend-systems/random-walk-index-high-low";
```

## Signature

```ts
randomWalkIndexHighLow(input)
```

Scores how far price has travelled against what a random walk would explain, by taking the largest displacement-over-expected-range ratio across every lookback length from 2 up to `period`, once upward and once downward.

## 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 only `period` (integer, minimum 2, default 14), the longest lookback the maximum is taken over. |

## Returns

`TopicResult`

`series` and `latest` carry `high` and `low`, the upward and downward random-walk scores, and no combined line. Both share one warm-up.

## Warm-up

The first `period bars (14 by default)` positions are `null`. The scan starts at index `period` because the longest lookback reaches that far back, so with the default period indices 0 to 13 are null and `ready_at` is 14.

## Errors

- When `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 * period^2)`, 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
randomWalkIndexHighLow(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F02-A16",
  "title": "Random Walk Index (High/Low)",
  "state": "calculated",
  "ready": true,
  "ready_at": 14,
  "series": {
    "high": [null, null, null, null, null, null],
    "low": [null, null, null, null, null, null]
  },
  "latest": {
    "high": 0.16740171878302448,
    "low": 1.3252890024447201
  },
  "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/random-walk-index-high-low/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-systems/random-walk-index-high-low/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt