# Rolling Quantile

`D07-F09-A02` · Technical Indicators → Rolling Statistical Indicators · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/rolling-statistical-indicators/rolling-quantile/
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 { rollingQuantile } from "fintech-algorithms/technical-indicators/rolling-statistical-indicators/rolling-quantile";
```

## Signature

```ts
rollingQuantile(input)
```

Returns the requested quantile of the close over a trailing window, sorting each window and interpolating linearly between the two neighbouring ranks.

## 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; only `close` is used. From `parameters` this topic reads `period` (integer, minimum 2, default 20), the window length, and `q` (number between 0 and 1, default 0.5, so the default output is the median). |

## Returns

`TopicResult`

`series` and `latest` carry a single `value` key, in price units. After the warm-up every bar has a value.

## Warm-up

The first `period - 1 bars (19 by default)` positions are `null`. The first full window closes at index `period - 1`, so with the default period indices 0 to 18 are null and `ready_at` is 19.

## Errors

- When `parameters.period` is present but is not an integer of at least 2 — throws Error
- When `parameters.q` is not a finite number between 0 and 1 — 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 * log 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
rollingQuantile(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F09-A02",
  "title": "Rolling Quantile",
  "state": "calculated",
  "ready": true,
  "ready_at": 19,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 103.797121585
  },
  "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/rolling-statistical-indicators/rolling-quantile/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/rolling-statistical-indicators/rolling-quantile/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt