# Rolling Beta

`D07-F09-A03` · 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-beta/
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 { rollingBeta } from "fintech-algorithms/technical-indicators/rolling-statistical-indicators/rolling-beta";
```

## Signature

```ts
rollingBeta(input)
```

Regresses the asset's simple returns on the benchmark's over a trailing window and returns the slope, using the population covariance and variance of the window.

## 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. Every bar must additionally carry a `benchmark` field, a finite positive number, from which the benchmark return series is built. From `parameters` this topic reads only `period` (integer, minimum 2, default 20), the regression window in returns. |

## Returns

`TopicResult`

`series` and `latest` carry a single `beta` key; the intercept is not emitted by this topic. A bar is null when the benchmark returns in its window have zero variance. Returns cost one bar, which lengthens the warm-up by one over a plain window.

## Warm-up

The first `period bars (20 by default)` positions are `null`. Both return series start at index 1, so the first window with `period` paired returns closes at index `period`: with the default period indices 0 to 19 are null and `ready_at` is 20.

## Errors

- When any bar omits `benchmark`, so the benchmark return series cannot be built — throws Error
- When a bar's `benchmark` is present but is not a finite number, or is not greater than zero — throws Error
- 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)`, 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
rollingBeta(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F09-A03",
  "title": "Rolling Beta",
  "state": "calculated",
  "ready": true,
  "ready_at": 20,
  "series": {
    "beta": [null, null, null, null, null, null]
  },
  "latest": {
    "beta": -5.216643800648915
  },
  "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-beta/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/rolling-statistical-indicators/rolling-beta/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt