# Standard Deviation Channel

`D07-F07-A04` · Technical Indicators → Bands, Envelopes, and Squeezes · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/bands-envelopes-and-squeezes/standard-deviation-channel/
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 { standardDeviationChannel } from "fintech-algorithms/technical-indicators/bands-envelopes-and-squeezes/standard-deviation-channel";
```

## Signature

```ts
standardDeviationChannel(input)
```

Standard Deviation Channel: a simple moving average of close with bands `multiplier` population standard deviations above and below it.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is the required OHLCV array -- each bar carries `timestamp`, `open`, `high`, `low`, `close`, `volume` and an optional `basis`, strictly ordered by timestamp. From `parameters` this topic reads `period` (default 20, integer >= 2), the window for both the moving average and the standard deviation, and `multiplier` (default 2, a finite number >= 0), the band width in deviations. |

## Returns

`TopicResult`

`series` holds `center`, `upper` and `lower`; `latest` carries the last of each. All three share a warm-up of `period - 1` leading nulls, so `ready_at` is 19 at the default period.

## Warm-up

The first ``period - 1` bars (19 at the default period)` positions are `null`. The standard deviation is computed over the population of the window, with no degrees-of-freedom correction, and emits only once the window is full.

## Errors

- When `parameters.period` is not an integer >= 2 — throws Error
- When `parameters.multiplier` is not a finite number, or is negative — throws Error
- When a bar is missing open, high, low, close, or volume, or one of them is not a finite number — 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
standardDeviationChannel(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F07-A04",
  "title": "Standard Deviation Channel",
  "state": "calculated",
  "ready": true,
  "ready_at": 19,
  "series": {
    "center": [null, null, null, null, null, null],
    "upper": [null, null, null, null, null, null],
    "lower": [null, null, null, null, null, null]
  },
  "latest": {
    "center": 104.20055051999998,
    "upper": 108.52982269312228,
    "lower": 99.87127834687767
  },
  "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/bands-envelopes-and-squeezes/standard-deviation-channel/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/bands-envelopes-and-squeezes/standard-deviation-channel/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt