# Projection Bands

`D07-F07-A09` · 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/projection-bands/
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 { projectionBands } from "fintech-algorithms/technical-indicators/bands-envelopes-and-squeezes/projection-bands";
```

## Signature

```ts
projectionBands(input)
```

Projection Bands: fits a least-squares slope to the highs and to the lows of the last `period` bars, projects every bar in the window forward along that slope, and takes the highest projected high and the lowest projected low.

## 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 only `period` (default 20, integer >= 2), the regression and projection window. `period` (default 20, integer >= 2) and `multiplier` (default 2, a finite number >= 0) are read and validated by the band family for every topic in it. `multiplier` is not used by this branch. |

## Returns

`TopicResult`

`series` holds only `upper` and `lower` -- this topic emits no `center` -- and `latest` carries the last of each. Both 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`. Each band is recomputed from a full window of highs or lows; there is no partial-window output and no carry forward between windows.

## Errors

- When `parameters.period` is not an integer >= 2 — throws Error
- When a bar is missing open, high, low, close, or volume, or one of them is not a finite number — throws Error
- When bars are not strictly ordered by timestamp, or a bar's high is 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
projectionBands(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F07-A09",
  "title": "Projection Bands",
  "state": "calculated",
  "ready": true,
  "ready_at": 19,
  "series": {
    "upper": [null, null, null, null, null, null],
    "lower": [null, null, null, null, null, null]
  },
  "latest": {
    "upper": 109.63429948293232,
    "lower": 98.68874251
  },
  "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/projection-bands/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/bands-envelopes-and-squeezes/projection-bands/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt