# Inverse Fisher Transform

`D07-F03-A20` · Technical Indicators → Momentum · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/momentum/inverse-fisher-transform/
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 { inverseFisherTransform } from "fintech-algorithms/technical-indicators/momentum/inverse-fisher-transform";
```

## Signature

```ts
inverseFisherTransform(input)
```

Squashes a scaled one-bar close change into -1..1 with the inverse Fisher transform, which is the hyperbolic tangent of the scaled input.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is a chronological array of OHLCV rows, each with a non-empty `timestamp` plus finite `open`, `high`, `low`, `close` and `volume`. From `parameters` this topic reads `source_scale` (finite number >= 0, default 0.1), the multiplier applied to the one-bar close change before the transform. The shared momentum preamble still validates `period` (default 14), `fast_period` (default 5) and `slow_period` (default 34) before branching, so a bad value for any of them throws even though this topic reads none of them. |

## Returns

`TopicResult`

`series` and `latest` carry one key, `value`, equal to `(exp(2y) - 1) / (exp(2y) + 1)` where `y` is `source_scale` times the one-bar close change. Unlike the other momentum topics there is no null warm-up prefix.

## Warm-up

The first `none` positions are `0 at the first bar`. The first bar has no prior close, and the missing change is treated as 0 rather than propagated, so `value` is 0 at index 0 and `ready_at` is 0 on the canonical fixture.

## Errors

- When `source_scale` is negative or not a finite number — throws Error
- When `parameters` is supplied but is not an object — throws Error

## Complexity

Time `O(n)`, 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
inverseFisherTransform(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F03-A20",
  "title": "Inverse Fisher Transform",
  "state": "calculated",
  "ready": true,
  "ready_at": 0,
  "series": {
    "value": [
      0,
      0.17691016466328705,
      0.11617573521901128,
      0.027727270131488183,
      -0.04007677888344102,
      -0.05619814139841276
    ]
  },
  "latest": {
    "value": -0.1468007517369847
  },
  "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/momentum/inverse-fisher-transform/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/momentum/inverse-fisher-transform/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt