# Ehlers Instantaneous Trendline

`D07-F01-A24` · Technical Indicators → Trend Smoothing · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/trend-smoothing/ehlers-instantaneous-trendline/
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 { ehlersInstantaneousTrendline } from "fintech-algorithms/technical-indicators/trend-smoothing/ehlers-instantaneous-trendline";
```

## Signature

```ts
ehlersInstantaneousTrendline(input)
```

Splits close into a smoothed centre line and what is left over: the trendline is an EMA of `max(4, period)` and the detrended series is the bar's close minus that trendline.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is a non-empty array of OHLCV records with strictly increasing `timestamp`, finite `open`, `high`, `low`, `close` and non-negative `volume`, all sharing one adjustment basis. From `parameters` this topic reads only `period`, an integer of at least 2, default 14. The EMA length is `max(4, period)`, so periods of 2 and 3 are both treated as 4. |

## Returns

`TopicResult`

`series` and `latest` carry two keys, `trendline` and `detrended`. Both are null for the first `max(4, period) - 1` bars while the EMA seeds, so with the default period `ready_at` is 13.

## Warm-up

The first `max(4, period) - 1 bars (13 at the default period of 14)` positions are `null`. The EMA seeds from the mean of its first `max(4, period)` closes, so the trendline first prints at index `max(4, period) - 1`, and `detrended` is null wherever the trendline is. `ready_at` is that index.

## Errors

- When `parameters.period` 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, or a timestamp that does not increase — 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
ehlersInstantaneousTrendline(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F01-A24",
  "title": "Ehlers Instantaneous Trendline",
  "state": "calculated",
  "ready": true,
  "ready_at": 13,
  "series": {
    "trendline": [null, null, null, null, null, null],
    "detrended": [null, null, null, null, null, null]
  },
  "latest": {
    "trendline": 103.6493158929627,
    "detrended": -3.6585014229627006
  },
  "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/trend-smoothing/ehlers-instantaneous-trendline/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-smoothing/ehlers-instantaneous-trendline/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt