# Ehlers Decycler

`D09-F06-A08` · Statistical Time Series → Hilbert and Ehlers Cycle Analytics · archetype `record-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/statistical-time-series/hilbert-and-ehlers-cycle-analytics/ehlers-decycler/
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 { ehlersDecycler } from "fintech-algorithms/statistical-time-series/hilbert-and-ehlers-cycle-analytics/ehlers-decycler";
```

## Signature

```ts
ehlersDecycler(input)
```

Subtracts a two-pole high-pass residual from `close`, leaving a trend line with the sub-`period` wiggle removed and far less lag than a moving average of the same span. Any contract failure is rethrown as an `Error` whose message begins `topic calculation failed: `.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is a non-empty array of rows with `timestamp`, `open`, `high`, `low`, `close` and `volume`, strictly ordered by timestamp. This topic genuinely uses `parameters.period`, which defaults to 20 and must be an integer of at least 4; it sets the high-pass cutoff coefficient and so decides which cycles are removed. |

## Returns

`TopicResult`

Two series, both mirrored in `latest`: `high_pass` is the removed high-frequency residual and `value` is `close` minus that residual, in price units. `parameters` echoes the supplied parameters and `diagnostics` reports `causal` and `input_count`. There is no null prefix at all, so the warm-up is zero bars and `ready_at` is 0.

## Warm-up

The first `0` positions are `no nulls are emitted`. The high-pass recursion holds its first two outputs at zero rather than leaving them null, so `high_pass` is defined from index 0 and `value` simply equals `close` there. `ready_at` is 0, but the opening bars are seed values rather than converged filter output.

## Errors

- When `parameters.period` is present but is not an integer of at least 4 — throws Error
- When `bars` is empty, a `timestamp` is missing or not strictly increasing, an OHLCV field is not finite, `volume` is negative, or `high` and `low` do not bracket `open` and `close` — 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
ehlersDecycler(input)
```

### Returns

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

```json
{
  "topic_id": "D09-F06-A08",
  "title": "Ehlers Decycler",
  "state": "calculated",
  "ready": true,
  "ready_at": 0,
  "series": {
    "high_pass": [
      0,
      0,
      -0.46270692883549364,
      -1.335377436005075,
      -2.201684726094235,
      -2.614761522250397
    ],
    "value": [
      100,
      101.78791214,
      103.41764582883549,
      104.56766012600508,
      105.03298485609423,
      104.8834874922504
    ]
  },
  "latest": {
    "high_pass": -1.4080590702156108,
    "value": 101.39887354021562
  },
  "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/statistical-time-series/hilbert-and-ehlers-cycle-analytics/ehlers-decycler/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/statistical-time-series/hilbert-and-ehlers-cycle-analytics/ehlers-decycler/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/statistical-time-series/llms.txt