# Ehlers Cyber Cycle

`D09-F06-A06` · 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-cyber-cycle/
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 { ehlersCyberCycle } from "fintech-algorithms/statistical-time-series/hilbert-and-ehlers-cycle-analytics/ehlers-cyber-cycle";
```

## Signature

```ts
ehlersCyberCycle(input)
```

Runs `close` through a two-pole high-pass filter tuned to `period`, then smooths the residual with an EMA of the same span, leaving an oscillator centred on zero that tracks the shorter-than-`period` swings. 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 both the high-pass cutoff coefficient and the span of the EMA applied afterwards. |

## Returns

`TopicResult`

One series, `value`, mirrored as `latest.value`, holding the smoothed high-pass residual in price units and oscillating about zero. `parameters` echoes the supplied parameters and `diagnostics` reports `causal` and `input_count`. Warm-up is `period - 1` leading nulls, which is 19 at the default period, and `ready_at` matches it.

## Warm-up

The first ``period - 1` (19 at the default period of 20)` positions are `null`. The high-pass recursion itself emits a number from the first bar, seeding the first two bars at zero, but the EMA laid over it is seeded from the first full window of `period` values, so `value` and `ready_at` begin at index `period - 1`.

## 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
ehlersCyberCycle(input)
```

### Returns

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

```json
{
  "topic_id": "D09-F06-A06",
  "title": "Ehlers Cyber Cycle",
  "state": "calculated",
  "ready": true,
  "ready_at": 19,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": -0.5033672802018834
  },
  "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-cyber-cycle/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/statistical-time-series/hilbert-and-ehlers-cycle-analytics/ehlers-cyber-cycle/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