# Ehlers Roofing Filter

`D09-F06-A07` · 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-roofing-filter/
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 { ehlersRoofingFilter } from "fintech-algorithms/statistical-time-series/hilbert-and-ehlers-cycle-analytics/ehlers-roofing-filter";
```

## Signature

```ts
ehlersRoofingFilter(input)
```

Stacks the two halves of a roof: a two-pole high-pass filter tuned to `period` removes the slow drift, and an Ehlers Super Smoother run at half that span removes the fast noise, leaving the band in between. 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, and the smoother stage runs at `max(4, floor(period / 2))`, which is 10 by default. |

## Returns

`TopicResult`

Two series, both mirrored in `latest`: `high_pass` is the intermediate high-pass residual and `value` is that residual after the Super Smoother pass. `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`. Both stages are seeded rather than gated. The high-pass recursion holds its first two outputs at zero, and the Super Smoother copies its input for its first two bars, so every index carries a number and `ready_at` is 0. The opening bars are seed values, not 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
ehlersRoofingFilter(input)
```

### Returns

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

```json
{
  "topic_id": "D09-F06-A07",
  "title": "Ehlers Roofing Filter",
  "state": "calculated",
  "ready": true,
  "ready_at": 0,
  "series": {
    "high_pass": [
      0,
      0,
      -0.46270692883549364,
      -1.335377436005075,
      -2.201684726094235,
      -2.614761522250397
    ],
    "value": [
      0,
      0,
      -0.058577494525456325,
      -0.29546823437612796,
      -0.7658592036228475,
      -1.375141122806132
    ]
  },
  "latest": {
    "high_pass": -1.4080590702156108,
    "value": -1.0173197105824179
  },
  "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-roofing-filter/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/statistical-time-series/hilbert-and-ehlers-cycle-analytics/ehlers-roofing-filter/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