# Detrended Price Oscillator

`D07-F03-A26` · Technical Indicators → Momentum · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/momentum/detrended-price-oscillator/
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 { detrendedPriceOscillator } from "fintech-algorithms/technical-indicators/momentum/detrended-price-oscillator";
```

## Signature

```ts
detrendedPriceOscillator(input)
```

Removes the trend by subtracting the current `period` simple average from a close shifted back half that window, leaving the short cycle around the average.

## 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 `period` (integer >= 2, default 14), which sets both the average length and the backward shift of `floor(period / 2) + 1` bars. The preamble also validates `fast_period` (default 5) and `slow_period` (default 34) before branching, so a bad value for either throws even though this topic does not use them. |

## Returns

`TopicResult`

`series` and `latest` carry one key, `value`, equal to the close from `floor(period / 2) + 1` bars ago minus the current `period` simple average. Note the average is not itself displaced; the shift is applied to the price. A null warm-up prefix precedes the first reading.

## Warm-up

The first `period - 1 bars (13 with the default 14)` positions are `null`. The shift is 8 bars with the default `period` of 14, so the simple average, not the shift, is the binding constraint and `ready_at` is 13 on the canonical fixture.

## Errors

- When `period` is not an integer >= 2 — throws Error
- When `bars` do not all share one adjustment `basis` — throws Error

## Complexity

Time `O(n * period)`, 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
detrendedPriceOscillator(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F03-A26",
  "title": "Detrended Price Oscillator",
  "state": "calculated",
  "ready": true,
  "ready_at": 13,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 2.2657371385714242
  },
  "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/detrended-price-oscillator/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/momentum/detrended-price-oscillator/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt