# Rate-of-Change Variants (ROC, ROCP, and ROCR)

`D07-F03-A10` · Technical Indicators → Momentum · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/momentum/rate-of-change-variants-roc-rocp-and-rocr/
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 { rateOfChangeVariantsRocRocpAndRocr } from "fintech-algorithms/technical-indicators/momentum/rate-of-change-variants-roc-rocp-and-rocr";
```

## Signature

```ts
rateOfChangeVariantsRocRocpAndRocr(input)
```

Expresses the same `period`-bar price ratio three ways: as a percentage, as a proportion, and as the raw ratio.

## 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), the lookback in 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 three keys. `rocp` is `close / close[-period] - 1`, `roc` is 100 times `rocp`, and `rocr` is `1 + rocp`. All three share the same null warm-up prefix.

## Warm-up

The first `period bars (14 by default)` positions are `null`. The first `period` bars have no reference close, so all three keys are null and `ready_at` is `period`, 14 on the canonical fixture. A close of exactly 0 `period` bars back also produces a null later in the series.

## Errors

- When `period` is not an integer >= 2 — throws Error
- When `bars` are not strictly increasing by `timestamp` — 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
rateOfChangeVariantsRocRocpAndRocr(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F03-A10",
  "title": "Rate-of-Change Variants (ROC, ROCP, and ROCR)",
  "state": "calculated",
  "ready": true,
  "ready_at": 14,
  "series": {
    "roc": [null, null, null, null, null, null],
    "rocp": [null, null, null, null, null, null],
    "rocr": [null, null, null, null, null, null]
  },
  "latest": {
    "roc": -3.185757936162148,
    "rocp": -0.03185757936162148,
    "rocr": 0.9681424206383785
  },
  "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/rate-of-change-variants-roc-rocp-and-rocr/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/momentum/rate-of-change-variants-roc-rocp-and-rocr/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt