# Variable Index Dynamic Average (VIDYA)

`D07-F01-A17` · Technical Indicators → Trend Smoothing · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/trend-smoothing/variable-index-dynamic-average-vidya/
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 { variableIndexDynamicAverageVidya } from "fintech-algorithms/technical-indicators/trend-smoothing/variable-index-dynamic-average-vidya";
```

## Signature

```ts
variableIndexDynamicAverageVidya(input)
```

Scales the EMA constant `2 / (period + 1)` by the absolute Chande momentum oscillator of the last `period` one-bar changes, so the average speeds up in one-sided moves and nearly freezes when gains and losses balance.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is a non-empty array of OHLCV records with strictly increasing `timestamp`, finite `open`, `high`, `low`, `close` and non-negative `volume`, all sharing one adjustment basis. From `parameters` this topic reads only `period`, an integer of at least 2, default 14, which sets both the base smoothing constant and the momentum lookback. |

## Returns

`TopicResult`

`series` and `latest` carry a single key, `value`. It is null for the first `period` bars, is seeded with the close at index `period`, and recurses from there, so with the default period `ready_at` is 14.

## Warm-up

The first `period bars (14 at the default period of 14)` positions are `null`. The momentum window is taken over one-bar changes, whose own first entry is undefined, so the loop starts at index `period` and seeds `value` with the close there. `ready_at` is that index. A window with no gains and no losses scores 0, which holds the average flat.

## Errors

- When `parameters.period` is not an integer of at least 2 — throws Error
- When `bars` is empty or a bar violates the OHLCV contract — 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
variableIndexDynamicAverageVidya(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F01-A17",
  "title": "Variable Index Dynamic Average (VIDYA)",
  "state": "calculated",
  "ready": true,
  "ready_at": 14,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 104.2557087704378
  },
  "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/trend-smoothing/variable-index-dynamic-average-vidya/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-smoothing/variable-index-dynamic-average-vidya/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt