# Tillson T3 Moving Average

`D07-F01-A11` · Technical Indicators → Trend Smoothing · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/trend-smoothing/tillson-t3-moving-average/
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 { tillsonT3MovingAverage } from "fintech-algorithms/technical-indicators/trend-smoothing/tillson-t3-moving-average";
```

## Signature

```ts
tillsonT3MovingAverage(input)
```

Chains six exponential moving averages of the same `period` over close and combines the third through sixth with the Tillson volume-factor coefficients, trading warm-up length for a smoother, less laggy curve.

## 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 `period`, an integer of at least 2, default 14, and `volume_factor`, a finite number between 0 and 1, default 0.7. |

## Returns

`TopicResult`

`series` and `latest` carry a single key, `value`, the T3 curve. The warm-up is long because the six EMAs are stacked, so with the default period `ready_at` is 78 rather than 13.

## Warm-up

The first `6 * (period - 1) bars (78 at the default period of 14)` positions are `null`. Each EMA in the chain seeds from a full `period` of non-null inputs, so every stage pushes the first print `period - 1` bars further out. `value` is null until all four of the third-to-sixth stages are non-null, and `ready_at` is the index where that first happens.

## Errors

- When `parameters.volume_factor` is not a finite number between 0 and 1 — throws Error
- 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)`, 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
tillsonT3MovingAverage(input)
```

### Returns

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

```json
{
  "topic_id": "D07-F01-A11",
  "title": "Tillson T3 Moving Average",
  "state": "calculated",
  "ready": true,
  "ready_at": 78,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 104.92677609155169
  },
  "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/tillson-t3-moving-average/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-smoothing/tillson-t3-moving-average/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt