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Tillson T3 Moving Average

Install and import#

bash
npm install fintech-algorithms
ts
import { tillsonT3MovingAverage } from "fintech-algorithms/technical-indicators/trend-smoothing/tillson-t3-moving-average";

Signature#

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#

NameTypeNotes
inputTopicInputbars 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#

executed 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
{
  "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#

tillsonT3MovingAverage(input)

Returns#

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

{
  "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
  }
}

Diagrams#

Tillson T3 Moving Average — article hero
Tillson T3 Moving Average — concept map
Tillson T3 Moving Average — decision comparison
Tillson T3 Moving Average — worked example

Calculation flow#

Tillson T3 Moving Average calculation flow 
flowchart LR
    A["an oldest-to-newest finite price series, declared price so"] --> B["Validate order, basis, and finite values"]
    B --> C["Apply the selected Tillson T3 Moving Average convention"]
    C --> D["Emit value, readiness, and diagnostics"]
    D --> E["Interpret descriptively; test outcomes separately"]
    B -->|invalid or insufficient| X["Withhold output with a reason"]
Tillson T3 Moving Average readiness and evidence states 
stateDiagram-v2
    [*] --> Waiting
    Waiting --> Ready: enough valid causal observations
    Waiting --> Rejected: malformed or unsupported input
    Ready --> Calculated: selected formula applied
    Calculated --> Interpreted: diagnostic and limitation retained
    Interpreted --> Ready: next observation arrives
    Rejected --> Waiting: corrected input and deterministic reset

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

  • TA-Lib function groups — see linked primary or authoritative record
  • TA-Lib C/C++ API — see linked primary or authoritative record
  • TA-Lib maintained source — see linked primary or authoritative record
  • Evidence decision
  • Level 1 evidence map

The rest of the Trend Smoothing family#