Triple Exponential Moving Average (TEMA)

Layered Warm-Up and Signed Weights

Install and import

bash

npm install fintech-algorithms

import { calculateTemaComponents } from "fintech-algorithms/technical-indicators/trend-smoothing/tema";

Signature

calculateTemaComponents(values, span)

Triple exponential moving average: 3 × EMA − 3 × EMA(EMA) + EMA(EMA(EMA)). More lag cancellation than DEMA, and correspondingly more overshoot.

Parameters

Name	Type	Notes
`values`	`(number \| null)[]`	Observation series in chronological order, oldest first. nulls: propagate
`span`	`number`	Smoothing span used for all three EMA passes; the decay factor is 2 / (span + 1). min: 1 · integer: true

Returns

{ ema1, ema2, ema3, tema }[] · length same-as-input

One record per position carrying all three intermediate EMAs alongside the result.

Warm-up

The first 3 × (span − 1) positions are null. All three passes must fill before the combination is defined.

Errors

When span < 1 or is not an integer — throws RangeError

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

values

[10, 13, 12, 15, 14, 18]

Showing 6 of 10 elements.

span

Call

calculateTemaComponents(values, span)

Returns

array of 10 objects

[
  {
    "value": 10,
    "ema1": null,
    "ema2": null,
    "ema3": null,
    "tema": null,
    "status": "warming_ema1"
  },
  {
    "value": 13,
    "ema1": null,
    "ema2": null,
    "ema3": null,
    "tema": null,
    "status": "warming_ema1"
  },
  {
    "value": 12,
    "ema1": 11.666666666666666,
    "ema2": null,
    "ema3": null,
    "tema": null,
    "status": "warming_ema2"
  }
]

Showing 3 of 10 elements.

Other exports

This module also exports calculateTema, temaSteadyStateWeight. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.

Diagrams

Triple Exponential Moving Average (TEMA) — tema components

Triple Exponential Moving Average (TEMA) — tema effective weights

Triple Exponential Moving Average (TEMA) — tema path

Calculation flow

TEMA calculation flow

flowchart LR
    A["Validate ordered finite value"] --> B["Seed or update EMA1"]
    B --> C{"EMA1 ready?"}
    C -- "No" --> D["Emit warming EMA1"]
    C -- "Yes" --> E["Feed EMA1 into EMA2"]
    E --> F["Seed or update EMA2"]
    F --> G{"EMA2 ready?"}
    G -- "No" --> H["Emit warming EMA2"]
    G -- "Yes" --> I["Feed EMA2 into EMA3"]
    I --> J["Seed or update EMA3"]
    J --> K{"EMA3 ready?"}
    K -- "No" --> L["Emit warming EMA3"]
    K -- "Yes" --> M["Calculate EMA3 + 3 × (EMA1 − EMA2)"]
    M --> N["Emit ready components and TEMA"]

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

Smoothing Data With Faster Moving Averages — Patrick G. Mulloy; *Technical Analysis of Stocks & Commodities*
Smoothing Data With Less Lag — Patrick G. Mulloy; *Technical Analysis of Stocks & Commodities*
TA-Lib TEMA definition and reference implementation — TA-Lib project
TC2000 TEMA methodology — Worden / TC2000
Local EMA and DEMA foundation — The Fintech Builder
Evidence and design reconciliation