Triple Exponential Moving Average (T3) (T3)

Summary

Tillson's T3: a low-lag moving average built from six chained EMAs, combined via volume-factor-weighted coefficients. Not the same as EMA3, despite both being called "triple EMA".

Chart

Reference data (CSV) · Chart (SVG)

Chart metadata i

Outputs

• outReal: line

Formula

k = 2/(period+1); e1=EMA(x), e2=EMA(e1), ... e6=EMA(e5) (six chained EMAs). v = vFactor: c1 = -v^3; c2 = 3(v^2 - c1); c3 = -6v^2 - 3(v - c1); c4 = 1 + 3v - c1 + 3v^2. T3 = c1e6 + c2e5 + c3e4 + c4e3

Notes

• A period of 1 performs no smoothing: the output is a copy of the input. Allowed since 0.6.5 (issues #48/#59).

Inputs

• inReal — Source series to smooth

Outputs

• outReal — T3 smoothed line

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	5	1–100000	EMA period for each of the six stages
optInVFactor	real	0.7	0–1	Volume factor weighting the coefficients (0 = plain triple EMA, higher = more DEMA-like sharpening)

Properties

Numerical Stability: Initial Unstable Period

✅ Overlap Input i
☐ Independent Y-Axis
☐ Candlestick
☐ Display Shift

☐ Can Output NaN or ±Inf
✅ Identity at Period 1 i
☐ Uses Transcendental
☐ Input Must Be Positive

Example

C

#include <stdio.h>
#include <ta_libc.h>

int n = 252;
double series[252]; /* your data, oldest first */
double out[252];
int outBegIdx, outNBElement;

TA_Initialize();
TA_T3( 0, n - 1, series, 5, 0.7, &outBegIdx, &outNBElement, out );
printf( "%d values from bar %d; last out = %f\n", outNBElement, outBegIdx, out[outNBElement - 1] );

Rust

use ta_lib::Core;

let series = vec![0.0; 252]; // your data, oldest first
let mut out = vec![0.0; 252];

let core = Core::new();
let range = core.t3(0, series.len() - 1, &series, 5, 0.7, &mut out)?;
println!("{} values from bar {}; last out = {}", range.count, range.beg_idx, out[range.count - 1]);

Java

import io.github.talib.Core;
import io.github.talib.OutRange;

double[] series = new double[252]; // your data, oldest first
double[] out = new double[252];

Core core = Core.DEFAULT;
OutRange r = core.t3(0, series.length - 1, series, 5, 0.7, out);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last out = " + out[r.count() - 1]);

C#

using System;
using TALib;

var series = new double[252]; // your data, oldest first
var outReal = new double[252];

var core = Core.Default;
OutRange r = core.T3(0, series.Length - 1, series, 5, 0.7, outReal);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last outReal = {outReal[r.Count - 1]}");

TypeScript

import { t3 } from 'ta-lib';

const series = new Float64Array(252); // your data, oldest first

const { begIdx, values } = t3(series, { timePeriod: 5, vFactor: 0.7 });
console.log(values.length + ' values from bar ' + begIdx + '; last values = ' + values[values.length - 1]);

Implementation

Added in 0.4.0.

TA-Lib Definition: t3.c · t3.yaml

Native	File
C	ta_T3.c
Rust	t3.rs
Java	Core_T3.java
C#	Core_T3.cs
TypeScript	t3.ts

Python: talib.T3, see ta-lib-python.

TA-Lib is also available for R and more using a wrapper.

Aliases

Tillson T3, Triple Exponential Moving Average

See Also

EMA · DEMA · TEMA · MA

References

• Tim Tillson, Smoothing Techniques for More Accurate Signals, Technical Analysis of Stocks & Commodities, V.16:1 (January 1998)