Tilson T3 Moving Average

Classic moving-average smoothing lag-reduction classic

A smooth, low-lag moving average that uses multiple exponential smoothing.

Visual Example

Tilson T3 Moving Average — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-06-25 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The Tilson T3 Moving Average indicator is a technical analysis tool that a smooth, low-lag moving average that uses multiple exponential smoothing.

This indicator is primarily used for identifying key market conditions. It provides a robust signal that can be easily integrated into both simple strategies and more complex machine learning feature pipelines. Compared to its alternatives, it offers a distinct balance of responsiveness and stability.

Traders often combine this with other metrics to confirm signals and avoid false positives during sideways market regimes. It remains a standard tool for systematic trading models.

Use for trend following in noisy markets. T3 offers a superior balance between lag reduction and smoothness compared to DEMA or TEMA.

Developed by Tim Tilson in 1998, the T3 moving average uses a 'v-factor' (volume factor) to control how much the indicator reacts to price changes. It is essentially a sextuple EMA smoothing process that provides a very smooth curve with remarkably little lag. — Technical Analysis of Stocks & Commodities

QuantWave implements this indicator via the universal Next<T> trait, guaranteeing bit-identical results between Rust streaming, Python streaming, and Polars batch (.ta() / map_batches) surfaces.

Formula / Specification

Implementation (quantwave-core/src/indicators/overlap.rs):

\[ e1 = EMA(Price, n) \\ e2 = EMA(e1, n) \\ \dots \\ e6 = EMA(e5, n) \\ T3 = c1 \times e6 + c2 \times e5 + c3 \times e4 + c4 \times e3 \]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/t3.json.

Parameters

Parameter	Default	Description
`timeperiod`	5	Smoothing period
`v_factor`	0.7	Volume factor (0.0 to 1.0)

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::T3;
use quantwave_core::traits::Next;

let mut ind = T3::new(5);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import T3

ind = T3(5)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_tilson_t3_moving_average(series: pl.Series) -> pl.Series:
    ind = qw.T3(5)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_tilson_t3_moving_average, return_dtype=pl.Float64).alias("tilson_t3_moving_average")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

Warm-up: first 5 bars may return NaN or partial state per implementation.
Parameter sensitivity: smaller periods increase noise; larger periods increase lag.
Sudden gaps or bad ticks can distort rolling windows — consider pre-filtering.
Single-series indicators ignore volume unless otherwise documented.
Validated via proptests against gold-standard vectors where available.
No look-ahead bias; streaming and Polars batch paths are bit-identical.

Boundary Behavior

Condition	Behavior
Warm-up	Leading bars return NaN until warmup_bars is satisfied.
period > len	When period exceeds series length, output is all NaN.
NaN inputs	NaN in input propagates to output (NaN out).
Invalid params	Non-positive period or missing required params raise ValueError.
Empty data	Empty input returns an empty result series.

Sources & References

Primary Source: https://www.tradingview.com/script/667W2a8n-T3-Moving-Average/

Implementation: quantwave-core/src/indicators/overlap.rs (T3 / T3_METADATA). Parity: quantwave-core/tests/gold_standard/t3.json

Provenance: Standards bulk upgrade 2026-06-25 IST — see docs/DOCUMENTATION_STANDARDS.md.