zeonta.t3() — Tillson’s T3: cascaded generalized DEMA, smoother than DEMA/TEMA with less overshoot.
What it measures
Tim Tillson’s “Generalized DEMA” blends a plain EMA and a full dema by the volume_factor — at v=1 GD is exactly dema’s own formula, so T3 is literally dema cascaded through itself three times at that setting. Tillson’s recommended v=0.7 sits short of that, trading a little of dema/tema’s speed for meaningfully less overshoot on a sharp reversal.
Formula
GD(x, v) = (1 + v) x EMA(x, n) - v x EMA(EMA(x, n), n); T3 = GD(GD(GD(Close)))
Parameters
Required inputs: close
| Parameter | Default |
|---|---|
length |
5 |
volume_factor |
0.7 |
Returns
| Column |
|---|
T3_5_0.7 |
Usage
Examples run against the 300-bar OHLCV fixture in tests/data/ohlcv.csv, loaded as df. The output shown is the real output.
import pandas as pd
import zeonta
df = pd.read_csv('tests/data/ohlcv.csv', parse_dates=['date']).set_index('date')
zeonta.t3(df['close']).tail(3)
date
2024-10-25 90.078567
2024-10-26 89.952661
2024-10-27 89.676947
Name: T3_5_0.7, dtype: float64
Accessor form: df.zta.t3(...)
How to read it
Read it like dema/tema — a fast-reacting trend line to hug price closely — but expect fewer of the sharp overshoot spikes those two produce on a sudden reversal, which is the entire reason Tillson built it.
Pitfalls
Neither StockCharts nor Wikipedia document T3 — Tillson published it in Technical Analysis of Stocks & Commodities, January 1998, not through either of those channels. The default length here (5) follows an independently maintained reference implementation (Stock Indicators for .NET/Python); no source surveyed states one length as canonical the way Tillson’s own 0.7 volume factor is agreed on everywhere.
Reference
Formula source: https://c.mql5.com/forextsd/forum/173/tillson_t3_better_mas_and_oscillators.pdf