Tillson T3: A Smoother, Faster Moving Average

Key Takeaways

• T3 chains three generalized DEMAs and blends them so that a chosen volume factor controls response speed.
• The recommended volume factor is 0.7 or the golden ratio 0.618; values of 0 produce an EMA, 1 produces a DEMA.
• Investors often misuse T3 as a pure replacement for an EMA without re-tuning entry rules to its faster response.
• T3 reacts much faster than an EMA of the same length while preserving smoothness, which makes crossover whipsaws less frequent.

What It Is

T3 is a sequence of six exponential moving averages applied to price, then combined with a closed-form formula that depends on a single parameter v, the volume factor. The "volume" name is historical: it refers to how "volumed" or aggressive the response is, not to share volume.

Tillson's design goal was a moving average that responds quickly to real moves while filtering minor noise. He set out to improve on the DEMA and TEMA work by Patrick Mulloy, both of which reduced lag but amplified short-term wiggles. T3 hits a middle ground.

The Intuition

A double EMA (DEMA) cuts lag by subtracting the EMA of an EMA from twice the EMA. The math compensates for the smoothing delay. The cost is louder noise, since the correction term reacts strongly to small price moves.

Tillson generalized that idea. He introduced a generalized DEMA, written GD(n, v), where v between 0 and 1 dials between an EMA and a full DEMA. He then chained three GDs in series. Three chained corrections, each tuned by v, produce a line that is much closer to current price than an EMA of the same length, but smoother than a single DEMA. The cost is more lookback bars to warm up.

How It Works

The building block is the generalized DEMA:

GD(n, v) = EMA(n) * (1 + v) - EMA(EMA(n)) * v

EMA(n) is the exponential moving average over n bars; v is the volume factor between 0 and 1. When v = 0, GD collapses to a plain EMA. When v = 1, GD equals a DEMA.

T3 chains three GDs:

T3(n, v) = GD(GD(GD(n, v), v), v)

Tillson also gave a closed-form expression using six successive EMAs e1 through e6:

c1 = -v^3
c2 = 3*v^2 + 3*v^3
c3 = -6*v^2 - 3*v - 3*v^3
c4 = 1 + 3*v + v^3 + 3*v^2
T3 = c1*e6 + c2*e5 + c3*e4 + c4*e3

Default settings are n = 5 or n = 8, with v = 0.7. Some traders prefer v = 0.618, the golden ratio. The line warms up after roughly 6n bars, since six chained EMAs need time to stabilize.

Worked Example

Place a T3(8, 0.7) and an EMA(8) on the same daily chart of a stock that has just broken out of a tight range.

Before the breakout, both lines hug price closely. On breakout day, price jumps from 100 to 104. The EMA(8) advances by roughly 2 / 9 * 4 = 0.89. The T3(8, 0.7) advances noticeably more, often by 2 to 3 times that amount, because the chained corrections amplify the change in the input.

Three days later, if price holds at 104, the EMA(8) catches up slowly and is still around 101.5. The T3(8, 0.7) is already near 103.8. A trader using T3 as a fast filter would have flagged the breakout earlier, while a trader using EMA(8) might still be debating it.

The same example in reverse explains why T3 cuts whipsaws: a single one-bar pullback from 104 to 103 barely moves T3 because the chained EMAs absorb the wiggle. A simple fast EMA of the same length would tilt down on the bar.

Common Mistakes

1. Setting v above 1 or below 0. Values outside the unit interval can produce unstable, oscillating output. Stick to Tillson's range.
2. Using a very short n with high v. A T3(3, 0.9) is almost raw price. It defeats the smoothing purpose. Match n and v to the volatility of the instrument.
3. Misreading the warmup. The line is unstable for the first 30 to 50 bars at default settings. Backtests should drop early bars from the equity curve.
4. Treating T3 as a perfect substitute for EMA. Crossover thresholds and stop placements that suit an EMA can produce more frequent signals on T3. Re-tune the rules.
5. Ignoring volume factor sensitivity. Switching v from 0.5 to 0.7 changes the line meaningfully. Document and stick to a single setting per strategy.

Frequently Asked Questions

What is the Tillson T3 moving average in simple terms? T3 is a moving average that chains three smoothed averages together so it follows price closely without picking up much short-term noise. A single volume factor parameter sets how fast it responds.

How does Tillson T3 moving average affect investment decisions? Because T3 reacts faster than an EMA of the same length without adding much noise, crossover and slope signals fire earlier in trends. Traders use it as a fast filter that still avoids the whipsaws of a raw short EMA.

What is a real-world example of Tillson T3? On a daily chart, a T3(8, 0.7) crosses above price several bars before an EMA(8) does after a sharp rally. On a slow drift sideways, the T3 line stays smooth while a 5-period EMA chops up and down.

How can investors use Tillson T3 effectively? Start with Tillson's defaults of length 5 to 8 and volume factor 0.7. Add a separate trend filter such as ADX. Drop the first 30 to 50 bars of any backtest to avoid warmup noise.

How is Tillson T3 different from a DEMA? A DEMA is a single correction layer over an EMA. T3 chains three such corrections and weights them with the volume factor. T3 is smoother than DEMA and tunable; DEMA has only the period to set.

Sources

1. Tillson, T. Better Moving Averages. Technical Analysis of Stocks and Commodities, January 1998. https://c.mql5.com/forextsd/forum/173/tillson_t3_better_mas_and_oscillators.pdf
2. MultiCharts. T3 Average. https://www.multicharts.com/support/base/averages-gt-t3-average/
3. Stock Indicators for .NET. Tillson T3 Moving Average. https://dotnet.stockindicators.dev/indicators/T3/
4. TC2000. Tillson T3 Moving Average. https://help.tc2000.com/m/69445/l/755023-tilson-t3-moving-average

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.