T3: Tillson's Generalized DEMA Moving Average

Key Takeaways

• T3 moving average applies a generalized DEMA, GD(n, v) = EMA(n)*(1+v) - EMA(EMA(n))*v, three times in succession.
• The volume factor v controls aggressiveness; Tillson recommends 0.7 as a default for daily charts.
• The most common mistake is using high v values on noisy data, which makes T3 oscillate and produce false signals.
• T3 is widely used as a fast trend overlay in MultiCharts, MetaTrader, and TradingStation templates.

What It Is

T3 is a triple-nested generalized DEMA. Tim Tillson introduced it in a 1998 magazine article titled "Better Moving Averages." The construction is intentionally heavy: three smoothing stages, each of which is itself a tunable blend of EMA and DEMA.

The point of all that machinery is to produce a curve that hugs price closely (low lag) but does not look jittery (low noise). Tillson framed T3 as a six-pole nonlinear Kalman-style filter, though in practice it is implemented as nested EMAs and a single user parameter.

The Intuition

DEMA reduces the lag of an EMA by computing 2*EMA - EMA(EMA). The trick works because the second smoothing reveals exactly how much the first stage lagged, and subtracting it back projects the line forward. The cost is more noise.

Tillson generalized the trick. Instead of always projecting fully (the DEMA case), let the user pick how much to project with a parameter v between 0 and 1. Then apply the generalized step three times. The first pass cleans noise; the second sharpens response; the third stabilizes the result.

How It Works

The published formulas, available in the original 1998 paper and reproduced by MultiCharts, are:

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

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

When v = 0, GD reduces to EMA(n) and T3 becomes a triple-nested EMA, which behaves like a slow smoother. When v = 1, GD equals DEMA and T3 becomes a triple-nested DEMA, which is aggressive and noisy. Tillson recommends v = 0.7 as a middle setting that captures most of the lag reduction with bearable noise.

Default lengths vary. Tillson worked examples with n = 5 on daily charts, which produces an effective response speed similar to a 14- to 21-period SMA. Many platforms default to n = 8 or 14 with v = 0.7.

A useful mental model: each GD stage adds about one bar of lag and removes about half the remaining noise. After three stages the line is visually clean while still tracking turns within a few bars on liquid daily series.

Worked Example

Take n = 5 and v = 0.7. Start with raw prices and compute EMA(5) and EMA(EMA(5)) recursively. Suppose at a given bar:

• EMA(5) = 102.0
• EMA(EMA(5)) = 101.4

Compute GD:

GD = 102.0 * (1 + 0.7) - 101.4 * 0.7
   = 102.0 * 1.7 - 70.98
   = 173.40 - 70.98
   = 102.42

That output is the input to the next GD stage. Apply EMA(5) and EMA(EMA(5)) to the GD series and compute GD again, then once more. Each pass moves the line a small amount closer to the most recent price.

In practice, traders do not compute T3 by hand. The point of the example is to show that GD lifts the EMA toward where the data is heading. Stacking three GDs amplifies that lift while letting the EMAs absorb the noise that the lift would otherwise expose.

Common Mistakes

1. Pushing v too high. Values above 0.8 make T3 nearly equivalent to triple DEMA, which on noisy intraday data produces wiggles in the line and false direction changes. Stay near 0.7 unless the instrument is unusually smooth.

2. Treating T3 as a leading indicator. The line tracks price closely but cannot predict the next bar. Marketing copy that frames T3 as "ahead of price" misreads the math.

3. Ignoring warmup. T3 chains three EMA stages, so its effective warmup is roughly 3 * 3 * n bars before the line settles. Backtests that start measuring from bar one include unstable T3 values.

4. Mixing length and v changes without testing. Both length and v affect responsiveness. Changing both at once makes it hard to attribute a backtest difference to one or the other. Vary one at a time.

5. Using T3 alone on illiquid names. Like other low-lag smoothers, T3 amplifies single-bar spikes. On thin stocks or gappy series, pair it with a volume filter or a wider trend confirmation.

Frequently Asked Questions

What is T3 moving average in simple terms? The T3 moving average is a low-lag price line built by chaining three of Tim Tillson's generalized DEMA filters. A single parameter v controls how aggressive it is.

How does T3 affect investment decisions? Active swing and intraday traders use T3 in place of EMA for faster, smoother trend confirmation. The single tuning knob makes it easier to match an instrument than retuning multiple EMA lengths.

What is a real-world example of T3 use? T3 is a built-in study in MultiCharts, MetaTrader, NinjaTrader, and many TradingStation templates. Period 8 with v = 0.7 on a daily chart of a liquid index ETF is a common starting point.

How can investors use T3 effectively? Pick a length tied to your horizon, keep v near 0.7, and verify signals with a longer trend filter or volatility regime. Treat T3 as a smoother, not a forecaster.

How is T3 different from TEMA? TEMA uses a fixed combination of single, double, and triple smoothed EMAs (3EMA1 - 3EMA2 + EMA3). T3 chains three generalized DEMA stages and adds a tunable volume factor v that adjusts aggressiveness.

Sources

1. Tillson, T. (1998). "Better Moving Averages." Technical Analysis of Stocks & Commodities, January 1998. https://c.mql5.com/forextsd/forum/173/tillson_t3_better_mas_and_oscillators.pdf
2. Traders.com Archive. "Traders' Tips, February 1998." http://traders.com/documentation/feedbk_docs/1998/02/TradersTips/Tips9802.html
3. MultiCharts Knowledgebase. "T3 Average." https://www.multicharts.com/support/base/averages-gt-t3-average/
4. TechnicalIndicators.net. "T3 Moving Average." https://www.technicalindicators.net/indicators-technical-analysis/150-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.