T3 moving average (Tillson T3): smooth with little lag

The T3 is a moving average designed to be both smooth and quick. Tim Tillson introduced it in Technical Analysis of Stocks & Commodities in January 1998. He started from Patrick Mulloy's double exponential moving average, which cuts lag but overshoots and wiggles, and softened it with an adjustable "volume factor." Then he applied the softened version three times in a row. The result is a line that tracks price nearly as closely as a short EMA while changing direction far less often.

The name has nothing to do with trading volume. Tillson's "volume factor" is simply a dial between an ordinary EMA and a DEMA. This guide explains the construction, works through the coefficient arithmetic for Finabase's default settings, measures the T3 against a 5-day EMA on Meta Platforms' volatile 2026 chart, and covers how Finabase displays and scores it.

From DEMA to the generalized DEMA

Mulloy's DEMA is 2 × EMA − EMA(EMA): it adds the full estimated lag back onto the EMA. Tillson asked what happens if you add back only part of it. His generalized DEMA (GD) uses a factor v between 0 and 1:

• v = 0 gives GD = EMA, the plain average with its full lag.
• v = 1 gives GD = 2 × EMA − EMA(EMA), the DEMA, with no lag on a straight trend but a pronounced overshoot.
• v = 0.7, Tillson's recommendation, removes 70% of the lag and keeps most of the smoothness.

A single GD is still a bit rough. Tillson's insight was to run GD on its own output twice more, GD(GD(GD(price))), which removes the remaining jaggedness while each pass's partial lag correction keeps the total delay small.

The formula

A worked example: the coefficients at v = 0.7

Finabase's default T3 uses n = 5 (so α = 2 ÷ 6 = 1/3) and v = 0.7. Plugging v in:

The coefficients sum to exactly 1, so a flat price gives a flat T3 at the same level. The large positive and negative weights on adjacent layers are what cancel the lag; they are also why T3 can still overshoot slightly at sharp turns.

A worked example: the lag on a steady trend

On a series that rises by the same amount each bar, an EMA with α = 1/3 trails by (1 − α) ÷ α = 2 bars. One GD pass trails by (1 + v) × 2 − v × 4 = 2 × (1 − v) = 0.6 bars. Three passes trail by 3 × 0.6 = 1.8 bars. So the T3 (5) carries almost the same delay as a plain EMA (5) on a steady trend, but it is far smoother, because it is built from six layers of averaging instead of one.

The T3 on a real chart

Meta Platforms (META) had a turbulent half-year: a low of $524.49 on July 30, 2026 after a gap down, and a high of $779.82 on September 24, with a close of $624.52 at the end of October.

Smoothness. Over the six months the T3 (5) changed direction 14 times, the EMA (5) 24 times. On the chart the EMA kinks at almost every two- or three-day swing; the T3 draws gentle arcs.

The cost at a shock. On July 30 Meta gapped down to close at $539.03. The EMA (5) fell to $578.53 that day; the T3 (5), still carrying momentum from its six layers, fell only to $586.98. The T3 then kept drifting lower for three more sessions, to $567.38 on August 4, while price had already rebounded to $587.94. A smoother line pays with a short delay after sudden events.

At the top. On July 17 Meta fell 2.8% to $646.01, but the T3 still ticked up to its local peak of $668.53 and only turned down the next day. That one-bar overshoot is the residue of the lag correction.

How traders use the T3

A smooth trend line with few false turns. The most common use is to read the slope: T3 rising, uptrend; T3 falling, downtrend. Because it turns so much less often than a short EMA, a change in its slope tends to mark a real shift in the short-term trend.

Colour-change rules. Many platforms colour the T3 by slope and use the colour change as the signal. Finabase draws it as a single line, but the same reading applies.

Crossovers. Price crossing the T3, or a short T3 crossing a long T3, gives cleaner crossover signals than equivalent EMAs, at the cost of a slightly later entry after shocks.

Tuning the volume factor. Lower v (0.5) makes the T3 smoother and slower; higher v (0.8 to 0.9) makes it quicker and more prone to overshoot. Tillson found 0.7 a good middle ground, and most platforms default to it.

Pitfalls and limitations

Six layers need history. Each EMA layer needs time to settle, and the T3 has six of them. On a chart that starts the calculation at the first visible bar, the first few dozen T3 values can be distorted. Finabase computes from a longer history than the range you view.

Shock delay. As the Meta gap shows, the T3 can trail a sudden gap by several bars while its layers catch up.

Hidden parameters. Two T3s with the same period but different volume factors look alike and give different signals. Always state both numbers when you compare.

Comparison with related averages

For the DEMA and TEMA see Double exponential moving average (DEMA): reducing lag and Triple exponential moving average (TEMA): fast, with a catch; for the plain EMA, Exponential moving average (EMA): formula and how to use it.

How Finabase calculates and scores the T3

Finabase computes the T3 with TA-Lib's T3 function on closing prices. A new T3 study defaults to a period of 5 and a volume factor of 0.7; the chart title shows the period, for example "T3 (5)". It is drawn on the price chart as an overlay.

In the technical gauge on the symbol page, the T3 (5) is one of the overlay rows: a close at or above it counts as Bullish, below it as Bearish. The Scanner's crossover list uses a slower T3 (10) with the same 0.7 factor and lists stocks whose close crossed it, with the date. Both describe where price sits relative to the line today, not what it will do next.

Frequently asked questions

What does the volume factor in T3 mean?

It is not trading volume. It is Tillson's name for the share of the EMA's lag that each generalized-DEMA pass adds back: 0 gives a plain EMA, 1 gives a DEMA. The default 0.7 is a compromise between smoothness and speed.

What are the best T3 settings?

Tillson's own examples used periods around 5 to 8 with a volume factor of 0.7, and that remains the common default. Finabase uses 5 and 0.7. Longer periods suit swing and position trading.

Is T3 better than an EMA?

It is much smoother for about the same lag on a steady trend, so it gives fewer false turns. After a sudden gap it reacts later, because its six layers take a few bars to absorb the shock.

Summary

The T3 chains three generalized DEMAs, each correcting 70% of an EMA's lag, into one smooth line built from six EMA layers. With Finabase's defaults it trails a steady trend by about 1.8 bars, nearly the same as a 5-day EMA, while changing direction 14 times on Meta's six-month chart against the EMA's 24. Expect it to lag a few bars after a shock, state both of its parameters, and read its slope rather than every crossing.