T3 Moving Average Indicator: Tim Tillson's Ultra-Smooth Trend Filter

Tim Tillson was not a Wall Street quant. He was a software project manager at Hewlett-Packard with degrees in mathematics and computer science, and he had been privately trading options and equities for fifteen years when he sat down to solve a problem that had bugged him for a while: every moving average on the market forced traders to choose between speed and smoothness. Short-period EMAs react fast but whipsaw like crazy. Long-period SMAs are smooth but signal entries so late you are already giving back half the move.

His solution, published in the January 1998 issue of Technical Analysis of Stocks and Commodities magazine under the title "Better Moving Averages," was elegant. Instead of running price through one EMA calculation, Tillson ran it through six — but he did not simply chain them sequentially like TEMA does. He introduced a Generalized Double Exponential Moving Average (GDEMA) function and applied it three times recursively: T3(n) = GD(GD(GD(n))).

The GDEMA function itself is straightforward: GD(n, v) = EMA(n) x (1 + v) - EMA(EMA(n)) x v, where v is the volume factor parameter. This recursive triple application produces six layers of EMA smoothing, but the clever weighting means the result does not pile on phase delay the way six sequential EMAs would.

The fully expanded formula combines EMA layers 3 through 6 using four coefficients derived from the volume factor (a):

• c1 = -a^3
• c2 = 3a^2 + 3a^3
• c3 = -6a^2 - 3a - 3a^3
• c4 = 1 + 3a + a^3 + 3a^2
• T3 = c1 x EMA6 + c2 x EMA5 + c3 x EMA4 + c4 x EMA3

In signal processing terms, T3 is a six-pole nonlinear Kalman filter. Kalman filters use the error between the time series and its smoothed version to self-correct — which is why technical analysts call these adaptive moving averages. When price makes a large move, T3 tracks aggressively. When price chops sideways, T3 flattens out and ignores the noise.

Tillson himself noted that the result not only looks good on a chart but serves as a powerful building block inside other indicators and trading systems. He was right. Two decades later, T3 appears in custom indicators on MetaTrader 4, MetaTrader 5, TradingView, NinjaTrader, and virtually every charting platform that supports custom coding.

One warmup detail worth noting: T3 requires at least 6 x (N - 1) + 100 periods of data to fully converge. With the default period of 5, that is 124 bars. On an H1 chart, you need about five days of history before the T3 line is mathematically stable. If your chart only loads 50 bars, the first readings will be unreliable — a common gotcha that catches new users.

What made Tillson's approach genuinely novel was not just the six EMA layers — it was the volume factor concept. Every previous smoothed moving average, including Mulloy's DEMA and TEMA from 1994, had a fixed aggression level. You could change the period, but the fundamental tradeoff between responsiveness and overshoot was locked in by the formula. Tillson gave traders a second dial to turn. That dial — the volume factor — transformed T3 from a clever mathematical exercise into a practical, tunable trading tool that could be adapted to any market condition, any volatility regime, and any trading style. It is this tunability, more than the raw smoothing quality, that explains why T3 has outlasted dozens of competing indicators introduced in the years since.

Most traders who add T3 to their chart adjust the period and never touch the second parameter. That is a mistake. The volume factor (v) is what makes T3 fundamentally different from every other moving average — it is the knob that controls the balance between lag reduction and smoothness, and it transforms T3's behavior more dramatically than changing the period ever could.

Here is how it works at the extremes. When v = 0, the GDEMA function collapses to a plain EMA, and T3 becomes equivalent to three chained EMAs — essentially a triple EMA with standard behavior. When v = 1, GDEMA becomes a full DEMA, and T3 turns into a triple-DEMA — extremely reactive, almost aggressive, and prone to overshooting price on sharp reversals. Tillson recommended v = 0.7 as the default because it sits in the sweet spot: fast enough to catch trend changes within one or two bars of a standard EMA crossover, smooth enough to filter out the random wick noise that generates false signals on lower timeframes.

But 0.7 is not sacred. Here are three volume factor profiles I have tested across EUR/USD, GBP/USD, and USD/JPY from 2020 through 2025:

v = 0.4-0.5 (Conservative) T3 behaves like a heavily smoothed trend filter. The line barely reacts to individual candle spikes and produces very few crossover signals — roughly 40-50% fewer than v = 0.7 on H1 charts. Use this when you want T3 as a background trend direction filter, not as an entry trigger. Works well on volatile pairs like GBP/JPY where noise is extreme.

v = 0.618 (Fibonacci) A popular alternative among systematic traders. The golden ratio value produces approximately 12% fewer false signals than v = 0.7 on M15 EUR/USD charts, according to backtesting data circulated in the MQL5 community. The smoothness gain is subtle but measurable. If you are a scalper running T3 on M15, this is worth testing as your default.

v = 0.7 (Tillson Default) The all-rounder. On H1 and H4 timeframes, this produces the best balance between signal timeliness and noise rejection for most major forex pairs. Stick with this unless you have a specific reason to change it.

v = 0.8-0.9 (Aggressive) T3 starts hugging price almost as tightly as a raw EMA. You gain maybe one bar of signal lead time compared to v = 0.7, but you lose the smoothing advantage that makes T3 worth using in the first place. The overshoot problem that Tillson specifically designed T3 to avoid starts creeping back in. I would only use values above 0.8 if T3 is being fed into another indicator's calculation — not for direct chart reading.

A practical way to find your ideal volume factor: plot two T3 lines on the same chart with the same period but different v values — say 0.618 and 0.7. Watch them for a week. The one that produces fewer false slope changes on your preferred pair and timeframe is your answer. The difference is usually obvious within 30-40 signals.

One thing the volume factor does not do: it does not change the number of bars used in the calculation. Period controls the lookback window; volume factor controls how aggressively T3 leans into the trend within that window. Confusing these two parameters is the most common setup mistake I see on trading forums.

The practical case for T3 over a standard EMA comes down to one thing: fewer false entries during choppy price action. Every EMA crossover trader has experienced the frustration of entering a long because price closed above the EMA, only to watch price immediately drop back below it on the next candle. T3's six-layer smoothing makes this significantly less likely because random single-candle spikes are absorbed into the calculation rather than jerking the indicator line around.

Here is a concrete example. Take EUR/USD on the H1 chart during a typical London session. A standard 10-period EMA might produce 6-8 price crossovers in a single session during a ranging market. The same period T3 with v = 0.7 will typically produce 2-4 crossovers in the same conditions — a reduction of roughly 50-60%. The crossovers that do occur tend to be followed by actual directional moves rather than immediate reversals, because it takes sustained buying or selling pressure to move a six-layer smoothed line.

Setup 1: T3 Slope Reversal Entry (H1)

This is the cleanest T3 signal and the one I use most frequently.

Conditions for a long entry:

1. T3(5, 0.7) has been declining for at least 4-5 candles
2. The T3 line flattens visually — the slope approaches zero
3. T3 begins turning upward, confirmed by 2 consecutive bars with rising T3 values
4. A bullish candlestick pattern forms at or near the T3 line (engulfing, pin bar, or morning star)
5. ATR(14) is above 8 pips — ensuring the market has enough volatility to reach your target

Entry: Market order on the open of the candle following the pattern confirmation. Stop loss: 3-5 pips below the candlestick pattern's low (or the recent swing low if it is within 15 pips). Target: 2:1 reward-to-risk minimum. For H1 EUR/USD, this typically means 30-60 pip targets against 15-30 pip stops.

Why this works: T3 slope changes carry more statistical weight than EMA slope changes because six layers of smoothing have already filtered out random noise. When T3 actually turns, it means sustained buying pressure has built up — not just a single large candle.

Setup 2: Dual T3 Trend Alignment (M15 Scalp)

Conditions:

1. Plot T3(5, 0.7) and T3(20, 0.7) on M15
2. Wait for the fast T3(5) to cross above the slow T3(20)
3. Both lines must be angled upward at the moment of the cross — reject crosses where T3(20) is still flat or declining
4. Confirm that H1 T3(5) is also pointing up (multi-timeframe alignment)

Entry: Limit order at the fast T3(5) line on the first pullback after the cross. Stop loss: Below T3(20) at the time of entry. Target: 15-25 pips, or exit when T3(5) crosses back below T3(20).

This dual-line approach filters out most of the false crosses that plague single-line EMA strategies on M15. The requirement for both lines to be angled upward eliminates the dangerous scenario where you buy into a dead cat bounce during a downtrend.

Setup 3: T3 as a Trailing Stop Reference (H4 Swing)

For longer-term swing trades on H4, T3(7, 0.7) serves as an excellent dynamic trailing stop reference. Enter using whatever method you prefer — breakout, support bounce, pattern completion — and then trail your stop loss 5-10 pips below the T3 line as it rises. Because T3 is smooth, it does not jerk your trailing stop around the way a 7-period EMA would. You stay in the trade through normal pullbacks but exit when genuine momentum shifts occur.

One critical rule applies to all three setups: avoid trading T3 signals during the 15-30 minutes before and after major economic releases. T3's six-layer calculation means it reacts to explosive news-driven moves slightly slower than raw price, creating a brief window where your entry signal is based on pre-news conditions while price has already moved 30-50 pips.

Combining T3 with the Relative Strength Index creates a strategy that solves two problems simultaneously. RSI tells you whether momentum is overbought or oversold, but it generates too many signals in choppy markets — anyone who has tried trading raw RSI(14) crossovers above 70 or below 30 knows the frustration. T3 tells you the trend direction with minimal noise, but it says nothing about momentum extremes. Together, they filter each other's weaknesses.

There are two distinct approaches to combining these indicators, and they serve very different trading styles.

Approach 1: T3 Trend Filter + Standard RSI Entry

This is the simpler and more conservative method.

Rules for a long trade:

1. T3(5, 0.7) on H1 is pointing upward (confirmed bullish trend)
2. RSI(14) on H1 pulls back below 40 (not oversold at 30 — we want a dip, not a reversal)
3. RSI then crosses back above 40 while T3 is still pointing up
4. Enter long at market on the RSI cross-back candle

Stop loss: Below the most recent swing low or 1.5x ATR(14), whichever is tighter. Target: Next resistance level, or 2:1 R:R if no clear resistance is visible.

The logic is clean: T3 confirms the trend is bullish, and the RSI pullback below 40 tells you price has temporarily dipped within that trend. The cross back above 40 is your timing signal. You are buying dips in confirmed uptrends — one of the highest-probability setups in technical trading.

What to avoid: do not take this trade when RSI drops below 30 while T3 is pointing up. That level of oversold reading within an uptrend often signals the trend is about to break down, and T3 just has not caught up yet due to its smoothing lag.

Approach 2: T3-Smoothed RSI (Advanced)

Instead of using T3 and RSI as separate indicators, you can apply T3 smoothing directly to the RSI values themselves. This creates a T3(RSI) line that replaces the standard RSI on your chart.

The implementation is straightforward in MetaTrader 5 or TradingView Pine Script: calculate RSI(14), then apply a T3(5, 0.7) calculation to the RSI output instead of to price. The result is a momentum oscillator that oscillates between 0 and 100 like normal RSI but with dramatically less chatter.

Signal rules:

1. Plot both standard RSI(14) and T3(RSI) on the same oscillator panel
2. Buy signal: RSI crosses above the T3(RSI) line from below, and both are below 50 (catching momentum shift early)
3. Sell signal: RSI crosses below the T3(RSI) line from above, and both are above 50
4. Divergence bonus: If price makes a lower low but T3(RSI) makes a higher low, that is a high-probability reversal signal

The T3-smoothed RSI approach eliminates approximately 60-70% of the false crossover signals that standard RSI produces on M15 charts. On H1, the reduction is less dramatic — around 30-40% — because H1 RSI is already smoother than M15 RSI. The tradeoff is a slight delay in signal generation, usually one candle on H1.

Optimal Settings by Timeframe:

On H4 charts, I prefer the T3-smoothed RSI approach because the longer timeframe already provides decent trend definition, and what you really need is a cleaner momentum signal to time entries. On M15, the standard T3 trend filter plus RSI pullback method works better because you need T3's directional clarity more than you need smoother RSI.

Risk note: this combination performs poorly during strong one-directional moves where RSI stays above 70 (or below 30) for extended periods. In trending markets where RSI essentially pins to one extreme, the T3 slope signal alone is more reliable than waiting for RSI pullbacks that never come.

If you have spent any time researching smoothed moving averages, you have probably encountered all three of these: DEMA, TEMA, and T3. They are related — T3 is built on top of the same mathematical foundation — but they behave differently enough in live trading that choosing the right one matters. Let me cut through the confusion.

DEMA (Double Exponential Moving Average)

Developed by Patrick Mulloy in 1994, DEMA uses two EMA layers and the formula: DEMA = 2 x EMA - EMA(EMA). It reduces lag compared to a standard EMA by roughly 30-40%, but it introduces a subtle overshoot problem — when price reverses sharply, DEMA can temporarily move past the actual price level before correcting itself. Think of it as an eager student who raises their hand before the teacher finishes the question. Useful? Yes. Occasionally embarrassing? Also yes.

TEMA (Triple Exponential Moving Average)

Also by Patrick Mulloy, TEMA extends the concept to three EMA layers: TEMA = 3 x EMA - 3 x EMA(EMA) + EMA(EMA(EMA)). TEMA is faster than DEMA and significantly faster than a standard EMA. The problem is that it inherits the overshoot issue and amplifies it. On M15 charts with volatile pairs like GBP/JPY, TEMA produces so many price crossovers that it becomes nearly useless as a standalone signal generator. It hugs price so tightly that distinguishing signal from noise requires a second indicator.

T3 (Tillson Triple-Smoothed)

Tillson's innovation was recognizing that Mulloy's approach — simply subtracting lag — created an overshoot problem. His solution was the volume factor parameter, which lets you dial back the aggressiveness. When v = 1, T3 is essentially a triple-DEMA with full overshoot. At v = 0.7, the overshoot is largely eliminated while retaining most of the lag reduction. At v = 0, T3 degenerates to a simple triple-EMA chain.

This is the core difference: DEMA and TEMA have fixed aggression levels. T3 has adjustable aggression. That single parameter makes it fundamentally more flexible.

Head-to-Head Comparison on EUR/USD H1 (2023-2025)

I ran all three through a simple slope-change signal test: buy when the indicator turns up, sell when it turns down. Period 10 for all three, v = 0.7 for T3.

T3 produced fewer signals but higher quality ones. The 48% win rate with a 33:19 pip average winner-to-loser ratio gave it the best profit factor. TEMA had the worst performance because its aggressive tracking generated too many false reversals. DEMA sat in the middle — decent but unspectacular.

When to Use Each:

Use DEMA when you need a simple lag-reduction upgrade from EMA and do not want to worry about an extra parameter. It works adequately on H4 and D1 where noise is lower and overshooting is less of an issue.

Use TEMA when building it into another indicator's calculation where you need maximum speed and will be applying your own smoothing or threshold logic on top. TEMA is an excellent input for oscillators and custom signal generators. As a standalone chart overlay, it is too noisy for most traders.

Use T3 when you want the best standalone chart overlay. The volume factor parameter means you can tune it precisely for your pair and timeframe. It works well on everything from M15 scalping to H4 swing trading. The only downside is the longer warmup period — T3 needs about 124 bars at the default settings to fully converge, versus roughly 20-30 bars for DEMA and TEMA.

The Verdict:

T3 is not just a minor improvement over TEMA and DEMA — it is a generation ahead in design philosophy. Tillson understood that removing lag is not enough; you have to control the side effects of lag removal. The volume factor is that control mechanism, and it is why T3 remains the smoothed moving average of choice for serious systematic traders nearly three decades after its publication.