Triple Exponential Moving Average (TEMA)

Mulloy's triple-stage lag compensator — 3·EMA1 − 3·EMA2 + EMA3 — often confused with TRIX, which shares the core but plots something else entirely.

What it is

The Triple Exponential Moving Average is Patrick Mulloy's 1994 follow-up to DEMA, published in Technical Analysis of Stocks & Commodities. Like DEMA, the name is misleading: TEMA is not an EMA smoothed three times. It combines three nested smoothing stages into a lag-compensated line: TEMA = 3·EMA1 − 3·EMA2 + EMA3, where EMA2 = EMA(EMA1) and EMA3 = EMA(EMA2). At equal length it tracks price more tightly than both EMA and DEMA. TEMA is frequently confused with TRIX because both are built on a triple-nested EMA — but they are different indicators: TRIX triple-smooths price and then plots the one-bar rate of change of that smoothed line as an oscillator around zero, while TEMA combines the three stages into a moving-average line plotted on price itself. Same core, different output. TEMA is a deterministic function of past prices; it describes recent price with less delay and predicts nothing. This is educational content only, not financial advice, and all trading carries risk of loss.

How it works

Each EMA stage adds roughly one unit of lag: EMA1 lags price, EMA2 lags EMA1, EMA3 lags EMA2. DEMA cancels the first-order lag by adding back the gap between EMA1 and EMA2. TEMA carries the same correction one order further: expanding 3·(EMA1 − EMA2) + EMA3 shows it cancels both the first- and second-order lag terms, leaving a line that hugs price more tightly than DEMA at the same length. The cost scales with the benefit — the higher-order correction amplifies overshoot at reversals and sensitivity to noise, because the terms being added back always describe the trend that just ended, not the one starting. That frames the honest answer to 'when would you use TEMA over DEMA': when you want less lag and are willing to accept more overshoot and more false moves. There is no correct choice between them; EMA, DEMA, and TEMA are the same dial turned progressively further toward responsiveness. One practical consequence of the three nested recursions: TEMA needs a longer warm-up than an EMA, so values near the start of loaded history differ between platforms with different data depth.

How traders read it

• Slope and side: as with any moving average, price relative to a rising or falling TEMA describes recent drift — it is context, not a trigger.
• Place it on the lag ladder: at equal length TEMA turns before DEMA, which turns before EMA; compare all three on one chart to see the trade-off directly.
• Discount the overshoot zone: after sharp reversals TEMA regularly extends beyond price before correcting — crosses and touches during that snap-back are formula artifacts.
• Crossovers are earlier and noisier: a TEMA pair crosses sooner than the equivalent EMA pair and produces more false crosses in ranges; earlier does not mean more reliable.
• Verify the formula: if a platform's 'TEMA' oscillates around zero, you are looking at TRIX; if a 'triple EMA' lags more than a plain EMA, it is EMA(EMA(EMA(price))), not Mulloy's TEMA.

Common settings

Lengths of 9 to 21 are common for short-term reads and 50 for an intermediate view, on the closing price. Because TEMA(n) runs much faster than EMA(n), some traders use longer TEMA lengths to keep smoothness while retaining some lag reduction. The most instructive setup is EMA, DEMA, and TEMA at one identical length side by side — it makes the responsiveness/overshoot trade-off visible rather than theoretical.

Strengths

• The least lag in the EMA/DEMA/TEMA family at equal length, with the mechanism fully derivable from the published formula.
• Exact and deterministic: three EMAs and one linear combination, easy to validate against any implementation.
• Drop-in replacement for an EMA, enabling controlled comparisons on identical data.
• Completes a clean lag-compensation ladder with EMA and DEMA, making it a useful teaching case for how de-lagging actually works.
• Transparent failure mode: the overshoot is predictable from the math rather than a mystery.

Pitfalls to watch

• Strongest overshoot in the family: the higher-order correction pushes TEMA further past price at reversals than DEMA does.
• More whipsaw in ranges: greater responsiveness means more false direction changes and crossovers when price moves sideways.
• TRIX confusion: articles and platforms mix up TEMA and TRIX; using one while reading documentation for the other produces wrong conclusions.
• Warm-up dependence: three nested recursive EMAs mean early-history values vary with loaded data depth, so platforms can disagree near the chart's left edge without either being wrong.
• Lag is reduced, not eliminated: TEMA remains a function of past prices and confirms moves after they begin.
• No predictive power: tighter tracking is a property of the formula, not a forecast, and no setting removes the risk of loss.

Pine v6 example

//@version=6
indicator("TEMA Example", overlay = true)

len = input.int(20, "Length", minval = 1)
src = input.source(close, "Source")

e1 = ta.ema(src, len)
e2 = ta.ema(e1, len)
e3 = ta.ema(e2, len)
tema = 3 * (e1 - e2) + e3

plot(tema, "TEMA", color = color.blue,   linewidth = 2)
plot(e1,   "EMA",  color = color.new(color.orange, 40))

Pro tip: Before using any 'TEMA' script, check its output scale: a line on price is TEMA, an oscillator around zero is TRIX — the two are routinely mislabelled because they share the triple-EMA core. Then compare EMA, DEMA, and TEMA at one length and choose your spot on the lag/overshoot ladder deliberately. This is educational material only, not financial advice; indicators describe past price, and trading involves risk of loss.

Educational only — not financial advice, not a recommendation to trade. No indicator is predictive; trading involves substantial risk of loss.