Indicators · Published May 13, 2026 · 6-min read
Double Exponential Moving Average (DEMA) was Patrick Mulloy's 1994 attempt to keep EMA's smoothness while removing most of its lag. Here is the formula, the math, and when DEMA outperforms a plain EMA on Indian indices.
The Double Exponential Moving Average (DEMA) was developed by Patrick Mulloy in 1994 with a specific goal: keep the smoothness of an EMA while removing most of the lag. The trick was nesting EMAs and using a clever subtraction step. The result is a moving average that reacts to trend changes 1–3 bars earlier than the equivalent EMA on daily Indian-index charts, with comparable smoothness in trends.
This guide walks through what DEMA is, derives the formula, computes a worked example, and explains when DEMA earns its keep over EMA, HMA, or TEMA on NIFTY 50 and BANK NIFTY.
Every standard moving average lags real price moves. The lag scales with the period: a 50-EMA lags by roughly 25 bars at trend changes. There are two ways to reduce lag:
Patrick Mulloy’s DEMA uses approach #2. By computing an EMA, then computing an EMA of that EMA (which lags even more), then subtracting the second from twice the first, you produce a series whose lag is approximately the negative of the original EMA’s lag — i.e., the lag has been cancelled.
EMA1 = EMA(P, n)
EMA2 = EMA(EMA1, n)
DEMA = 2 × EMA1 − EMA2
EMA1 is the standard n-period EMA of closing prices. EMA2 is the n-period EMA of EMA1 — a doubly smoothed series that lags both noise and trend. The subtraction step removes the lag without restoring the noise.
For an EMA(P, n) with smoothing factor α = 2/(n+1), both EMA1 and EMA2 use the same α. The recursion for each is identical to the standard EMA — the only addition is that EMA2 takes EMA1 (not P) as its input.
Suppose you have 30 daily closes of NIFTY 50. To compute DEMA(10):
Step 1. Compute EMA(P, 10) for every bar where there are at least 10 closes. The smoothing factor is α = 2/11 ≈ 0.1818. Each new EMA value blends 18.18% of today’s close with 81.82% of yesterday’s EMA — see our EMA formula post for the full derivation.
Step 2. Compute EMA(EMA1, 10) using the EMA1 series from step 1 as input. Same α, same recursion. The output is a smoother, more lagged version of EMA1.
Step 3. For every bar where both EMA1 and EMA2 are defined, compute 2 × EMA1 − EMA2. This is the DEMA value.
For example, if EMA1 today = 24,360 and EMA2 today = 24,300, then DEMA = 2 × 24,360 − 24,300 = 48,720 − 24,300 = 24,420. The DEMA value (24,420) sits ahead of EMA1 (24,360) — exactly what we wanted.
For an n-period EMA with smoothing factor α = 2/(n+1), the effective lag (center of mass of the weighting) is approximately (n−1)/2. For a 10-EMA, that is about 4.5 bars; for a 50-EMA, about 24.5 bars.
DEMA’s lag is approximately the negative of EMA’s lag, meaning DEMA leads price by a small amount in steady trends. In practice, the effective DEMA lag is close to zero — somewhere between −1 and +1 bar in most equity data. That is the difference DEMA achieves over EMA: a 5-bar lag advantage on a 10-period MA.
Importantly, DEMA does not “predict” the future. The lead it generates is a mathematical effect of the subtraction step, not foresight. In a sudden price spike, DEMA reacts fast — but it has no information that EMA does not also have. The advantage shows up at trend changes, where DEMA flips on or near the actual turn while EMA flips a few bars later.
DEMA and HMA share the same core idea: subtract a slower-lagging series from a faster-lagging one to cancel lag, then optionally re-smooth. The differences are in the construction:
| DEMA | HMA | |
|---|---|---|
| Subtraction step | 2 × EMA − EMA(EMA) |
2 × WMA(n/2) − WMA(n) |
| Final smoothing | None | WMA over √n |
| Smoothness in trends | Good | Slightly better |
| Speed at trend changes | Fast | Comparably fast |
| Sensitivity to single-bar volatility | Higher than HMA | Lower than DEMA |
In practice, HMA (with its final √n smoothing) is slightly cleaner than DEMA in noisy markets. DEMA is slightly faster on the leading bar. For NIFTY 50 daily trend definition, the two produce very similar curves — pick based on which one your charting platform implements better.
DEMA wins when:
EMA wins when:
For traders who already use 50-EMA on NIFTY daily as a regime filter, swapping in 50-DEMA produces a fractionally faster filter with comparable behaviour. Most discretionary traders cannot tell the difference visually unless they overlay both lines.
If subtracting once removes one layer of lag, why not subtract twice? That is the idea behind TEMA (Triple Exponential Moving Average):
TEMA = 3 × EMA1 − 3 × EMA2 + EMA3
Where EMA1 = EMA(P, n), EMA2 = EMA(EMA1, n), EMA3 = EMA(EMA2, n). TEMA removes two layers of lag and is correspondingly faster than DEMA.
The trade-off compounds: TEMA is more sensitive to noise than DEMA, which is more sensitive than EMA. For most traders, DEMA hits the sweet spot — fast enough to feel modern, smooth enough to be usable. TEMA is for situations where lag is genuinely intolerable. See our upcoming TEMA guide for the details.
A practical observation: 50-DEMA on NIFTY daily flips, on average, 1-2 trading days before 50-EMA at trend changes. Over 5 years, that adds up to 8-12 fewer trades caught at the bad end of a turn — a modest but consistent edge.
In Pine Script (TradingView):
//@version=5
indicator("DEMA", overlay=true)
length = input.int(50, title="Period")
ema1 = ta.ema(close, length)
ema2 = ta.ema(ema1, length)
dema = 2 * ema1 - ema2
plot(dema, color=color.orange, linewidth=2)
In Python / pandas:
import pandas as pd
def dema(prices: pd.Series, n: int) -> pd.Series:
ema1 = prices.ewm(span=n, adjust=False).mean()
ema2 = ema1.ewm(span=n, adjust=False).mean()
return 2 * ema1 - ema2
Three lines, including the def. Most charting platforms have DEMA built in.
DEMA is EMA with one layer of lag removed via a clever subtraction step. It reacts to trend changes faster than EMA, stays nearly as smooth, and has been used by trend-followers since Patrick Mulloy published it in 1994. For NIFTY 50 traders who like EMA as a trend filter but find it slightly slow, DEMA is a clean upgrade. For traders who already use HMA, DEMA does roughly the same job — pick whichever your charting platform implements more accurately.
As always, the moving average is one ingredient. Pair DEMA with the regime classifier, whipsaw tracker, and multi-timeframe alignment tools on emaindicator.com to filter trades to the contexts where DEMA is most reliable.