# Double Exponential Moving Average (DEMA): Formula and Use

URL: https://emaindicator.com/blog/double-exponential-moving-average/
Published: 2026-05-13T09:00:00+05:30
Modified: 2026-05-06T06:00:00+05:30
Category: Indicators
Type: Spoke (hub: moving-averages-complete-guide)

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.

## The core idea — lag and how to remove it

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:

1. **Shorten the period.** This works but increases noise — a 5-EMA reacts fast but whipsaws in chop.
2. **Subtract a slower-lagging series from a faster-lagging series.** The over-correction cancels most of the lag without shortening the period.

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.

## The formula

```
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.

## A worked example — DEMA(10) on NIFTY 50

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](/blog/exponential-moving-average-formula/) 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.

## How much lag does DEMA remove?

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 vs HMA — both are lag-reducing tricks

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 vs EMA — when each wins

DEMA wins when:

- You want to catch trend changes 1-3 bars earlier than EMA at the same period.
- The instrument is reasonably trend-following (NIFTY 50 in trending phases, single stocks with clean direction).
- You can tolerate slightly more sensitivity to single-bar moves.

EMA wins when:

- You want maximum smoothness for trend definition.
- The instrument is choppy or news-driven (BANK NIFTY around RBI policy days, single stocks around earnings).
- You combine the moving average with a slow filter — in which case the EMA's lag is less of a problem.

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.

## DEMA vs TEMA — pushing the trick further

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](/blog/triple-exponential-moving-average/) for the details.

## Common DEMA periods on Indian indices

- **9-DEMA / 14-DEMA** on 5-min and 15-min — intraday momentum
- **21-DEMA** on 15-min — intraday trend bias
- **50-DEMA** on daily — primary trend filter (a faster alternative to 50-EMA)
- **100-DEMA / 200-DEMA** on daily — long-term filters

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.

## Implementation

In **Pine Script** (TradingView):

```pine
//@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**:

```python
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.

## Putting it together

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](/nifty-regime/), [whipsaw tracker](/whipsaw-tracker/), and [multi-timeframe alignment](/timeframe-alignment/) tools on emaindicator.com to filter trades to the contexts where DEMA is most reliable.

## Frequently asked questions

**What is the Double Exponential Moving Average?**

DEMA is a moving average defined as 2 × EMA(P, n) − EMA(EMA(P, n), n). It was developed by Patrick Mulloy in 1994 as a way to retain the smoothness of EMA while removing most of the lag inherent in any moving-average calculation. The 'double' refers to using two nested EMAs.

**What is the formula for DEMA?**

DEMA = 2 × EMA(P, n) − EMA(EMA(P, n), n). Compute the n-period EMA of price. Then compute the n-period EMA of that EMA series. Subtract the second from twice the first. The result leads price by approximately the same amount that the original EMA lagged.

**Is DEMA better than EMA?**

DEMA reacts to trend changes earlier than EMA at the same period — usually by 1-3 bars on daily charts. The trade-off is that DEMA is slightly more sensitive to single-bar volatility because the lag-removal step amplifies the effect of fresh data. For trend-following with quick exits, DEMA can be preferable; for slower trend definition, EMA is steadier.

**What is the difference between DEMA and TEMA?**

TEMA (Triple Exponential Moving Average) extends the same idea by one more layer: TEMA = 3 × EMA − 3 × EMA(EMA) + EMA(EMA(EMA)). DEMA removes one layer of lag, TEMA removes two. TEMA is even faster than DEMA but also more sensitive to noise — the trade-off compounds with each additional EMA in the chain.

**What are the best DEMA settings for trading NIFTY?**

On NIFTY 50 daily, common DEMA periods are 9, 14, and 21 for intraday signals; 50 for swing-trade trend; 100 or 200 for long-term filter. As with any moving average, shorter periods give faster but noisier signals. DEMA at 21 on the 15-minute chart is a popular intraday setting for Indian-index momentum traders.