Exponential Moving Average — Technical Indicators

02 — Moving Averages

Exponential Moving Average#

Debated1 min read

◆ The PatternTrust recent data more than old, with weights that fade exponentially, as in smoothing and optimizer momentum

The Exponential Moving Average applies an exponential smoothing factor that weights recent prices more heavily.

Multiplier k = 2 / (N + 1)
EMA = (Close − EMA_prev) × k + EMA_prev

Because each new EMA is built on the previous, all past prices influence the result — but their weight decays exponentially.

Key pair: The 12-period and 26-period EMAs form the foundation of the MACD indicator.

More responsive than SMA to sudden price changes — preferred in faster-moving markets.

Worked example

Five-day EMA, so k = 2 / (5 + 1) = 1/3. On day 14 the EMA is 101.80; day 15 closes at 104, so EMA = 101.80 + (104 − 101.80) × 1/3 = 102.53. That is already above the five-day SMA (102.0): today’s close carries a third of the weight.

The example data: 15 days, used in every indicator here

Day	High	Low	Close	Volume
1	101	99	100	50,000
2	103	100	102	62,000
3	103	100	101	48,000
4	105	101	104	70,000
5	108	104	107	85,000
6	108	105	106	60,000
7	110	106	109	90,000
8	110	107	108	72,000
9	108	104	105	80,000
10	105	102	103	66,000
11	105	102	104	55,000
12	104	101	102	75,000
13	102	98	99	95,000
14	102	99	101	64,000
15	105	101	104	71,000

Where it misleads

It still lags, only less: it reacts faster than the SMA but still turns after the price has.
Faster also means noisier — more crossovers, and more false ones, in a choppy market.
The starting value matters. Seeded from the first close (as here) or from a simple average, the first values differ until the old weight has faded.

In code

df['ema5'] = df['close'].ewm(span=5, adjust=False).mean()   # k = 2/(5+1)

Python, in your browser — edit the code and run it again

Assumes import numpy as np, import pandas as pd, and a DataFrame df with columns high, low, close and volume — the 15 days above.

Sources

J. S. Hunter, “The Exponentially Weighted Moving Average”, Journal of Quality Technology 18(4), 1986 — the same smoother in industrial process control
Technical Analysis of the Financial Markets, J. J. Murphy, New York Institute of Finance, 1999

Last reviewed October 2026 · How this site checks its content · Report a mistake

Pattern bridge: Exponential weighting of recent data is exactly how Adam’s momentum tracks gradient history.

Linked from 5

← Previous

Simple Moving Average

Weighted Moving Average

Open in the full reader, with the topic sidebar