By Islam BarakaDefinitions
In plain terms
An EMA remembers its previous value and moves part of the way toward each new observation, so recent data matters more while older data fades gradually.
Technical
An EMA updates as EMA_t = EMA_(t-1) + alpha times (z_t - EMA_(t-1)), where alpha is a dimensionless smoothing constant between zero and one.
Scope
The recurrence does not by itself choose the seed, missing-data policy, rounding policy, or period label; those must be declared separately.
Formula
EMA_t = EMA_(t-1) + alpha * (z_t - EMA_(t-1))EMA_t = EMA_{t-1} + \alpha\left(z_t-EMA_{t-1}\right)| Symbol | Meaning | Unit |
|---|---|---|
EMA_t | Updated exponential moving average | same as input |
EMA_{t-1} | Previous exponential moving average | same as input |
z_t | Current observation | input unit |
\alpha | Smoothing constant | dimensionless |
Output unit: same as input
Examples
- With prior EMA 80, new input 100, and alpha 0.10, the updated EMA is 82.
Common misconceptions
- Older observations do not fall out of a standard EMA after exactly N periods.
Concept relationships
Prerequisites
Required by
- EMA Period-Label Equivalence
- Zweig Breadth Thrust
- Double Exponential Moving Average
- EMA of EMA
- Triple Exponential Moving Average
- Moving Average Convergence Divergence
- MACD Line
- True Strength Index
- First EMA of Momentum
- Second EMA of Momentum
- First EMA of Absolute Momentum
- Second EMA of Absolute Momentum
- Modern Keltner Variant
- Keltner EMA Basis
- Force Index
- Raw Force
- Price–Volume Unit
- Force EMA Seed
- Force EMA Update
- Force Index Warm-Up
- Force Index Zero-Change State
- Force Index Zero-Volume State
- Force Index Recursive Revision
- Force Index versus VPT
Where this concept is used
Tutorials planned
These catalogued topics use this concept, but their complete build has not shipped yet.
- D04-F02-A01 Prerequisite
- D04-F02-A02 Prerequisite
- D04-F02-A03 Prerequisite
- D04-F02-A04 Prerequisite
- D04-F02-A05 Prerequisite
- D04-F02-A06 Prerequisite
- D07-F01-A02 Primary
- D07-F01-A05 Prerequisite
- D07-F01-A06 Prerequisite
- D07-F02-A01 Prerequisite
- D07-F02-A02 Prerequisite
- D07-F03-A07 Prerequisite
- D07-F04-A04 Prerequisite
Evidence and governance
- Calculating the McClellan Oscillator McClellan Financial Publications · first party methodology
Supports: preferred label, short definition, technical definition, formula, units
Limits: Does not prescribe one universal initialization, missing-session, revision-resolution, rounding, or software interface policy.
- McClellan Oscillator StockCharts ChartSchool · secondary methodology
Supports: variant distinction
Limits: Platform symbols, displayed thresholds, universe choices, and implementation details are vendor-specific rather than universal methodology requirements.
- Reviewed by
- Islam Baraka
- Last reviewed
- 2026-07-26
- Next review
- 2027-07-26
- Record status
- published