IVBULIS IVBUL GAMES
EN
ENLVRU
GAMES
Menu

Moving averages

Simple Moving Average

SMA

The simple moving average is the arithmetic mean of a fixed number of consecutive observations. As a new observation enters the window, the oldest one leaves, so every included value always has equal influence.

01 / Formula

Formula

SMAₜ = (Pₜ + Pₜ₋₁ + … + Pₜ₋ₙ₊₁) / n

Notation

SMAₜ
simple moving average at time t
Pₜ₋ᵢ
observed price or value i periods before time t
n
number of observations in the rolling window

02 / Explanation

A small numerical example

Suppose five monthly closing prices are €100, €104, €102, €108 and €111. The five-period SMA is:

(100 + 104 + 102 + 108 + 111) / 5 = 105

If the next closing price is €115, the window drops €100 and includes €115. The updated SMA becomes (104 + 102 + 108 + 111 + 115) / 5 = 108.

How the indicator is calculated

  1. Choose a window length that matches the frequency and purpose of the analysis.
  2. Take the latest n observations, including the current one.
  3. Add those observations and divide the total by n.
  4. Move the window forward by one period and repeat.

A longer window produces a smoother series but reacts more slowly. A shorter window follows recent movements more closely, while retaining more short-term variation.

Practical application

SMA is useful for describing the direction and level of a noisy time series. An analyst can compare a market price with its SMA, compare a short-window SMA with a long-window SMA, or use it as a baseline for evaluating other smoothing methods. The same calculation can summarise prices, volumes, rates or operational measurements when equal treatment of observations is appropriate.

Advantages

  • The calculation is transparent and easy to reproduce.
  • Every observation within the window receives the same weight.
  • It provides a stable baseline for comparing more responsive moving averages.
  • Its fixed window makes the underlying data scope immediately understandable.

Limitations

  • Equal weighting may understate the relevance of the newest information.
  • The average reacts only when values enter or leave the selected window.
  • A sharp old observation can cause a visible change when it drops out.
  • Window choice is subjective and does not remove uncertainty or forecast future values by itself.

Comparison with EMA and WMA

Unlike the exponential moving average, SMA does not retain a diminishing influence from observations outside a strict window. Unlike the weighted moving average, it does not assign a custom or linearly declining set of weights. SMA is therefore the simplest of the three, but usually the least responsive when they use comparable periods.