Arnaud Legoux Moving Average (ALMA)

Name Type Prerequisite Use Cases
Arnaud Legoux MA (ALMA) Trend OHLC Data Superior trend tracking that filters "noise" without sacrificing timing.

Definition

The Arnaud Legoux Moving Average (ALMA) is a moving average designed to reduce lag associated with traditional moving averages while preserving responsiveness and smoothness. It uses a Gaussian distribution to weight the prices in the moving window, allowing the user to control the offset (lag) and the width (sigma) of the distribution.

Mathematical Equation

ALMA applies a weight to the price at time \(t-i\) according to a Gaussian function:

\[ w_i = \exp \left( - \frac{(i - \text{offset})^2}{2 \sigma^2} \right) \]

Where:

  • \(i\) ranges from 0 to \(N-1\) (window size).

  • \(\text{offset} = \text{floor}(\text{offset\_fraction} \times (N - 1))\).

  • \(\sigma\) controls the width of the filter.

The ALMA value is the weighted sum of prices:

\[ ALMA_t = \frac{\sum_{i=0}^{N-1} w_i P_{t-i}}{\sum_{i=0}^{N-1} w_i} \]

Special cases

  • Maximum possible value: Unbounded (Follows Price)
  • Minimum possible value: Unbounded (bounded by 0)
  • Behavior: Follows the price like moving averages, acting as a smoother trend-following indicator with reduced lag. Plotted on the price chart.

Visualization

ALMA

Trading Significance

  1. Trend Identification: Like other MAs, ALMA helps identify the trend direction. An uptrend is indicated when price is above ALMA, and downtrend when below.

  2. Reduced Lag: ALMA is often preferred over SMA or EMA because it hugs the price action closer without introducing excessive noise, making it effective for signal generation in shorter timeframes.

  3. Support/Resistance: It frequently acts as dynamic support or resistance.