QuanTAlib/docs/indicators/averages/alma/calc.md

The Math Behind ALMA

Components of ALMA

ALMA is a single-formula moving average that incorporates elements of several advanced techniques:

• Gaussian distribution
• Weighted moving average
• Offset parameter

ALMA Formula

ALMA_t = \sum_{i=0}^{n-1} w_i \cdot P_{t-i}

Where:

• ALMA_t is the ALMA value at time t
• n is the window size (number of periods)
• P_{t-i} is the price at time t-i
• w_i are the weights

Weight Calculation

The weights w_i are calculated using a Gaussian distribution function with an offset:

w_i = \exp\left(-\frac{(i - m)^2}{2s^2}\right)

Where:

• i is the position of the price in the window (0 to n-1)
• m is the offset of the Gaussian distribution, calculated as m = \text{floor}(offset \cdot (n - 1))
• s is the standard deviation of the Gaussian distribution, calculated as s = \frac{n}{sigma}

Parameter Definitions

ALMA uses three main parameters:

• Window size (n): Affects the overall reactivity of the indicator.
• Offset: Influences the lag of the moving average. Lower values reduce lag but may increase noise.
• Sigma: Controls the smoothness of the indicator. Higher values increase smoothness but may increase lag.

Computational Process

For each new data point:

• Calculate the weights for the entire window.
• Apply these weights to the most recent n prices.
• Sum the weighted prices to produce the final ALMA value.