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46 lines
1.4 KiB
Markdown
46 lines
1.4 KiB
Markdown
# The Math Behind ALMA
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## Components of ALMA
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ALMA is a single-formula moving average that incorporates elements of several advanced techniques:
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- Gaussian distribution
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- Weighted moving average
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- Offset parameter
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### ALMA Formula
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$ ALMA_t = \sum_{i=0}^{n-1} w_i \cdot P_{t-i} $
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Where:
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- $ALMA_t$ is the ALMA value at time $t$
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- $n$ is the window size (number of periods)
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- $P_{t-i}$ is the price at time $t-i$
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- $w_i$ are the weights
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### Weight Calculation
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The weights $w_i$ are calculated using a Gaussian distribution function with an offset:
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$ w_i = \exp\left(-\frac{(i - m)^2}{2s^2}\right) $
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Where:
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- $i$ is the position of the price in the window (0 to $n-1$)
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- $m$ is the offset of the Gaussian distribution, calculated as $m = \text{floor}(offset \cdot (n - 1))$
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- $s$ is the standard deviation of the Gaussian distribution, calculated as $s = \frac{n}{sigma}$
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### Parameter Definitions
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ALMA uses three main parameters:
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- **Window size** ($n$): Affects the overall reactivity of the indicator.
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- **Offset**: Influences the lag of the moving average. Lower values reduce lag but may increase noise.
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- **Sigma**: Controls the smoothness of the indicator. Higher values increase smoothness but may increase lag.
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### Computational Process
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For each new data point:
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- Calculate the weights for the entire window.
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- Apply these weights to the most recent $n$ prices.
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- Sum the weighted prices to produce the final ALMA value.
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