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Miha Kralj
49 lines
1.5 KiB
Markdown
49 lines
1.5 KiB
Markdown
# EMA: Exponential Moving Average
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period = 10
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EMA needs very short history buffer and calculates the EMA value using just the previous EMA value. The weight of the new datapoint (k) is k = 2 / (period-1)
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## Calculation
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There is an adopted practice to calculate $SMA$ when $n < period$.
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$$
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EMA_n = \left\{ \begin{array}{cl}
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\frac{1}{p}\left( data_{n}-data_{n-p}\right)+SMA_{n-1} & : \ n \leq period \\
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{k}\times ({data_{n}} - EMA_{n-1}) + EMA_{n-1} & : \ x > period
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\end{array} \right.
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$$
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## Reference Calculation
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period = 5
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```
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TSeries data = new() {81.59, 81.06, 82.87, 83.00, 83.61, 83.15, 82.84, 83.99, 84.55, 84.36, 85.53, 86.54, 86.89, 87.77, 87.29};
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EMA_Series ema = new(data, 5, useNaN: false);
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EMA_Series ema_nan = new(data, 5, useNaN: true);
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for (int i=0; i< data.Count; i++)
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Console.WriteLine($"{i}\t{data[i].v,7:f2}\t{ema_nan[i].v,7:f3}\t{ema[i].v,7:f3}");
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```
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|#|input|ema_NaN|ema|
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|--|:--:|:--:|:--:|
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|0| 81.59| NaN| 81.590|
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|1| 81.06| NaN| 81.325|
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|2| 82.87| NaN| 81.840|
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|3| 83.00| NaN| 82.130|
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|4| 83.61| 82.426| 82.426|
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|5| 83.15| 82.667| 82.667|
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|6| 82.84| 82.725| 82.725|
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|7| 83.99| 83.147| 83.147|
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|8| 84.55| 83.614| 83.614|
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|9| 84.36| 83.863| 83.863|
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|10| 85.53| 84.419| 84.419|
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|11| 86.54| 85.126| 85.126|
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|12| 86.89| 85.714| 85.714|
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|13| 87.77| 86.399| 86.399|
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|14| 87.29| 86.696| 86.696|
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## References
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- https://en.wikipedia.org/wiki/Exponential_smoothing |