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Miha Kralj
51 lines
1.8 KiB
Markdown
51 lines
1.8 KiB
Markdown
# SMA: Simple Moving Average
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period = 10
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SMA is is an arithmetic moving average where the weights in SMA are **equally** distributed across the given period, resulting in a mean() of the data within the period.
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## Calculation
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SMA is a rolling calculation that is looking backwards from the position ${n}$ and is denoted as ${SMA}_{p}{(data)}$ where $p$ represents the period and $data$ represents the list of data points:
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$$
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SMA_p{(data)} = \frac{1}{p}\sum_{i=n-p+1}^{n} data_i
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$$
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When calculating the value of the next $SMA_{p,next}$ while knowing all previous SMA values, SMA calculation can be reduced to:
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$$
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SMA_{p,next} = SMA_{p,prev}+\frac{1}{p}\left( data_{n+1}-data_{n+1-p}\right)
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$$
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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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SMA_Series sma = new(data, 5, useNaN: false);
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SMA_Series sma_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{sma_nan[i].v,7:f3}\t{sma[i].v,7:f3}");
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```
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|#|input|sma_NaN|sma|
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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| 82.738| 82.738|
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|6| 82.84| 83.094| 83.094|
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|7| 83.99| 83.318| 83.318|
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|8| 84.55| 83.628| 83.628|
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|9| 84.36| 83.778| 83.778|
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|10| 85.53| 84.254| 84.254|
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|11| 86.54| 84.994| 84.994|
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|12| 86.89| 85.574| 85.574|
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|13| 87.77| 86.218| 86.218|
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|14| 87.29| 86.804| 86.804|
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## References
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- https://en.wikipedia.org/wiki/Moving_average#Simple_moving_average
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- Kaufman, Perry J. (2013) Trading Systems and Methods
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- Murphy, J. (1999) Technical Analysis of the Financial Markets |