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Miha Kralj
57 lines
2.8 KiB
Markdown
57 lines
2.8 KiB
Markdown
# SMA: Simple Moving Average
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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 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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## Implementation
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`TSeries SMA_Series (TSeries source, int period = 0, bool useNaN = false)`
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- SMA_Series returns TSeries list
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- `source`: input of type TSeries; SMA_Series automatically subscribes to events of new data added to the source
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- `period`: optional size of a lookback window; if set to 0, SMA calculates cumulative average across the whole source
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- `useNaN`: if set to _true_, SMA_Series will hide values within the initial period with NaN (for compatibility with other libraries)
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## Behavior
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## Reference Calculation & Validation
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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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```
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| #| Input | **QuanTAlib** | _TA-LIB_ | _Skender_ | _Pandas-TA_ | _Tulip_ |
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|--|:--:|:--:|:--:|:--:|:--:|:--:|
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| 0| 212.80|**212.80**| _NaN_| _NaN_| _NaN_| _NaN_|
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| 1| 214.06|**213.43**| _NaN_| _NaN_| _NaN_| _NaN_|
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| 2| 213.89|**213.58**| _NaN_| _NaN_| _NaN_| _NaN_|
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| 3| 214.66|**213.85**| _NaN_| _NaN_| _NaN_| _NaN_|
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| 4| 213.95|**213.87**| _213.87_| _213.87_| _213.87_| _213.87_|
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| 5| 213.95|**214.10**| _214.10_| _214.10_| _214.10_| _214.10_|
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| 6| 214.55|**214.20**| _214.20_| _214.20_| _214.20_| _214.20_|
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| 7| 214.02|**214.23**| _214.23_| _214.23_| _214.23_| _214.23_|
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| 8| 214.51|**214.20**| _214.20_| _214.20_| _214.20_| _214.20_|
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| 9| 213.75|**214.16**| _214.16_| _214.16_| _214.16_| _214.16_|
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|10| 214.22|**214.21**| _214.21_| _214.21_| _214.21_| _214.21_|
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|11| 213.43|**213.99**| _213.99_| _213.99_| _213.99_| _213.99_|
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|12| 214.21|**214.02**| _214.02_| _214.02_| _214.02_| _214.02_|
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|13| 213.66|**213.85**| _213.85_| _213.85_| _213.85_| _213.85_|
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|14| 215.03|**214.11**| _214.11_| _214.11_| _214.11_| _214.11_|
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|15| 216.89|**214.64**| _214.64_| _214.64_| _214.64_| _214.64_|
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|16| 216.66|**215.29**| _215.29_| _215.29_| _215.29_| _215.29_|
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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 |