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# 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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$$
SMA_p{(data)} = \frac{1}{p}\sum_{i=n-p+1}^{n} data_i
$$
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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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$$
SMA_{p,next} = SMA_{p,prev}+\frac{1}{p}\left( data_{n+1}-data_{n+1-p}\right)
$$
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## Implementation
`TSeries SMA_Series (TSeries source, int period = 0, bool useNaN = false)`
- SMA_Series returns TSeries list
- `source` : input of type TSeries; SMA_Series automatically subscribes to events of new data added to the source
- `period` : optional size of a lookback window; if set to 0, SMA calculates cumulative average across the whole source
- `useNaN` : if set to _true_ , SMA_Series will hide values within the initial period with NaN (for compatibility with other libraries)
## Behavior
## Reference Calculation & Validation
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period = 5
```
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};
SMA_Series sma = new(data, 5, useNaN: false);
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```
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| #| Input | **QuanTAlib** | _TA-LIB_ | _Skender_ | _Pandas-TA_ | _Tulip_ |
|--|:--:|:--:|:--:|:--:|:--:|:--:|
| 0| 212.80|**212.80**| _NaN_ | _NaN_ | _NaN_ | _NaN_ |
| 1| 214.06|**213.43**| _NaN_ | _NaN_ | _NaN_ | _NaN_ |
| 2| 213.89|**213.58**| _NaN_ | _NaN_ | _NaN_ | _NaN_ |
| 3| 214.66|**213.85**| _NaN_ | _NaN_ | _NaN_ | _NaN_ |
| 4| 213.95|**213.87**| _213.87_ | _213.87_ | _213.87_ | _213.87_ |
| 5| 213.95|**214.10**| _214.10_ | _214.10_ | _214.10_ | _214.10_ |
| 6| 214.55|**214.20**| _214.20_ | _214.20_ | _214.20_ | _214.20_ |
| 7| 214.02|**214.23**| _214.23_ | _214.23_ | _214.23_ | _214.23_ |
| 8| 214.51|**214.20**| _214.20_ | _214.20_ | _214.20_ | _214.20_ |
| 9| 213.75|**214.16**| _214.16_ | _214.16_ | _214.16_ | _214.16_ |
|10| 214.22|**214.21**| _214.21_ | _214.21_ | _214.21_ | _214.21_ |
|11| 213.43|**213.99**| _213.99_ | _213.99_ | _213.99_ | _213.99_ |
|12| 214.21|**214.02**| _214.02_ | _214.02_ | _214.02_ | _214.02_ |
|13| 213.66|**213.85**| _213.85_ | _213.85_ | _213.85_ | _213.85_ |
|14| 215.03|**214.11**| _214.11_ | _214.11_ | _214.11_ | _214.11_ |
|15| 216.89|**214.64**| _214.64_ | _214.64_ | _214.64_ | _214.64_ |
|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
- Kaufman, Perry J. (2013) Trading Systems and Methods
- Murphy, J. (1999) Technical Analysis of the Financial Markets
