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![Alt text](./img/SMA_chart.svg)
# SMA: Simple Moving Average
SMA is one of the most basic trend-following indicators used in Technical Analysis. It is calculated as the *unweighted mean* of the previous $p$ (period) data-points.
period = 10
![Alt text](./img/SMA_chart.svg)
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.
## Calculation
SMA is a rolling calculation 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:
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:
$$
SMA_p{(data)} = \frac{1}{p}\sum_{i=n-p+1}^{n} data_i
$$
When calculating the value of next $SMA_{p,next}$ while knowing all previous SMA values, SMA calculation can be reduced to:
When calculating the value of the next $SMA_{p,next}$ while knowing all previous SMA values, SMA calculation can be reduced to:
$$
SMA_{p,next} = SMA_{p,prev}+\frac{1}{p}\left( data_{n+1}-data_{n+1-p}\right)
$$
## Implementation
``` csharp
SMA_Series mean = new(source: data, period: p, useNaN: false);
## Reference Calculation
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);
SMA_Series sma_nan = new(data, 5, useNaN: true);
for (int i=0; i< data.Count; i++)
Console.WriteLine($"{i}\t{data[i].v,7:f2}\t{sma_nan[i].v,7:f3}\t{sma[i].v,7:f3}");
```
- `TSeries source` - List of value tuples (DateTime, double)
- `int period` - Integer representing the period of SMA
- `bool useNaN` - if true, initial values from 1 to period-1 will be replaced with NaN. If false, the initial calculation will return values for SMA(length) instead of SMA(period)
## Comparison & Validation
Validation tests
Performance tests
## Visual analysis
|#|input|sma_NaN|sma|
|--|:--:|:--:|:--:|
|0| 81.59| NaN| 81.590|
|1| 81.06| NaN| 81.325|
|2| 82.87| NaN| 81.840|
|3| 83.00| NaN| 82.130|
|4| 83.61| 82.426| 82.426|
|5| 83.15| 82.738| 82.738|
|6| 82.84| 83.094| 83.094|
|7| 83.99| 83.318| 83.318|
|8| 84.55| 83.628| 83.628|
|9| 84.36| 83.778| 83.778|
|10| 85.53| 84.254| 84.254|
|11| 86.54| 84.994| 84.994|
|12| 86.89| 85.574| 85.574|
|13| 87.77| 86.218| 86.218|
|14| 87.29| 86.804| 86.804|
## References
- https://www.tradingtechnologies.com/help/x-study/technical-indicator-definitions/simple-moving-average-sma/
- 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