QuanTAlib/docs/SMA.md

SMA: Simple Moving Average

period = 10

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 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 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)

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}");

#	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://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