QuanTAlib/docs/SMA.md

SMA: Simple Moving Average

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 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

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

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);

#	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

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