QuanTAlib/docs/EMA.md

EMA: Exponential Moving Average

Also known as exponentially weighted moving average, as it places greater weight on the most recent data points. EMA reacts more agressively to recent data changes and calculates the current value using just the previous EMA value and current data point. The weight applied to the new value is typically k = 2 / (period-1)

Calculation

EMA is a rolling calculation requiring only one historical data point to calculate the current value and is denoted as {EMA}_{p}{(data)} where p represents the period and data represents the list of data points.

Some implementations of EMA calculate a seeding value of EMA as a {SMA}_{p} when n < period - and start the EMA calculation only after the warm-up period. QuanTAlib offers an option to enable/disable SMA warm-up.

EMA_n = \left\{ \begin{array}{cl}
\frac{1}{p}\left( data_{n}-data_{n-p}\right)+SMA_{n-1} & : \ n \leq period \\
{k}\times ({data_{n}} - EMA_{n-1}) + EMA_{n-1} & : \ n > period
\end{array} \right.

Behavior

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};
EMA_Series ema = new(data, 5, useNaN: false);
EMA_Series ema_nan = new(data, 5, useNaN: true);
for (int i=0; i< data.Count; i++)
    Console.WriteLine($"{i}\t{data[i].v,7:f2}\t{ema_nan[i].v,7:f3}\t{ema[i].v,7:f3}");

#	Input	QuanTAlib	TA-LIB	Skender	Pandas-TA	Tulip
0	81.59	81.590	NaN	NaN	NaN	NaN
1	81.06	81.840	NaN	NaN	NaN	NaN
2	82.87	81.840	NaN	NaN	NaN	NaN
3	83.00	82.130	NaN	NaN	NaN	NaN
4	83.61	82.426	82.426	82.426	82.426	82.426
5	83.15	82.667	82.667	82.667	82.667	82.667
6	82.84	82.725	82.725	82.725	82.725	82.725
7	83.99	83.147	83.147	83.147	83.147	83.147
8	84.55	83.614	83.614	83.614	83.614	83.614
9	84.36	83.863	83.863	83.863	83.863	83.863
10	85.53	84.419	84.419	84.419	84.419	84.419
11	86.54	85.126	85.126	85.126	85.126	85.126
12	86.89	85.714	85.714	85.714	85.714	85.714
13	87.77	86.399	86.399	86.399	86.399	86.399
14	87.29	86.696	86.696	86.696	86.696	86.696

References

• https://en.wikipedia.org/wiki/Exponential_smoothing