QuanTAlib/docs/EMA.md

EMA: Exponential Moving Average

period = 10

EMA needs very short history buffer and calculates the EMA value using just the previous EMA value. The weight of the new datapoint (k) is k = 2 / (period-1)

Calculation

There is an adopted practice to calculate SMA when n < period.

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} & : \ x > period
\end{array} \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};
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	ema_NaN	ema
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	82.667	82.667
6	82.84	82.725	82.725
7	83.99	83.147	83.147
8	84.55	83.614	83.614
9	84.36	83.863	83.863
10	85.53	84.419	84.419
11	86.54	85.126	85.126
12	86.89	85.714	85.714
13	87.77	86.399	86.399
14	87.29	86.696	86.696

References

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