QuanTAlib/docs/WMA.md

WMA: Weighted Moving Average

period = 10

WMA is linearly weighted moving Average where the weights are linearly decreasing over the period and the most recent data has the heaviest weight.

Calculation

WMA is a rolling calculation that is looking backwards from the position {n} and is denoted as {WMA}_{p}{(data)} where p represents the period, w represents the assigned weight and data represents the list of data points:

WMA_p{(data)} = \frac{1}{\sum w }\sum_{i=n-p+1}^{n} w_i data_i

Weights w are linearly increasing from 1 to p. For example, the weights w for a p=5 would be {1, 2, 3, 4, 5}

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

#	input	wma_NaN	wma
0	81.59	NaN	81.590
1	81.06	NaN	81.237
2	82.87	NaN	82.053
3	83.00	NaN	82.432
4	83.61	82.825	82.825
5	83.15	83.066	83.066
6	82.84	83.100	83.100
7	83.99	83.399	83.399
8	84.55	83.809	83.809
9	84.36	84.053	84.053
10	85.53	84.637	84.637
11	86.54	85.399	85.399
12	86.89	86.031	86.031
13	87.77	86.763	86.763
14	87.29	87.121	87.121

References

• https://en.wikipedia.org/wiki/Moving_average#Weighted_moving_average
• Kaufman, Perry J. (2013) Trading Systems and Methods
• Murphy, J. (1999) Technical Analysis of the Financial Markets