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Miha Kralj
49 lines
1.7 KiB
Markdown
49 lines
1.7 KiB
Markdown
# WMA: Weighted Moving Average
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period = 10
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WMA is linearly weighted moving Average where the weights are linearly decreasing over the _period_ and the most recent data has the heaviest weight.
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## Calculation
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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:
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$$
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WMA_p{(data)} = \frac{1}{\sum w }\sum_{i=n-p+1}^{n} w_i data_i
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$$
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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}
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## Reference Calculation
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period = 5
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```
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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};
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WMA_Series wma = new(data, 5, useNaN: false);
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WMA_Series wma_nan = new(data, 5, useNaN: true);
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for (int i=0; i< data.Count; i++)
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Console.WriteLine($"{i}\t{data[i].v,7:f2}\t{wma_nan[i].v,7:f3}\t{wma[i].v,7:f3}");
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```
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|#|input|wma_NaN|wma|
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|--|:--:|:--:|:--:|
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|0| 81.59| NaN| 81.590|
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|1| 81.06| NaN| 81.237|
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|2| 82.87| NaN| 82.053|
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|3| 83.00| NaN| 82.432|
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|4| 83.61| 82.825| 82.825|
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|5| 83.15| 83.066| 83.066|
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|6| 82.84| 83.100| 83.100|
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|7| 83.99| 83.399| 83.399|
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|8| 84.55| 83.809| 83.809|
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|9| 84.36| 84.053| 84.053|
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|10| 85.53| 84.637| 84.637|
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|11| 86.54| 85.399| 85.399|
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|12| 86.89| 86.031| 86.031|
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|13| 87.77| 86.763| 86.763|
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|14| 87.29| 87.121| 87.121|
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## References
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- https://en.wikipedia.org/wiki/Moving_average#Weighted_moving_average
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- Kaufman, Perry J. (2013) Trading Systems and Methods
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- Murphy, J. (1999) Technical Analysis of the Financial Markets |