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fix on JMA

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Miha Kralj
2023-03-19 18:35:34 -07:00
parent bbd3ccb641
commit 167f20e3a8
13 changed files with 391 additions and 433 deletions
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docs/EMA.md
+25 -24
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@@ -1,22 +1,23 @@
# EMA: Exponential Moving Average
period = 10
![Alt text](./img/EMA_chart.svg)
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)
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
There is an adopted practice to calculate $SMA$ when $n < period$.
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.
$$
EMA_n = \left\{ \begin{array}{cl}
\frac{1}{p}\left( data_{n}-data_{n-p}\right)+SMA_{n-1} & : \ n \leq period \\
{k}\times ({data_{n}} - EMA_{n-1}) + EMA_{n-1} & : \ x > period
{k}\times ({data_{n}} - EMA_{n-1}) + EMA_{n-1} & : \ n > period
\end{array} \right.
$$
## Behavior
![Alt text](./img/EMA_chart.svg)
## Reference Calculation
period = 5
@@ -27,23 +28,23 @@ 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|
| #| 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