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# Exponential Moving Average

Exponential Moving Average calculation by candles

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Well, after a long break, let's continue to deal with technical indicators.

For those who still do not know what are the technical indicators, candles and currency pairs I recommend start the reading from the first article of the series - Simple Moving Averageе. And we will cut to the chase.

By the way, the break was partly due to the fact that I felt a pressing need to deal with the exponential smoothing, which resulted in the creation of three articles - Exponential smoothing, Double exponential smoothing and Triple exponential smoothing.

Now I feel quite savvy in theory, to tell, and, as usual, to calculate Exponential Moving Average.

Last time I wrote about Weighted moving average. It was devised so the latest data has a great influence on the result of averaging. That is, so the indicator has been more sensitive to the unexpected reversals in the trend.

The exponential moving average also uses this principle. The exponential smoothing method itself was invented a long time ago (see articles above) and in the form of a simple exponential smoothing it has turned into a technical indicator. The calculation, as usual, is carried out for the last n periods, hence the name moving.

The basic formula is taken from the exponential smoothing.

$S_t = \alpha y_{t-1} + (1-\alpha)S_{t-1}$

We just need to determine the initial S and the coefficient $\alpha$.

In the case exponential smoothing, I'll remind you, the following approach is used:
$S_1$ - undefined
$S_2 = y_1$
and $\alpha$ is selected so as to minimize the mean square error.

In the case of the exponential moving average everything is very different. In those sources/articles/source code that I have seen the following approach is used:
$S_1$ - undefined
...
$S_{n-1}$ - undefined
$S_n=\frac{\sum_{i=1}^{n}y_i}{n}$, that is, the simple average for n periods

$\alpha$ calculated in the following voluntarist manner
$\alpha=\frac{2}{n+1}$

It's clear that such alpha has nothing to do with such minimum mean square error, but it is fulfilling its goal - the influence of older data decreases faster than in the case of just weighted moving average.

To see this, just compare the following charts

#### Weights comparison with the weighted moving average and the exponential moving average

Digits after the decimal point: 4
Current value

Value weight change with exponential smoothing

Here is the calculator itself. As usual, the default data used are USDJPY candles with a 15-minute compression. The exponential moving average is calculated and for comparison you can display simple and weighted moving averages on the graph.

#### Exponential Moving Average

Digits after the decimal point: 2
Moving average

#### Candles for USDJPY

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