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2015-11-24 09:29:32

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**2015-11-24**

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Moving Averages

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Exponentially Weighted What is EMA

Computation Benefits

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We explored the advantage of a weighted moving average over a simple moving average; that advantage is the increased contribution, or influence, from the most recent data. We change the amount of influence by changing the length of the average interval, which in turn changes the weighting factors. We

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showed a 5day weighted moving average that uses the values 5, 4, 3, 2, and 1 as the weighting factors. Thus, the most recent datum has 5 times the influence of the oldest datum. A 10day weighted moving average would give the most recent datum 10 times the influence of the oldest datum.

The exponential moving average (EMA) provides the same benefit by weighting the most recent datum more heavily than all preceding data. However, the weighting factor is constant, but is still derived from the length of the averaging interval. The EMA weighting factor is designated by the lowercase Greek (alpha) and is computed as:

= 2 / (N +

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1)

where

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"N" is the number of days in the averaging interval. Using our 5day intervals from our previous examples, would be:

= 2 / (5 + 1) = 2 / 6 = 1 / 3 = 0.33

Every computation of the present 5day EMA value will use 0.33 as the weighting factor. So how is this a benefit over our previous methods? It isn't! This feature of EMA, by itself, provides no benefit because it weights each datum identically; which means that there's no "weighting" at all.

We've only shown how to compute the weighting factor, or coefficient, piece of the exponential moving average computation. The computation of each new EMA value is:

Remember to ignore the EMA data from Day1 through Day4. Notice that all 3 moving average lines have the same basic shape. That's because they each show the overall trend, which is rising as the data values increase and then decline as the data values are less than the moving average value. The value in each of the different average computation methods is how quickly the average reacts to the data and how

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each individual data value affects the average. The EMA rises more quickly than the SMA but not as quickly as the WMA. This is because the WMA "front weights" the data, and for Day5, Day6, and Day7 the data is rising. Since the EMA also contains the data from Day1 through Day4, those lesser values cause the EMA to rise more slowly. We can now use these different moving average methods to determine short and longterm trends in stocks, indices, mutual funds, currencies, or any other vehicle that trades on the world financial markets. These moving averages are combined to form composite indicators, or are used individually or in comparison to define trends.

Now that we've got these tools, we'll venture into some technical analysis indicators to see what such indicators can tell us about past actions and likely upcoming actions.

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