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# Exponential Moving Average

Discussion in 'Trading' started by rrisch, Apr 14, 2002.

1. ### rrisch

Can anyone explain why a 10% EMA is associated with 19 days? I am wondering where the familiar formula,
Percentage = 2/(N + 1), comes from.

3. ### rrisch

There is no explanation there. He just gives the rule I stated. He has another formula: Moving Average Length = 1 + CycleLength/2, but I don't see the connection of that with my question.

4. ### limitdown

Uh, your question conveys the idea that you're using EMA for something that it wasn't designed for, and you weren't able to find anything even close to it/similar to its functionality.

Essentially, its objective to to provide a "smoothed" average line, based on, as you said, 19 periods/20 periods. This can be varied as you need. The objective is to provide a consistent moving average over multiple -multi-period intervals; a consistent moveing average over many days, with each of those days having a lessor impact upon that average, than just a simple moving average.

SMA is a truer average for a 1 time frame interval (whether that interval is 1 hour (within a 5 min chart) or 1 day (within a 15min chart).

EMA is a truer average over a broader period of time, closer to the Bollinger Band theorim, which uses 2 standard deviations from norm. EMA is closer, although not exactly, 1 deviation from norm.

If the configuration of the EMA is 1 less period within the time frame (i.e. 19 within 20) its because it needs one period to base its reference point from in its calculation. Hence, you have to start from somewhere and then average in the other periods and reflect it on its line chart. Simply put period one is fully discounted in the calculation. If you were to force the calculation to 20 periods for a 20 period EMA, then you'd have a mathematical problem which is similar to dividing by zero.

hope that makes some useful sense....

5. ### rrisch

Well thanks for trying Limitdown. Unfortunately, what you said makes absolutely no sense to me. The question was why is a 10% EMA should be associated with 19 periods, a 5% associated with 39 periods, etc. By the way, a correspondent told me there might be an explanation in Chande's book. Anybody have it and can let us know is that is true? Thanks.

6. ### dottom

The time period is just a way to determine the "exponent" in an exponential moving average. To calculate the exponent, divide 2 by the time period.

A percentage is just another way to determine the "exponent". The exponent percentage and time period are related by the formula Time Periods = (2 / Percentage) - 1.

So when you are talking about a 10% EMA or a 19-day EMA, your question shouldn't be "why am I using a %" or "why am I using a time period" but the question really is "what is the exponent I am using to smooth my average?"

Here's an example of how the "exponent" part of an EMA works.

To construct a 20 day exponential moving average you must first construct a 20 day simple moving average. This simple moving average is the starting point for the exponential moving average. Assume that the simple moving average value for day 20 is 42; the simple moving average value for day 21 is 43; and the simple moving average value for day 21 is 44. We then subtract the day 20 moving average value from day 21 simple moving average value and get a difference of 1.00. This value (1.00) is multiplied by an exponent. In this case, the exponent is .1. We then add .1 to the simple moving average value of day 20. The exponential moving average value of day 20 now becomes 42.100. And this goes on indefinitely. To calculate the exponent, divide 2 by the time period. In our case, we divided 2 by 20 to arrive at .1.

8. ### rrisch

Thank you TriPack. Unlike the other people who replied, you at least understood the question. . AFAIK, the appelation, "exponential" applied to this moving average, is a misnomer. It should be called the "geometric" moving average since the weights used, are the same as the weights for the geometic distribution, described in books on probability and statistics. I don't see what the "Rule of 70" of the reference, has to do with my question, but perhaps some other reader can explain it.

10. ### rrisch

Interesting reference Dbottom, but he doesn't give the formula we are used to. Here is a quote:

"If we were sampling the data at 20 times/second (h = 0.05) then the value of N is (0.8/0.05) = 16 and a = (16/17) = 0.9412".

The a is 1/100 of the percentage of the stock chart EMA. If you solve, 16/17 = 2/(days + 1), you get, days = 1.125. I can't relate that number to what he says.

#10     Apr 15, 2002
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