0091104160_Noor Azizah_Exponential Moving Average1

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Stock Exchange Mathematics

EXPONENTIAL MOVING AVERAGE

A. Definition of Exponential Moving AverageAn exponential moving average (EMA), also known as an exponentially weighted

moving average (EWMA), is a type of infinite impulse response filter that applies weighting

factors which decrease exponentially. The weighting for each older data point decreases

exponentially, never reaching zero. As is known that the weighting of high school is a cause

which resulted in a delay of the signal change in trend. Giving equal weight to the EMA as well

as WMA, involving periods. Only difference is when the WMA the longer the period that we

use, the greater weight of the final, then the EMA opposite happened: the longer the period that

we use the smaller weighting that we use the last value.

B. Theory of Exponential Moving AverageAn exponential moving average is another type of moving average. In a simple moving

average, the price data has an equal weight in the computation of the average. Also, the oldest

price data is removed from the moving average as a new price is added to the computation. The

exponential moving average assigns a weight to the price data as the average is calculated.

Thus, the oldest price data in the exponential moving average is never removed, but it has only

a minimal impact on the moving average. This study displays the exponential moving averages

as a crossover system. You may select up to three different averages. Generally, the lengths are

short, intermediate, and long term. A commonly used system is 4, 9, and 18 intervals. An

interval may be in ticks, minutes, days, weeks or months; it is a function of the chart type.

A buy signal occurs when the short and intermediate term averages cross from below to

above the longer term average. Conversely, a sell signal is issued when the short and

intermediate term averages cross from above to below the longer term average. You can use the

same signals with two moving averages, but most market technicians suggest using longer

term averages when trading only two exponential moving averages in a crossover system.

Another trading approach is to use the current price concept. If the current price is above

the exponential moving averages, you buy. Liquidate that position when the current price

crosses below either moving average. For a short position, sell when the current price is below

the exponential moving average. Liquidate that position when current price rises above the

exponential moving averages.

Overall, the regulation on the EMA is the same as in high school because it shall be the

same way only a difference in the weighting value alone. Here's a summary:


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Parameters:

Period1 (4) - the number of bars, or period, used to calculate the first moving average. Period2 (9) - the number of bars, or period, used to calculate the second moving average. Period3 (18) - the number of bars, or period, used to calculate the third moving average.

C. Calculation Methods

( )

Where:

The coefficients represents the degree of weighting decrease, a constantsmoothing factor between 0 and 1. A higher discounts older observations faster.

Alternatively, may be expressed in terms ofNtime periods, where = 2/(N+1).

For example, N= 19 is equivalent to = 0.1. The half-life of the weights (the

interval over which the weights decrease by a factor of two) is approximately

N/2.8854 (within 1% ifN> 5).

Is the observation at a time period t. Is the value of the EMA at any time period t.

This formulation is according to Hunter (1986). By repeated application of this formula for

different times, we can eventually write St as a weighted sum of the data points Yt, as:

( ( ) ( ) ( )

()) ( ) ()

For any suitable k = 0, 1, 2, ... The weight of the general data point is ( )

An alternate approach by Roberts (1959) uses Yt in lieu ofYt1

( )

This formula can also be expressed in technical analysis terms as follows, showing how the

EMA steps towards the latest data point, but only by a proportion of the difference (each time)

( )

Expanding out each time results in the following power series, showing how the

weighting factor on each data pointp1,p2, etc., decreases exponentially:

( ( ) ( ) ( ) )


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()()

()

()()(),

( ) ( )

In theory this is an infinite sum, but because 1- is less than 1, the terms become smaller and

smaller, and can be ignored once small enough. The denominator approaches 1/, and that

value can be used instead of adding up the powers, provided one is using enough terms that the

omitted portion is negligible.

The N periods in an N-day EMA only specify the factor. N is not a stopping point for the

calculation in the way it is in an SMA or WMA. The first N data points in an EMA represent

about 86% of the total weight in the calculation.

The power formula above gives a starting value for a particular day, after which the successive

days formula shown first can be applied.

The question of how far back to go for an initial value depends, in the worst case, on the data. If

there are huge p price values in old data then they'll have an effect on the total even if their

weighting is very small. If one assumes prices don't vary too wildly then just the weighting can

be considered. Simple approximation

D. Graphics Analysis


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In theory, every previous closing price on a set of data used in the calculation of each EMA thateventually form the EMA line. While the impact of past data over the longer shrinking, henever entirely disappeared. This is true regardless of the period EMA specifications. Theinfluence of past data more rapidly shrinking in the shorter EMA. But again, they'll neverdisappear completely.


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- The difference between SMA and EMAIn general, the difference between the exponential moving average and the simple moving

average would seem slim. For this example, which uses only 20 days of the data market, the

difference is minimal, although still distinct. Exponential moving average is consistently closerto the actual price. On average, closer EMA 3/8 points to the actual price of the SMA.

Observations in table and graph above shows that from day 10 to day-to-20, EMA is nearer to

the actual price of the SMA in 8 cases of the 11 cases were observed. The average absolute

difference between the EMA with the actual price is 1.52, while the school has an average

absolute difference of 1.69. This means that on average, the EMA is at 1.52 points above or

below the actual price, and SMA is at 1.69 points above or below the actual price. By the time

Kodak stopped falling and began trading on the horizontal direction, high school still continues

to decline. During this period, high school closer to the actual price of the EMA. EMA began tomove away from the actual price, and continue to stay away. This is caused by the actual price


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from the horizontal. Because of this slowness, SMA continues to go down and almost touch the

actual price on Dec. 13.

F. Conclusion-Advantages

Calculation of the EMA is a little more complex than the SMA but has the advantage that a

large record of data covering each and every closing price for the last 200 days (or however

many days are being considered) does not have to be kept. All you need are the EMA for the

previous day and today's closing price to calculate the new Exponential Moving Average. If

EMA done through the calculation of Mean Absolute Percentage Error (MAPE), the EMA

will give a smaller error than others. And then, EMA are compactness (it only requires two

lines on a spreadsheet - today and yesterday), and because they are more influenced bycurrent prices.

- DisadvantagesCalculation of the EMA is a little more complex than the SMA and just as a guide, the more

sensitive an indicator it will be very helpful to predict the price. But conversely, the more

sensitive it will be more and more are also generated false signals, which means that the

signal could be given was wrong or did not last long.

References:

- http://en.wikipedia.org/wiki/Moving_average- http://belajarforex.com/walking-lamb/6-moving-average-ma.htmlhttp://instaforex.co.id/belajar-forex-gratis/category/sekolah-forex/3-sekolah-

dasar/3-4-kelas-4/3-4-3-exponential-moving-average/

- http://www.pandacash.com/technical-analysis/moving-average/exponential.htmhttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:mov

ing_averages

- http://www.new.quote.com- http://elearning.gunadarma.ac.id/.../BAB%207.%20INDIKATOR-INDIKATOR
http://en.wikipedia.org/wiki/Moving_averagehttp://en.wikipedia.org/wiki/Moving_averagehttp://belajarforex.com/walking-lamb/6-moving-average-ma.htmlhttp://belajarforex.com/walking-lamb/6-moving-average-ma.htmlhttp://instaforex.co.id/belajar-forex-gratis/category/sekolah-forex/3-sekolah-dasar/3-4-kelas-4/3-4-3-exponential-moving-average/http://instaforex.co.id/belajar-forex-gratis/category/sekolah-forex/3-sekolah-dasar/3-4-kelas-4/3-4-3-exponential-moving-average/http://instaforex.co.id/belajar-forex-gratis/category/sekolah-forex/3-sekolah-dasar/3-4-kelas-4/3-4-3-exponential-moving-average/http://instaforex.co.id/belajar-forex-gratis/category/sekolah-forex/3-sekolah-dasar/3-4-kelas-4/3-4-3-exponential-moving-average/http://instaforex.co.id/belajar-forex-gratis/category/sekolah-forex/3-sekolah-dasar/3-4-kelas-4/3-4-3-exponential-moving-average/http://www.pandacash.com/technical-analysis/moving-average/exponential.htmhttp://www.pandacash.com/technical-analysis/moving-average/exponential.htmhttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://www.new.quote.com/http://www.new.quote.com/http://www.new.quote.com/http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://www.pandacash.com/technical-analysis/moving-average/exponential.htmhttp://instaforex.co.id/belajar-forex-gratis/category/sekolah-forex/3-sekolah-dasar/3-4-kelas-4/3-4-3-exponential-moving-average/http://instaforex.co.id/belajar-forex-gratis/category/sekolah-forex/3-sekolah-dasar/3-4-kelas-4/3-4-3-exponential-moving-average/http://belajarforex.com/walking-lamb/6-moving-average-ma.htmlhttp://en.wikipedia.org/wiki/Moving_average

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