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     peritech
Member
Username: peritech
Post Number: 10
Registered: 09-2003Rating: N/A
Votes: 0
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| | Sunday, February 18, 2007 - 05:49 pm: |  
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One smoothing factor that is quoted for use in the calculation of Exponential Moving Averages is 2/(N+1) where N is the number of items in the average.
Wikipedia gives a reason for this which if far from easy to understand. It was the only one I could locate.
I wonder if anyone has come across an alternative derivation for this term that they could let me have, please
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smallworld
Member
Username: smallworld
Post Number: 523
Registered: 01-2004Rating: N/A
Votes: 0
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| | Monday, February 19, 2007 - 11:15 am: |
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http://www.incrediblecharts.com/technical/moving_average_construction.htm
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peritech
Member
Username: peritech
Post Number: 11
Registered: 09-2003Rating: N/A
Votes: 0
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| | Monday, February 19, 2007 - 11:43 am: |
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Thank you for responding to my request. Yes, the determination of smoothing factors from the relationship 2/(N+1) as cited in the reference is clear - but why 2(N+1), why not 3/(N+1) or 2/(N+3)?
You will see in Wikipedia (about 1/2 way down the page):
http://en.wikipedia.org/wiki/Weighted_moving_average
an attempt to derive the 2/(N+1) term. I found this difficult to follow and was seeking an alternative. It appears, and I'm not even too sure of this, to be based on the concept that the total of all of the individual weighting factors should approach 1, but I wonder why?
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colin_twiggs
Member
Username: colin_twiggs
Post Number: 2804
Registered: 09-2002Rating: N/A
Votes: 0
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| | Monday, February 19, 2007 - 11:57 am: |
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2/(n+1) is to convert days to a percentage. Exponential MAs are not calculated using days, although that is how most of us express them, but as percentages.
The best way to prove this is to plot simple MAs against exponential MAs and compare the results.
Regards, Colin
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peritech
Member
Username: peritech
Post Number: 12
Registered: 09-2003Rating: N/A
Votes: 0
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| | Monday, February 19, 2007 - 12:35 pm: |
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Thankyou Colin for your comment. I am "afflicted" with the desire to go back to first principles and see why the term 2/(N+1) arose. The requirement goes back to a book I started to write some years back when I saw that as being the only way I would obtain an understanding of technical analysis.
The book has turned into an albatross that periodically plagues me to find more details on points I do not understand.
I think that most aspects of the mathematics of moving averages are clear enough - the relevant page of the book is attached - but the logic behind selecting a particular smoothing factor still escapes me. I can easily accept that experience could show that one is better than another but if I knew why then that would be much better!
The next problem will be if someone looks at the attached page and finds a mistake or two or more!  PDF Page - Moving Averages
m_av.pdf (221.3 k) |
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colin_twiggs
Member
Username: colin_twiggs
Post Number: 2809
Registered: 09-2002Rating: N/A
Votes: 0
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| | Monday, February 19, 2007 - 02:28 pm: |
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Can't help you there. Let us know if you find the proof.
Regards, Colin
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sam111
Member
Username: sam111
Post Number: 1
Registered: 03-2007Rating: N/A
Votes: 0
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| | Saturday, March 17, 2007 - 08:19 am: |
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I'm no mathematician, peritech, but maybe the reason the formula 2/(N+1) is used is so that after only 1 day the result of the formula is equal to 1 or 100%
The other formulas that you mentioned don't satisfy that condition, although the Welles Wilder formula α=1/N does.
Cheers Sam
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victor_h
Member
Username: victor_h
Post Number: 129
Registered: 04-2004
Rating: N/A
Votes: 0
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| | Saturday, March 17, 2007 - 03:27 pm: |
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Some lateral thinking is required here......
Instead of thinking of the smoothing factor as 2/(N+1) of todays value,
think of it as a smoothing factor of (N-1)/(N+1) of yesterdays value.
Remember, when they are added together...
2/(N+1) + (N-1)/(N+1) = 1
When the sum of the factors = 1, only then can the eMA be plotted on the same scale along with the price chart.
(Message edited by victor_h on March 17, 2007)
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sam111
Member
Username: sam111
Post Number: 4
Registered: 03-2007Rating: N/A
Votes: 0
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| | Saturday, March 17, 2007 - 04:10 pm: |
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Some software garbled my cut'n'paste of the Welles Wilder formula from Wikipedia.
What I was trying to post was Welles Wilder smoothing factor = 1/N
Thanks for your thoughts Victor, I knew I was out of my depth!
Cheers Sam
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