Exponential Moving Average Calculation

neil.p.b

Can anyone tell me if there's a direct connection between the actual formula for an EMA:



where alpha is a specified weighting between 1 and 0.


And the formula used for technical analysis:



where alpha = 2/(n+1) and n is equal to the number of days in the EMA.

Or is the latter just a 'sort of' EMA.


Thanks

neil.p.b

Any chance a mod could move this to the maths forum for me?

Thanks

D-Generate

Set k=0, t = 1. Then you will see that they are equivalent. It follows for all k and t > 0.

A decent book for technical analysis is New Trading Systems and Methods by Kaufman, pretty good at giving a bit more detail about the different technical indicators.

neil.p.b

But the alpha values are still both variable, so giving the first formula a different weighting will change the outcome. I guess what i'm wondering is: is there a connection between the chosen weighting in the first formula, to the size of N in the second. E.g. if N is equal to 12 in the second formula, is there a set value for alpha to be in the first formula so that they give the same answer?

Thanks for the reply

EDIT: Sorry i just noticed i posted the wrong formula, it should read

St = α(Yt + α(1-α)Yt-1 + α(1-α)^2*Yt-2 +.....+ α(1-α)^k*Yt-k)