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The EMA is a recursive formula, as it depend's upon it's own prior output. As such, the EMA actually has a lookback that is infinitely long. However, since the effect of historical bars trail off exponentially toward zero, for practical considerations, its lookback is indeterminate. So, how then to express the lookback of an EMA? It was decided that EMA "lookback" would be associated with a more concrete and measureable item: lag. An EMA with a chosen N, when applied to a straight "price" line, will have the same lag regardless of the momentum (angle, slope) of that line.
Bacause of this invariance to slope, lag can be predicted directly from N. Here are the lags for 3 basic moving averages:
TYPE LAG
---------------------
Simple (N-1)/2
Exponential (N-1)/2
Weighted (N-1)/3
Mark Jurik
Jurik Research
http://www.jurikres.com
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From: Paul Altman
Sent: Tuesday, September 26, 2000 8:14 PM
To: omega-list@xxxxxxxxxx
Subject: Exponential moving average
Could someone please explain to me what an exponential moving average is.
Here's what I've always assumed it is, and how I've always used it:
SC = Smoothing Constant
Today's EMA= ((Today's price) * SC) + ((Yesterday's EMA) * (1 - SC))
If the above is correct, then why do people talk of a "40-day" ema? The
only variable I see here as an input is the smoothing constant, which
usually seems to be useful in a range from ~0.1 to ~0.25.
Since # days is not an input, what's everyone talking about when they
mention a specific lookback period? Seems to me that Today's EMA value
includes a molecule or two of pricing that occurred even 10 years
ago. I.e., by it's very nature, an EMA includes all historical prices
before it, although the distant past ones are under-weighted to the point
of virtual non-existence.
I must have the formula wrong, though the formula I use is simple to use
and seems to work just fine when I want a moving average that's more
weighted to recent events than to ancient ones.
-Paul
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