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The formula for an exponential moving average is:
EMAn = (1 - Alpha) * EMAn-1 + Alpha * Pricen
where Alpha = 2 / (1 + Len)
In words, the Exp. MA on Day n is (1 -Alpha) times the Exp. MA on the
previous day plus Alpha times the current Price on Day n. Thus, the
moving average is a (large) fraction of the previous moving average with
a (small) fraction of the new price added in. This tends to weight the
new price more heavily than a simple moving average; thus it is more
responsive to change while retaining some memory of the entire past. The
fractional coefficient Alpha is found from the "Length" by the formula
above. This is intended to show some type of equivalence between the EMA
and SMA; however, that's a little tenuous. This is a more efficient
computation than the simple moving average. Thus, for an EMA of length
49, you get an alpha coefficient of 2 / 50 = 0.04. This is the formula
that is built into most charting packages, like TradeStation.
This is a somewhat smoother computation than SMA, where days are all
weighted equally, with the old ones dropping completely out of the
calculation suddenly.
Allan
_________________________________________________
JamesinLA@xxxxxxx wrote:
>
> Hope someone can help me with this. Maybe I'm the only one who doesn't
> already know this? Anyway, I'm reading an old book about systems and it talks
> about moving averages in terms of "0.04 exponential average" and "0.20
> exponential", etc. It says the 0.04 average is the equivalent of a 49-day or
> 10 week average. Anyway, my question is how is this being computed? Please
> help.
>
> Jim
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