An *exponentially smoothed moving average* is a weighted moving
average in which the weight factors are powers of *S*, the *smoothing constant*. An exponentially smoothed moving average is
computed over *all* the data accumulated so far instead of being
chopped off after some number of days. For day
*d* the
exponentially smoothed moving average is:

But this is just a geometric sequence! The next term in such a
sequence is given by:
*A _{d}*=(1-

This reformulation makes the operation of smoothing very intuitive.
Every day, we take the old trend number
*A*_{d-1},
calculate the
difference between it and today's measurement *M _{d}*, then add a
percentage of that difference

For example, with the smoothing constant *S*=0.9 we use on weight
data, we calculate the new trend value *A _{d}* from the previous
trend value

In discussions of exponentially smoothed moving averages,
particularly their financial applications, beware of confusing
the smoothing constant *S* with the variant form *P*=1-*S* introduced
to simplify calculation and make the effect of the new data on the
moving average more apparent. *P* is often referred to as the
``smoothing percentage''; the term ``10% smoothing'' refers to a
calculation in which *P*=10/100=0.1 and hence *S*=0.9.

By John Walker