Dr. Dobb's Journal September 1998

What Averaging Window?

Call me fussy, but if I'm using an average that has weights that decrease exponentially with the data's age, I'd like the characteristic time that governs this exponential decay to appear explicitly. The relationship between the more widely used alpha, and the less widely used characteristic time (Tau) that governs the decay of the exponential weights is alpha=exp(-dt/Tau) or Tau=-dt/ln(alpha). Here, dt is the sampling interval.

Although Tau can be loosely interpreted as the moving averaging window, bear in mind that exponential averaging windows are not as clear cut as ordinary equal weight-averaging windows. For example, although around 95 percent of the weights are associated with points less than 3*Tau time units old, a single monster data point -- despite being many more than three Taus old -- could still have a sizable impact on the average.

The largest possible averaging window is a function of numeric precision, with Taumax=-dt/ln(1-EPS)~=dt/EPS (EPS is the smallest number, such that 1+EPS>1).

-- J.C.G.