SuperSmoother & EWMA

Both the SuperSmoother and EWMA are online filters that smooth noisy time series one observation at a time. They share a single tuning knob (the period ) so they can be compared directly.

The SuperSmoother is a two-pole Butterworth filter that removes high-frequency noise with very little lag. EWMA applies exponential weighting with a decay derived from the same period, giving a simpler but slightly laggier result.

Use the slider below to see how the period affects both filters on BTCUSD daily closes.

EWMA smoothing factor

The EWMA smoothing factor is derived from the period:

Period and half-life

The half-life is the number of steps after which an observation's weight decays to half. For an exponential decay with half-life , the sum of all weights equals . This makes the period the continuous-time equivalent of the number of observations in a simple moving average:

The period is always larger than the half-life (by a factor of ), which means a period of 10 corresponds to a half-life of about 6.9 steps.