In [[statistics]], '''exponential smoothing''' refers to a particular type of moving average technique applied to time series data, either to produce smoothed data for presentation or to make forecasts.
Formula
Given a time series, yt, t = 1,...,T, the exponentially-smoothed series can be calculated from the following formulas:
where ω is the ''smoothing factor'', and 0 < ω < 1.
The exponential smoothing technique is an outgrowth of the simple moving average. The 
series is the fitted or forecasted value of the series.
How do we pick ω?
As ω gets closer to one, the smoothed series looks more like the original series, but lagged one period. The series will not be very 'smooth.' As ω gets closer to zero, the series looks more like the first value of the series. The series will look very 'smooth.' In other words, a smaller value of ω will produce a smoothed series with fewer ups and downs; a larger value of ω will produce a series that resembles the original series with more of the ups and downs in the original series replicated in the smoothed series.
Why is it "exponential"?
By direct substitution of the defining equation for simple exponential smoothing back into itself, we can show that
In English, as time passes, the smoothed statistic becomes the weighted average of a greater and greater number of the past observations yt, and the weights assigned to previous observations are in general proportional to the terms of the geometric progression. A [[geometric progression]] is the discrete version of an [[exponential function]], so that's how this smoothing method got its name.