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Simple Exponential Smoothing



Simple exponential smoothing is sometimes also referred to as single exponential smoothing.

It is most useful when used with a constant process, or a process that does not change rapidly or have trend, seasonal, or cyclic components.


If simple exponential smoothing is used with a time series that has a trend, then the smoothed series has a built-in bias and will always over- or under-estimate the original time series.
  • Bias = -b1 * (1 - lambda) / lambda  :  where b1 is the slope (trend) of the original time series, and lambda is the value of the smoothing constant.
What values of lambda are reasonable?
  • Lambda is often chosen by selecting the value that minimizes the one-step-ahead forecast errors, and/or improves any of the forecast accuracy metrics.
  • Montgomery (p. 179) suggests that values between 0.1 and 0.4 are common. 
  • Bowerman (p. 383, 3rd Ed.) suggests that values between 0.01 and 0.30 are common.
  • Bowerman also suggests (p. 386) that if the selection method for lambda suggests a value  greater than 0.3, other smoothing methods should be considered.



Initial estimate of the smoothing predictor a0(0) (using Bowerman's notation)
  • Bowerman (p. 381) suggests that an average of the first six observations is common.
  • Montgomery (p. 179) suggests two options
  • Set a0(0) equal to y1
  • Set a0(0) equal to the average of the data, or a subset of the data.






Resources



Relationship to EWMA control charts


From NIST
"Note: There is an alternative approach to exponential smoothing that replaces yt1 in the basic equation with yt, the current observation. That formulation, due to Roberts (1959), is described in the section on EWMA control charts. The formulation here follows Hunter (1986)."