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1991issue C011

Constructing an exponential average from a smoothing weight

Exponential smoothing of an ordered closing-price series is constructed as another form of moving average. A smoothing constant between 0 and 1 may be estimated from a simple-average lookback length, and each new average can be written from the prior average or as a two-term mix of the latest price and that prior average.

  • Exponential smoothing of an ordered closing-price series is constructed as another form of moving average.
  • Each new average equals the previous average plus the smoothing constant times the latest price minus that previous average.
  • The same update can be written as the smoothing constant times the latest price plus one minus that constant times the previous average.
  • The smoothing constant lies in the closed interval from 0 to 1 and may be estimated from a simple-average lookback length n as 2 divided by n plus 1; a 10-day length corresponds to 0.18.
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Current trackExponential smoothing183 readingsMoving average597 readings

A moving average with one weight

Exponential smoothing of an ordered closing-price series is constructed as another form of moving average.

The moving average is a lookback filter on ordered prices. Exponential smoothing is a recursive average that updates the previous value with a fraction of the latest observation minus that previous value.

Estimate the weight from a lookback length

The smoothing constant is a number in the closed interval from 0 to 1. It is the weight that scales how much of the latest price-versus-average gap enters the update.

The smoothing constant may be estimated from a simple moving-average length n as 2 divided by n plus 1. That window n is the lookback length used for the estimate.

Under that estimate, a 10-day simple-average length corresponds to a smoothing constant of 0.18.

Write the same update two ways

Each new average equals the previous average plus the smoothing constant times the latest price minus that previous average.

The same update can be written as the smoothing constant times the latest price plus one minus that constant times the previous average.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
8 of 41 in the Exponential smoothing track
19911-8 pp.Next on Exponential smoothingConstructing a double-smoothed momentum oscillator familyThe oscillator measures the current close against the highest close and the lowest close inside an integer lookback window labeled a.
All readings on this track · 41 readings
  1. 1984Matching average age across price filters
  2. 1984Residual-impact construction of exponential smoothers
  3. 1988Constructing simple and exponential moving averages as specified filters
  4. 1989Evaluating smoothed free reserves and funds-discount spreads
  5. 1990Integer construction of moving averages and exponential smoothing
  6. 1990Constructing incremental moving average filters
  7. 1991Constructing a double-smoothed stochastic oscillator
  8. 1991Constructing an exponential average from a smoothing weight
  9. 1991Constructing a double-smoothed momentum oscillator family
  10. 1991Competing certainty rules from exponential-average conditions
  11. 1991Hybrid construction of a mechanical timing system from smoothed signals
  12. 1991Constructing an exponential smoother from a moving-average length
  13. 1991Equivalent relative-strength-index constructions from a ratio and from smoothed momentum
  14. 1991Constructing the true strength index from double-smoothed momentum
  15. 1991True strength index from signed, double-smoothed momentum
  16. 1992Constructing exponential averages from simple lookbacks
  17. 1992Constructing exponential averages by the smoothing constant, startup length and lag
  18. 1992Nested range smoothing and windowed high-low damping
  19. 1992A weekly equity stance from the discount-bill spread
  20. 1993Double-smoothed stochastics momentum index construction
  21. 1993Constructing the true strength index with double exponential smoothing
  22. 1994Polarized fractal efficiency with a shared exponential smoother
  23. 1994Five-interval exponential smoothing of ten-interval signed path-efficiency
  24. 1994Hand-ranked price-volume series with stacked smoothing and stochastic
  25. 1995Range expansion filter on multi-horizon averages
  26. 1995The exponential smoothing constant from averaging lag
  27. 1997Construct a nested-average rainbow band and oscillator
  28. 1998Filter stacks that combine a moving average with exponential smoothing
  29. 2002Smoothed relative-strength construction from wilder-averaging and a price prefilter
  30. 2003Reverse-engineered RSI price targets
  31. 2004Piecewise trend quality from moving-average reversals
  32. 2004Nested smoothing recipes versus unaudited oscillator experiments
  33. 2008Weight construction beyond the N-day label
  34. 2010A consensus filter for objective RSI and smoothing construction
  35. 2012Sentiment-zone oscillator from signed closes
  36. 2012Classic RSI one-over-N smoothing versus the standard exponential average
  37. 2013Why exponential smoothing uses two over n plus one
  38. 2015Constructing ratio indicators with moving-average and exponential-smoothing weights
  39. 2015Slow relative-strength index from an exponentially smoothed price
  40. 2017Rebuilding the relative strength index as open-scale buy-sell pressure
  41. 2017Comparing Wilder and exponential smoothing inside a relative-strength index
By fieldIndicators and filters874 readingsBy year1991166 readings
All 183 readings tagged Exponential smoothing
Also on Exponential smoothing5 readings
1984Constructing TRIX from a cutoff to one shared alpha1984Matching average age across price filters1984Residual-impact construction of exponential smoothers1987Constructing a cycle-scaled trend oscillator1988Constructing moving averages: weights, smoothing and crossovers