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1991issue C101

Constructing an exponential smoother from a moving-average length

An exponentially smoothed series is constructed as another form of moving average on ordered closing prices. A simple-average lookback may be mapped to one smoothing constant and written as a one-step update.

  • An exponentially smoothed series is constructed as another form of moving average on ordered closing prices.
  • The one-step update adds a smoothing constant times the difference between today's closing price and yesterday's smoothed value.
  • The reduced recurrence writes today's value as the smoothing constant times today's price plus one minus that constant times yesterday's value.
  • The smoothing constant lies between 0 and 1 and may be estimated from a simple-average length n as 2/(n+1); a 10-day length corresponds to 0.18.
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Current trackExponential smoothing183 readingsMoving average597 readings

Another form of moving average

An exponentially smoothed series is constructed as another form of moving average on ordered closing prices.

A moving average is a baseline average of ordered closing prices over a stated lookback length. Exponential smoothing is a recursive update that blends the latest price with the prior smoothed value using one constant.

The one-step update

The one-step update adds a smoothing constant times the difference between today's closing price and yesterday's smoothed value. A smoothing constant is a weight between zero and one that scales how much of the latest price-versus-average gap enters the new value.

The smoothing constant is defined on the interval from 0 to 1.

The reduced recurrence writes today's value as the smoothing constant times today's price plus one minus that constant times yesterday's value.

From lookback length to one weight

That constant may be estimated from a simple-average length n as 2/(n+1). Lookback-to-weight is the mapping that turns a simple-average length n into the estimate 2/(n+1).

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

Educational research material, not investment advice. Historical source context does not establish present-day performance.
12 of 41 in the Exponential smoothing track
19911-1 pp.Next on Exponential smoothingEquivalent relative-strength-index constructions from a ratio and from smoothed momentumA 14-period relative-strength index can be constructed as 100 minus 100 divided by one plus the relative-strength ratio.
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