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2012issue C058-11

Classic RSI one-over-N smoothing versus the standard exponential average

The classic relative-strength-index update weights the newest observation by 1/N, while the usual price exponential average uses 2/(N+1). Mapping those smoothing-constants onto one scale converts a stated period into an effective-period that can be compared with other averages.

  • The classic RSI update weights the newest observation by 1/N, while the usual price exponential average uses 2/(N+1).
  • Both weights equal 1 when N equals 1, and the family (1+C)/(N+C) keeps that one-bar boundary, with C = 0 for the classic RSI smoother and C = 1 for the usual price exponential average.
  • A classic RSI period of 14 is equivalent to a standard-exponential period of 27; a desired true period T is entered in the classic RSI formula as (T+1)/2.
  • A stochastic calculation and classic RSI at the same stated period can mix two different effective lookbacks.
Entries in this reading3 entries
Current trackExponential smoothing183 readingsRelative Strength Index261 readingsMoving average597 readings

One-over-N and two-over-N-plus-one

The relative-strength-index is an oscillator of averaged up and down price changes whose classic construction updates with a one-over-N weight instead of the two-over-N-plus-one weight common on price series. Exponential-smoothing is a recursive blend of the latest observation and the prior average, using a constant that must equal one when the stated period is one. The smoothing-constant is the weight placed on the newest observation in that exponential update.

The classic RSI update weights the newest observation by 1/N, while the usual price exponential average uses 2/(N+1). Both of those weights equal 1 when N equals 1, so a one-bar result equals the latest observation.

A family of weights with a one-bar boundary

A family of weights that keep that one-bar boundary has the form (1+C)/(N+C) for C = 0, 1, 2, and so on. The usual price exponential average corresponds to C = 1. The classic RSI smoother corresponds to C = 0.

A moving-average is a lookback smoother of ordered prices. A simple average of length N is the reference that the usual C-equals-one exponential form tracks most closely. For a fixed N, C = 1 produces an exponential average closer to an N-bar simple moving average than any other integer C.

Period-conversion for a true lookback

Period-conversion is a mapping that sets a classic RSI input to the desired true period plus one, then halves that sum, so the smoother's effective length matches a chosen standard period. The effective-period is the lookback implied after converting one smoother's weight into the period convention of another average.

A classic RSI period of 14 is equivalent to a standard-exponential period of 27, which is 14 times 2 minus 1. A desired true period T is obtained in the classic RSI formula by entering (T+1)/2. A true period of 21 therefore uses an input of 11.

When a stochastic calculation and classic RSI share a stated period

Applying a stochastic calculation and classic RSI at the same stated period can mix two different effective lookbacks, such as a stated 14 that is about 27 for the RSI smoother and 14 for the stochastic.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
36 of 41 in the Exponential smoothing track
201322-26 pp.Next on Exponential smoothingWhy exponential smoothing uses two over n plus oneAn exponential average of an unlimited ordered series uses weights alpha times (1-alpha) to the power of each observation age. Those weights lie between 0 and 1 and sum to 1.
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 year2012165 readings
All 183 readings tagged Exponential smoothing
Also on Exponential smoothing5 readings
1991True strength index from signed, double-smoothed momentum2003Reverse-engineered RSI price targets2015Slow relative-strength index from an exponentially smoothed price2017Comparing Wilder and exponential smoothing inside a relative-strength index1991Constructing a double-smoothed momentum oscillator family