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2018issue C058-13

Half-cycle relative-strength index with a Fisher map for cyclic reversals

A relative-strength index can be written as a minus-one to plus-one oscillator whose lookback is half the dominant cycle. Zero-mean momentum removes trend bias, and a Fisher transform places reversal rules on explicit standard-deviation thresholds.

  • A relative-strength index can be written without the conventional factor of 100 and without averaging, by independently accumulating closes-up and closes-down and forming their ratio.
  • After a common-denominator scale shift, the oscillator equals accumulated up-closes minus accumulated down-closes, divided by their sum, and spans minus one to plus one.
  • The stated correct lookback is the half-cycle length of the dominant cycle; raw closes are replaced by zero-mean momentum over that same span so a trend does not shift the oscillator.
  • After clipping and a Fisher transform, a drop below minus two is the long-entry condition and a rise above plus two is the long-exit or short-entry condition, provided a dominant cycle exists.
Entries in this reading3 entries
Current trackMomentum strategy103 readingsDominant cycle detection119 readingsRelative Strength Index186 readings

How the oscillator is assembled

A relative-strength index can be written without the conventional factor of 100 and without averaging, by independently accumulating up-closes and down-closes and forming their ratio. Those closes-up-closes-down running sums replace averaged gains and losses.

After the accumulations share a common denominator and the scale is shifted, the oscillator equals accumulated up-closes minus accumulated down-closes, divided by their sum, and therefore spans minus one to plus one.

Lookback from the dominant half-cycle

On a 20-bar sinusoidal price path, an accumulation length of half that period traces the input with no lag and full amplitude. The stated correct relative-strength index length is half the dominant cycle. That half-cycle length is the accumulation window.

An accumulation length of 10 is used when the assumed dominant cycle is an approximately 20-bar monthly rhythm in stocks and stock indexes.

Input-side smoothing

Because the relative-strength index step is nonlinear, smoothing the input versus smoothing the output changes the waveform while leaving the same zero crossings for equivalent smoothing. Input-side smoothing is preferred so the output can still reach the plus-or-minus-one extremes.

The separate smoothing length can be as short as 3. It is described as offering no benefit once it exceeds the relative-strength index accumulation length, because extra smoothing only adds lag.

Zero-mean momentum as the input

The bounded oscillator does not have a zero mean in trending markets. The construction replaces raw closes with close-to-close momentum over the same half-cycle length before accumulation, so a trend does not shift the oscillator away from a zero mean.

Fisher transform and the two-standard-deviation rule

Oscillator values are clipped inside plus-or-minus 0.999, then mapped by one-half the logarithm of one plus the value over one minus the value. The vertical scale is in standard deviations of an approximately Gaussian distribution.

On that Gaussian scale, a reading beyond two standard deviations occurs about 2.4 percent of the time. The two-standard-deviation rule treats a drop below minus two as the long-entry condition and a rise above plus two as the long-exit or short-entry condition, provided a dominant cycle exists and the length equals half that cycle.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
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All readings on this track · 51 readings
  1. 1984Half-cycle differencing for momentum signals
  2. 1987Relative strength evaluation under competing optimization criteria
  3. 1988Weekly MACD as a two-clock momentum confirmation stack
  4. 1989Equal-weight zero-cross from smoothed spreads
  5. 1989Testing relative-strength-index reversal rules against trend continuation
  6. 1989Smoothed three-day futures filter for index option bounces
  7. 1989Cycle-length windows for momentum, Relative Strength Index, and stochastic construction
  8. 1991Filtered rally magnitude as a bull-regime breakout
  9. 1992Constructing true strength from double-smoothed momentum
  10. 1992Constructing a double-smoothed true strength index
  11. 1993When momentum structure and breadth break together
  12. 1993Constructing double-smoothed range and momentum oscillators
  13. 1993Constructing a two-parameter relative momentum index
  14. 1993Building a bounded momentum oscillator with RSI smoothing
  15. 1993Two-speed oscillators with divergence and trendline gates
  16. 1993Constructing a relative momentum index from the relative strength index
  17. 1994Constructing daily advance-decline breadth tools
  18. 1994Building a composite regime score from monetary climate and weekly trend
  19. 1994Averaging Relative Strength Index and the stochastic oscillator into one reversal oscillator
  20. 1995Dividend-yield regression as a hold versus momentum gate
  21. 1996Jump and hold filters for long-term Treasury yield direction
  22. 1997Constructing extendedness from a 10 percent swing filter
  23. 1997A range-expansion oscillator that can refuse its own stretch
  24. 1997RSI trend permission and Fibonacci pullback rules
  25. 1998Nested midpoint construction for a range-normalized oscillator
  26. 1999Evaluating Relative Strength Index momentum with zero-line and threshold rules
  27. 1999Treat RSI and momentum as three mechanical procedures
  28. 2000Thrust strength figure from moving-average swings
  29. 2001Constructing a non-range-bound balance of market power score
  30. 2004Cleaned breadth oscillator and new-high divergence: a swing-market case file
  31. 2004Evaluating advance-issues-momentum on a fixed-symbol-basket
  32. 2004Constructing a trend filter from two adjacent high-low windows
  33. 2006A dollar-versus-commodity extreme as a regime case
  34. 2008Zero-centered stochastic bands and bracket stops
  35. 2012Evaluating engulfing momentum across hold windows
  36. 2012Staged stops as one mechanical entry and exit procedure
  37. 2012Stacking a relative-strength-index forecast, a trend filter, and long-only momentum
  38. 2013Constructing fair-value filters from averages and momentum
  39. 2014Constructing a multi-window slope divergence entry
  40. 2015Bandedge trend filter construction with inverse crossover rules
  41. 2017Opposite rules for index price and volatility momentum
  42. 2018A three-state overlay that colors a trend only after the line clears the bar
  43. 2018Half-cycle relative-strength index with a Fisher map for cyclic reversals
  44. 2018Emotion as a rule input when momentum breaks
  45. 2018Two-bar body expansion as a momentum breakout construction
  46. 2019Pair a two-day high breakout with a volume-weighted exit on the same chart
  47. 2020Building reflex and trendflex cross and extreme entry rules
  48. 2020Construct a dual-series price momentum oscillator overlay
  49. 2020A multi-timeframe stochastic as a panel of weekly voters
  50. 2020Centerline crossovers that compare index momentums
  51. 2020Multi-timeframe stochastic voting as one mechanical rule
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1984Half-cycle differencing for momentum signals1987Relative strength evaluation under competing optimization criteria1989Cycle-length windows for momentum, Relative Strength Index, and stochastic construction1989Testing relative-strength-index reversal rules against trend continuation1992Constructing true strength from double-smoothed momentum