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1989issue C091-5

Cycle-length windows for momentum, Relative Strength Index, and stochastic construction

Editorial: treat the momentum lookback as a construction control that sets oscillator phase. A half-cycle-window can keep Relative Strength Index and stochastic oscillator rules aligned with a measured price cycle. A shorter window, including a quarter-cycle-window, yields a leading-indicator that is noisier than price and can mark false entries and exits.

  • Momentum is a difference of two time-separated observations, used as a discrete rate-of-change analog of a derivative, and it produces detrending that leaves shorter swings for tactical rules.
  • A half-cycle-window can restore phase-alignment: momentum of a half-cycle average cancels a 90-degree lag so Relative Strength Index and stochastic oscillator constructions can remain in phase with price.
  • A quarter-cycle-window, or any momentum window shorter than a half cycle, yields a leading-indicator that is noisier than price and can generate false entry and exit signals.
  • Averaging can reduce oscillator-noise only by reintroducing lag, so a usable leading construction depends on residual noise remaining modest relative to the intended lead.
Entries in this reading3 entries
Current trackMomentum strategy103 readingsStochastic oscillator170 readingsRelative Strength Index186 readings

Momentum as a constructed difference

Momentum is constructed as the difference of two time-separated observations. It is treated as a discrete rate-of-change analog of a derivative.

Differencing reduces slower trend variation relative to shorter swings. That reduction is detrending, and it leaves shorter swings available for shorter-horizon tactical rules.

Averages, lead, and averaged-momentum

A moving average lags like an integral. Momentum leads like a derivative. Combining the two is a construction path for a leading-indicator.

Averaged-momentum is momentum taken on successive moving averages. An n-period momentum of a simple moving average equals, up to a constant scale, the n-period price difference. That construction is smoother than a one-step momentum. Both smoothness and lag scale with n.

Phase-alignment with a half-cycle-window

Momentum of a sine-wave price cycle is a cosine that leads the original cycle by 90 degrees. A half-cycle moving average lags a sine by 90 degrees. Taking momentum of that average cancels the lag, so the result is in phase with price.

Relative Strength Index and stochastic oscillator constructions can be aligned with a price cycle by setting the momentum segment of each indicator to a half-cycle-window.

Shorter windows and oscillator-noise

Each successive momentum operation makes the series more discontinuous. Those discontinuities correspond to broadband noise that can mask the intended signal. That extra roughness is oscillator-noise.

A momentum window shorter than a half cycle, including a quarter-cycle-window, yields a leading-indicator that is noisier than price and can generate false entry and exit signals. Averaging can reduce momentum noise only by reintroducing lag. A usable leading construction depends on residual noise remaining modest relative to the intended lead.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
7 of 51 in the Momentum strategy track
19911-4 pp.Next on Momentum strategyFiltered rally magnitude as a bull-regime breakoutA filtered-swing is counted only after it exceeds a stated minimum percentage, so smaller fluctuations cannot mint a signal.
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
By fieldIndicators and filters682 readingsBy year198983 readings
All 103 readings tagged Momentum strategy
Also on Momentum strategy5 readings
1994Averaging Relative Strength Index and the stochastic oscillator into one reversal oscillator1998Nested midpoint construction for a range-normalized oscillator1993Constructing double-smoothed range and momentum oscillators2008Zero-centered stochastic bands and bracket stops2020A multi-timeframe stochastic as a panel of weekly voters