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2006issue C081-6

A dominant-cycle split into a trend filter and residual Relative Strength Index

Ordered price is split with one dominant-cycle lookback into a lag-corrected trend filter and a shorter cyclic residual. Relative Strength Index is then taken on that residual and withheld when the trend-filter slope points the other way.

  • A dominant-cycle length is the common lookback that splits ordered price into a low-pass trend filter and a high-pass cyclic residual.
  • A simple average equal to that period cancels the cycle and its harmonics. Adding half the slope across the same window offsets the average's half-length lag.
  • The cyclic residual can be smoothed with a four-weight finite-impulse-response average, then used as the input to Relative Strength Index instead of raw price.
  • Long oscillator signals are withheld when instantaneous-trendline slope is down, and short oscillator signals are withheld when that slope is up.
Entries in this reading3 entries
Current trackDominant cycle detection119 readingsTrend filter137 readingsRelative Strength Index186 readings

How price is split

Observed price can be treated as the sum of a freely curving trend component and a cyclic component whose period is allowed to vary. The dominant cycle is the prevailing oscillatory period taken from ordered price, and that length is the common lookback for both the low-pass and high-pass paths.

A fixed dominant-cycle length can be supplied as an input, with a demonstration default of 20 bars. If the period later varies, the simple average must be recomputed over the full window rather than updated by adding the newest bar and dropping the oldest.

The trend filter and its slope

A simple moving average whose length equals the dominant-cycle period cancels that cycle and its harmonics and passes lower-frequency components, acting as a tunable low-pass trend filter.

That simple-average trend filter lags by half its length. The instantaneous trendline offsets the lag by adding half the slope taken across the same dominant-cycle window.

Slope across one dominant-cycle interval equals current price minus the price one period earlier. That difference is the same at a cycle peak, trough, or intermediate phase. The trend filter therefore supplies both a lag-compensated trendline and its slope.

The cyclic residual

The cyclic residual is a high-pass output that keeps components shorter than the dominant cycle. It can be smoothed with a four-weight finite-impulse-response average that removes two-bar and three-bar fluctuations at a lag of 1.5 bars.

The reconstructed series is the instantaneous trendline plus the smoothed high-pass residual, which can be overlaid on the original price bars for visual comparison.

Relative Strength Index on the residual

Relative Strength Index and related oscillators can be computed on the cyclic residual instead of raw price. The oscillator is then gated so long signals are withheld when instantaneous-trendline slope is down and short signals are withheld when that slope is up.

Stochastic RSI on the cyclic residual, e-mini S&P daily

The fast Stochastic RSI pins at 0 and 1 for stretches of weeks, then crosses the slower line at the start of the larger residual swings. Those crosses are the article’s entries, later withheld when the instantaneous-trendline slope points the other way. Points were read from the lower pane of the source TradeStation screenshot, using the printed 0.88 / 0.71 finish and the month grid; dates are only good to about a week.
The fast Stochastic RSI pins at 0 and 1 for stretches of weeks, then crosses the slower line at the start of the larger residual swings. Those crosses are the article’s entries, later withheld when the instantaneous-trendline slope points the other way. Points were read from the lower pane of the source TradeStation screenshot, using the printed 0.88 / 0.71 finish and the month grid; dates are only good to about a week.E-mini S&P 500 futures, continuous contract · Daily · 2005-03-01T00:00:00.000Z to 2006-05-31T00:00:00.000Z

Residual is a 15-bar high-pass of (H+L)/2 with a 4-bar FIR smooth; the pane title shows Stochastic RSI length 20. Mid-scale readings are only good to about 0.05.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
20 of 31 in the Dominant cycle detection track
20071-2 pp.Next on Dominant cycle detectionConstruct a momentum difference from the dominant cycleDifferencing subtracts an earlier observation from the latest observation over a fixed interval and yields a signed series that regularly crosses through zero.
All readings on this track · 31 readings
  1. 1982Cycle phase windows for chart signal filters
  2. 1987Constructing a cycle-scaled trend oscillator
  3. 1987Constructing a dominant-cycle grid from marked lows
  4. 1988Cycle lead from staggered exponential averages
  5. 1988Auditing the forty-month stock-price cycle
  6. 1989When long-wave dominant cycles cannot be disproved
  7. 1991Half-cycle average plot shift versus cycle attenuation
  8. 1991Half-cycle average contact as an amplitude-ratio test
  9. 1993Building a restoring-pull indicator from cycle frequency and volume
  10. 1995Regime filters for a dominant long wave
  11. 1995A cycle-tuned lead filter from bounded oscillators
  12. 1998Testable cycle rules instead of fear and greed
  13. 1999Nested Euro cycle timing as one checkable procedure
  14. 2002Constructing an instantaneous trendline from a dominant cycle
  15. 2002Half-cycle center of gravity oscillator from moving-average balance
  16. 2004Testing a locked forty-week cycle with a hold-or-sit-out rule
  17. 2005Nested timing bands for dominant-cycle confirmation
  18. 2005Dominant-cycle baselines versus policy-news narratives
  19. 2006Pairing a dominant-cycle horizon with trend and oscillators
  20. 2006A dominant-cycle split into a trend filter and residual Relative Strength Index
  21. 2007Construct a momentum difference from the dominant cycle
  22. 2007Naive dominant-cycle rules fail without crowd tests
  23. 2012Constructing a dominant-cycle forecast as a timing window
  24. 2012Open-parameter construction of dominant-cycle baselines
  25. 2013Using a second-term election to check a predeclared dominant-cycle forecast
  26. 2014Constructing a dominant-cycle forecast baseline
  27. 2014Quotient transform as an early-onset trend filter
  28. 2014Construct a trough-to-trough cycle map with the Detrended Price Oscillator
  29. 2015Dominant-cycle alignment before an earnings catalyst
  30. 2017Causal reverse exponential average for cycle and trend
  31. 2020Constructing a cycle-plus-trend oscillator from a one-wavelength chord
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All 119 readings tagged Dominant cycle detection
Also on Dominant cycle detection5 readings
1988Auditing the forty-month stock-price cycle2000Switch trend and cycle indicators after a half-cycle dwell test2000Constructing a dominant-cycle squelch trend filter2002Low-lag trendline from elliptic and dominant-cycle notches2008Intermediate confirmation outranks secular phasing