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1987issue C021-6

Constructing a cycle-scaled trend oscillator

Measure the dominant short-term cycle first, then lock the short exponential smoother, the long exponential smoother, the oscillator signal average, and the price envelope to fixed multiples of that half-cycle.

  • Horizon is chosen by sampling interval before any lookback is set: daily for a few days to a few weeks, weekly for horizons longer than six months, and mixed daily-weekly for medium horizons.
  • A detrend of price minus a moving average is used to count the dominant cycle, which then becomes the sole scale for later smoothers.
  • The short exponential-smoothing span is one half of that cycle so the swing is not itself smoothed away; the long companion is six times the short span by experimental convention.
  • The oscillator is the short exponential average minus the long exponential average. Its signal average and the trading band both use three times the short span.
Entries in this reading3 entries
Exponential smoothing117 readingsCurrent trackDominant cycle detection119 readingsMoving average449 readings

One scale for every lookback

The archive workflow builds a trend oscillator as a single chain of periods. First the recurring short-term swing length in the series under study is counted. That dominant cycle is then the sole scale for the smoothers that follow.

Editorial reading: do not choose the short exponential smoother, the long exponential smoother, the oscillator signal average, or the price envelope as separate lookbacks. Lock each of them to a fixed multiple of the same half-cycle.

Map horizon to sampling

Horizon choice is mapped to sampling before any span is assigned. Daily observations are used for a few days to a few weeks. Weekly observations are used for horizons longer than six months. Mixed daily and weekly observations are used for medium horizons.

Count the cycle on a detrend

A detrend is constructed by subtracting a moving average from price. The moving-average span matches the trend horizon being isolated, and the plot is used so swing lows are easier to count. A 25-to-35-day span is specified for short-term cycle counting.

A moving average of a given span is described as reducing fluctuations of that same duration to zero, damping shorter fluctuations, and passing longer fluctuations with less attenuation as duration increases. The counted swing is the dominant cycle used from this point on.

Lock the exponential pair to the half-cycle

After the dominant short-term cycle is identified, the short exponential average is set to one half of that cycle so the dominant cycle is not itself smoothed away. Exponential smoothing is applied as that half-cycle short smoother and as a companion smoother whose period is six times as long. The six-times rule is presented as an experimental convention.

In the industrial-average example, a 14-to-15-day short-term cycle yields a 7-day short exponential average and a 42-day long exponential average.

Form the oscillator and its signal average

The oscillator is the short exponential average minus the long exponential average. It is treated as a timing series rather than as two raw average crossovers. Crossings of the arithmetic average of that oscillator are the stated signal rule.

That signal average is an arithmetic moving average of the oscillator whose period is three times the short exponential span. In the same industrial-average example, the arithmetic average applied to the difference is 21 days.

Gate signals with a matching trading band

A trading band is a percentage envelope around a price moving average that shares the signal-average period. The envelope is sized to contain about 90 to 95 percent of the data. Oscillator signals are accepted only when price is near the matching band. Out-of-band readings are treated as early.

The moving average therefore appears three times in the chain: as the detrend used to count the cycle, as the signal average on the two-average difference, and as the center of the percentage envelope on price.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
2 of 31 in the Dominant cycle detection track
19871-4 pp.Next on Dominant cycle detectionConstructing a dominant-cycle grid from marked lowsMany calculated cycle procedures cannot confirm that a cycle low occurred on the current day because delay is built into the calculations.
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
By fieldIndicators and filters682 readingsBy year198721 readings
All 119 readings tagged Dominant cycle detection
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