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1988issue C071-7

Cycle lead from staggered exponential averages

Once a dominant cycle is known, two exponential averages can be staggered so their difference isolates the cycle, and a third average then forms a residual that advances turning points without taking a first difference of price.

  • Averaging constructions delay their output, while momentum or rate-of-change constructions can lead but are typically noisy and need further smoothing.
  • Two exponential averages, sized from the dominant-cycle period, are subtracted to form a smoother, trend-reduced synthetic series that isolates the cycle.
  • A third exponential average of that synthetic series is subtracted from it to define the leading indicator.
  • The construction is specified only when a dominant cycle is present, and the same lead-from-lag stack can be rebuilt with simple moving averages.
Entries in this reading3 entries
Exponential smoothing117 readingsCurrent trackDominant cycle detection119 readingsMoving average449 readings

Lag as a design material

Averaging constructions delay their output relative to the input series. Momentum or rate-of-change constructions can lead, but they produce a noisy signal that typically needs further smoothing.

Editorial interpretation: TradersWeek treats that delay as material to budget, not as a defect to erase with a first difference of price. Once a dominant cycle is known, staggered exponential averages can be sized so their residual difference advances cyclic phase.

Budget two exponential averages

An exponential average is a recursive average that blends the current observation with the prior output using a constant alpha between zero and one. Alpha is the blending weight that sets the average's effective length. A larger alpha means a shorter average, less delay, and less amplitude loss.

The first exponential average uses an alpha of 4 divided by the dominant-cycle duration, which is equivalent to setting that average's length to half the cycle period. The second exponential average uses twice the first alpha, so its average period is half as long. The smaller-alpha average has greater amplitude attenuation and greater delay.

Isolate the cycle, then take the residual

Subtracting the two exponential averages yields a synthetic series. That difference is a smoother, trend-reduced intermediate that isolates the cycle. It is smoother than the original observations and tends to remove trend so the cycle is easier to isolate.

A third exponential average, using the same alpha as the second, is applied to the synthetic series. The leading indicator is the final residual formed by subtracting that third average from the synthetic series so the output can advance cyclic turning points.

Because the lead is formed from exponential averages and their differences rather than from a momentum function, the indicator is intended to be smoother than the generating price series.

Experimental defaults

Suggested experimental defaults are half the dominant cycle for the first average and one-fourth of the cycle for the second and third averages. A worked parameterization for a 14-day cycle uses a 7-day exponential average with alpha 0.286 and a 3.5-day exponential average with alpha 0.571.

The same stack with moving averages

The same lead-from-lag arrangement can be rebuilt with simple moving averages. A moving average is a lagging smoother of ordered observations, used here as the building block whose delay is deliberately stacked and differenced. Momentum-style adaptations can be added if further detrending is wanted.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
4 of 31 in the Dominant cycle detection track
19881-4 pp.Next on Dominant cycle detectionAuditing the forty-month stock-price cycleLock the 40.68-month length and phase first, then use later data only to test post-discovery-continuation of that same dominant-cycle.
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 year198866 readings
All 119 readings tagged Dominant cycle detection
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