Skip to main content
Track Dominant cycle detection
15 / 31
Search the archiveLibrary
Library

2002issue C051-3

Half-cycle center of gravity oscillator from moving-average balance

A finite-impulse-response smoother scales a coefficient-weighted sum of prices. Equal weights place the observation-window balance at the midpoint. Triangular weights that favor the newest bar move that balance toward recent prices. The same center-of-gravity arithmetic, with its sign reversed and delayed by one bar, is the half-dominant-cycle oscillator and its trigger line.

  • A finite-impulse-response smoother scales the sum of coefficient-times-price products by the sum of the coefficients.
  • Identical coefficients leave the observation-window balance at the midpoint. A newest-bar-heavy triangle shifts that balance toward recent prices.
  • Measured from the newest bar, the center of gravity shrinks when prices rise and grows when they fall. Reversing the sign keeps the series in phase with the swings.
  • The intended observation window is half the dominant cycle. A one-bar delay of the signed series is the trigger line.
Entries in this reading2 entries
Current trackDominant cycle detection119 readingsMoving average449 readings

Where a moving average sits

In a finite-impulse-response filter the scaled output is the sum of coefficient-times-price products divided by the sum of the coefficients. Those coefficients are the weights along a fixed observation window of ordered prices.

When every coefficient is identical, as in a simple moving average, the window balance sits at the midpoint of the filter length. The newest bar does not own that location. Equal weights hold the balance halfway along the lookback.

Triangular weights and the center of gravity

Triangular weights that assign the newest bar the full window length and older bars successively smaller integers shift the balance toward recent prices relative to an equal-length simple moving average. That coefficient pattern is the weighted moving average in this construction.

The window balance is the sum of each price times one plus its bar offset, divided by the sum of the prices. The added one keeps the newest bar, indexed at zero, inside the product. That location is the center of gravity of the observation window.

Measured from the newest bar, that balance shrinks when prices rise and grows when they fall. Reversing its sign produces a smoothed series that stays in phase with the price swings.

Half the dominant cycle

The intended observation length is half the dominant cycle so the window covers one full one-way cyclic move. The dominant cycle is the prevailing cyclic period used to choose that length.

A window equal to one full dominant cycle leaves half the prices pulling each way, so the balance stays near the middle and the oscillator shows little motion. A window that is too short forgoes the smoothing of a longer average and leaves higher-frequency components in the oscillator.

The worked example uses a 10-bar observation window.

The trigger line

A one-bar delay of the signed series can be plotted against the current value to form a crossover. That delayed series is the trigger line.

US 96H daily closes, September 1995 to 1 March 1996

The contract climbs from a September low near 112 to a January peak just under 122, then gives back most of that advance into early March. Ehlers shows this daily pane as the example where a 10-bar center-of-gravity oscillator and its one-bar-delayed trigger mark those swings with almost no lag. Closes were read from the printed candlesticks; the final 116.03 is the value posted on the chart header.
The contract climbs from a September low near 112 to a January peak just under 122, then gives back most of that advance into early March. Ehlers shows this daily pane as the example where a 10-bar center-of-gravity oscillator and its one-bar-delayed trigger mark those swings with almost no lag. Closes were read from the printed candlesticks; the final 116.03 is the value posted on the chart header.US 96H · Daily · 1995-09-13T00:00:00.000Z to 1996-03-01T00:00:00.000Z

The pane fixes the CG window at 10 bars of (H+L)/2. Dates are interpolated from the month ticks and the 03/01/1996 header. The oscillator trace is too compressed in the raster to recover as a second series.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
15 of 31 in the Dominant cycle detection track
20041-4 pp.Next on Dominant cycle detectionTesting a locked forty-week cycle with a hold-or-sit-out ruleLock a 40-week calendar-clock before looking at prices, then treat that clock as the dominant-cycle claim under test.
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 year200284 readings
All 119 readings tagged Dominant cycle detection
Also on Dominant cycle detection5 readings
1987Constructing a cycle-scaled trend oscillator1988Auditing the forty-month stock-price cycle1988Cycle lead from staggered exponential averages1991Half-cycle average contact as an amplitude-ratio test1991Half-cycle average plot shift versus cycle attenuation