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2011issue C0424-29

Phasing many cycles at once with nested envelopes

A historical workflow treats market movement as many concurrent, harmonically related cycles that combine by addition. Nested constant-depth channels around displaced moving averages mark likely troughs, and diamond stacks under price record the combined phase so the present up or down influence can be inferred.

  • Market movement is treated as many concurrent, harmonically related cycles that combine by addition, with troughs aligned when possible rather than peaks.
  • Phasing analysis estimates each cycle's position from time since its last trough, so the next trough and the present up or down influence can be inferred.
  • Three nested constant-depth channels around displaced moving averages give visual clues to where troughs sit when the channels approach one another.
  • A cycle that looks absent is treated as masked by combination rather than gone, which is why many cycles are phased at once.
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Current trackPrice channel77 readingsDominant cycle detection119 readingsMoving average449 readings

Concurrent cycles and aligned troughs

The construction treats market movement as many concurrent, harmonically related cycles that combine by addition. That combination is summation: contributing price waves are stacked by simple addition rather than by replacing one another.

When alignment is possible, troughs are brought together rather than peaks. That preference is synchronicity, the tendency for contributing waves to meet at simultaneous troughs.

Eight construction axioms

Eight construction axioms are specified: commonality, cyclicality, summation, harmonicity, synchronicity, proportionality, nominality, and variation.

Harmonicity is the tendency for neighboring cycle wavelengths to stand in a small-integer ratio. Variation is the expected departure from the harmonic, synchronous, proportional, and nominal tendencies. Beside those axioms sits a nominal model, a named set of harmonically related wavelengths treated as a common reference frame for price movement.

Nested envelopes as trough clues

The envelope construction plots several calculated displaced moving averages inflated into constant-depth nested channels around price. Each channel is a Hurst envelope: a constant-depth band around a displaced moving average, nested so several cycle lengths can be inspected at once.

Three nested channels are used as visual clues to where cycle troughs sit when the channels approach one another.

Phasing analysis and diamond notation

Phasing analysis estimates each cycle's position from time since its last trough so the next trough and the present up or down influence can be inferred. It is the process of locating the current phase of many concurrent cycles at the same time.

Completed phasing is plotted with diamond notation: diamond marks stacked under price, with a taller stack indicating a longer cycle troughing at that point.

Masked cycles and two constructions

The distinguishing construction choice is to phase many cycles acting at once. A cycle that looks absent is treated as masked by combination rather than gone.

Two published constructions of the same theory are distinguished: a largely mathematical book method versus a later course process that applies the full theory.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
46 of 55 in the Price channel track
201236-39 pp.Next on Price channelConstructing adaptive horizontal price channelsTwo price levels enclose movement between parallel support and resistance so later acceleration, slowdown, or range compression can be observed on a chart.
All readings on this track · 55 readings
  1. 1988Constructing price channels from trendlines
  2. 1988Three-point curved trend channel construction
  3. 1988Least-squares construction of channel trendlines
  4. 1988Three-zone price channel from quadratic smoothing
  5. 1989A variable-sensitivity stochastic built on three-sigma bounds
  6. 1989Close-minus-average oscillator for channel extremes
  7. 1989The six-stage hunt as a critique of one-click heroics
  8. 1990Fair-value gaps and a copper moving-average channel
  9. 1990Diversify markets, not systems, to cut trend-system variance
  10. 1991Constructing trendlines, price channels, and close-based breakouts
  11. 1991Constructing seasonal-cycle overlays with channel confirmation
  12. 1993Lag-compensated exponential trend channel construction
  13. 1993Constructing a lead-lag filter and price channel as one stack
  14. 1993Three stochastic warnings still need price-channel confirmation
  15. 1993Lead-lag smoothing for weekly trend-channel construction
  16. 1993Constructing zero-net-lag price channels
  17. 1995From a downtrend-line break to a regression channel
  18. 1995Validated trendline and price channel construction
  19. 1995Constructing price envelopes from averages, volatility, and regression
  20. 1996Constructing trendlines and channels from explicit swings
  21. 1998Fifty percent retracement as a channel regime test
  22. 1998Close-based channel rails as daily scenario maps
  23. 1999Constructing support, resistance, trendlines, and price channels
  24. 2001Cycle composites, price channels, and two-sided signals
  25. 2001Testing horizontal price channels with stops and scale
  26. 2002A two-stage momentum-shift and price-channel process
  27. 2002Wave-by-wave channel construction for Elliott counts
  28. 2002Affine channels as reusable trade hypotheses
  29. 2004Stress-test seasonal windows across regimes, then add channels
  30. 2004Regime permission from trendlines, channels, and range edges
  31. 2004Weekly-average and price-channel states on sector depositary baskets
  32. 2005Oil services catch-up after channel resistance breaks
  33. 2005Constructing a volatility-normalized cycle index
  34. 2005How a Darvas channel becomes a complete entry and exit procedure
  35. 2005Clustered Fibonacci and channel levels in news-driven forex
  36. 2005Treat a consolidating currency market as a time-frame problem
  37. 2005Channel walls that flip roles or recapture price
  38. 2006Stacking candlesticks, crossovers, and price channels
  39. 2006Failed uptrend channel breakout left the euro rangebound
  40. 2006Constructing a Wilson relative price channel from a range-bound strength index
  41. 2007Range bars change when a Bollinger squeeze counts as a breakout
  42. 2009One testable SPY procedure for a price channel, a trend rule, and a seasonal overlay
  43. 2010A gold-miner channel plan from value to false breakouts
  44. 2010A multi-timeframe channel from value to an overvalued zone
  45. 2010Asymmetric price channel construction for congested markets
  46. 2011Phasing many cycles at once with nested envelopes
  47. 2012Constructing adaptive horizontal price channels
  48. 2014Confirming support with trendlines, channels, and retracements
  49. 2015News-sentiment confirmation for support, channel, and volume tests
  50. 2015A three-layer permission stack: moving averages, a price channel, and weekly levels
  51. 2016Entropy-diff as a regime switch between trend following and a price channel
  52. 2017Competing rulers on a pound chart after Brexit
  53. 2017Test consolidation channel breakouts as one procedure
  54. 2020Constructing late-trend longs with a price channel, gap breakout, and trailing stop
  55. 2025Using IBM's multi-year price channel as a breakout teaching case
By fieldCycles and spectral analysis77 readingsBy year201165 readings
All 77 readings tagged Price channel
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