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2016issue C0722-25

Entropy-diff as a regime switch between trend following and a price channel

The archive quantized daily S&P closes as up, down, or split-flat and scored the mix with Shannon entropy. An idealized uptrend sat far from random entropy. An idealized channel sat close to it. On a historical SPX window, entropy-diff moving-average crossovers inside a high-entropy channeling zone were presented as candidate points for preferring trend following. Editorial reading: treat that score as a regime switch, and treat the crossover only as a hypothesis that the market is leaving a channel.

  • Daily closes can be quantized as up, down, or split-flat, then scored with Shannon entropy on those two outcomes.
  • An idealized uptrend sat far from random entropy, while an idealized channel sat close to it.
  • Entropy-diff moving-average crossovers inside a high-entropy channeling zone were presented as candidate points for preferring a trend-following procedure over a channel procedure.
  • Editorial reading: treat Shannon entropy as a regime switch, and treat a moving-average crossover on the entropy-diff series only as a hypothesis that the market is leaving a channel.
Entries in this reading3 entries
Current trackPrice channel77 readingsTrend following89 readingsMoving-average crossover108 readings

Quantized days and Shannon entropy

Daily S&P closes can be quantized as up, down, or split-flat using a 0.1 percent threshold, with a flat day counted as half an up day and half a down day. That labeled close-to-close change is a quantized day.

Under that two-outcome scheme, Shannon entropy is a dispersion score on quantized up versus down day frequencies. Higher values mean more mixed, less directional price action. Maximum random entropy equals 1, matching an even mix of up and down mass.

Diff is one minus calculated entropy, so a larger gap from random maximum entropy means more one-sided, trend-like concentration.

Idealized trend and channel

An idealized uptrend constructed with the same quantization produced entropy of 0.544 and a 45.64 percent gap from random entropy.

An idealized channel produced a much smaller gap from random entropy, reported as a 1.1 percent diff, than the trending constructions.

Candidate points in a channeling zone

A channeling zone is a stretch of high-entropy, low-diff price action treated as sideways or consolidating rather than directional.

On SPX from January 2014 to March 2016, moving-average crossovers of the entropy-diff series inside a high-entropy channeling zone were presented as candidate points where a trend-following procedure becomes more plausible than a channel procedure.

A diff moving-average crossover is a moving-average crossover on the entropy-diff series used as a candidate signal that a channeling market may be entering a trend.

S&P 500 close on the entropy-diff test window

Traders should see a 2014 grind higher, a 2015 stall near the highs, then the August 2015 and January 2016 breaks. The source used this same pane to mark entropy-diff moving-average crossovers that fired while the score sat in the high-entropy red band, and treated those marks only as candidate points to leave a channel and try trend following. Monthly closes were read from the published daily curve against the figure's 1700–2200 scale.
Traders should see a 2014 grind higher, a 2015 stall near the highs, then the August 2015 and January 2016 breaks. The source used this same pane to mark entropy-diff moving-average crossovers that fired while the score sat in the high-entropy red band, and treated those marks only as candidate points to leave a channel and try trend following. Monthly closes were read from the published daily curve against the figure's 1700–2200 scale.SPX · daily · 2014-01-01T00:00:00.000Z to 2016-03-31T00:00:00.000Z

The source quantized daily moves at 0.05 percent, scored 10-day Shannon entropy, and plotted diff = 1 − entropy with 15- and 20-day averages, split at 3.5 percent (green trend versus red channel). That oscillator uses a second 0–60 percent axis and was not traced, because the raster has no tick marks for it.

How the three procedures sit together

Editorial reading: the entropy score does not replace trend following, a price channel, or a moving-average crossover. It is only a way to ask which of those readings is more plausible.

When quantized days are one-sided and diff is large, a trend-following procedure is the more natural match. When entropy is high and diff is small, a price-channel procedure is the more natural match. The moving-average crossover belongs on the entropy-diff series, not on price, and only as a candidate that a channeling zone may be ending.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
51 of 55 in the Price channel track
201730-31 pp.Next on Price channelCompeting rulers on a pound chart after BrexitOne style treated the lower boundary of the daily price channel as the operative entry-and-exit reference.
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
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All 77 readings tagged Price channel
Also on Price channel5 readings
1990Diversify markets, not systems, to cut trend-system variance1990Fair-value gaps and a copper moving-average channel1992Channel-height ratios for equity trend evaluation2002A two-stage momentum-shift and price-channel process2009One testable SPY procedure for a price channel, a trend rule, and a seasonal overlay