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1993issue C031-2

Lag-compensated exponential trend channel construction

Editorial view: treat a price channel as a staged laboratory that isolates lag, width, and permission before the pieces are reassembled. The archive records how stacked exponential series, a residual envelope, and a slower filter are seeded and updated.

  • Each exponential series is seeded with the first period's closing price, and recursive smoothing begins on the following period.
  • The three-week prefilter uses a fixed alpha of 0.5 and the next period's close, so it is available only after a one-period delay.
  • The lead/lag centerline reuses the mid-stage alpha and a gamma term, while bands sit 2.5 modified-sigma units around that centerline.
  • A separate longer exponential series of closes, illustrated with N of 29, is the trend-filter rather than the channel centerline.
Entries in this reading3 entries
Current trackPrice channel77 readingsExponential smoothing117 readingsTrend filter137 readings

A staged laboratory

The editorial reading treats a price channel as a staged laboratory. Isolate lag in stacked exponential-smoothing, isolate width in a residual envelope, and isolate permission in a slower trend-filter so each constant can be inspected before the pieces are reassembled.

The archive describes a historical construction order for those pieces. It does not present the finished assembly as a trading recommendation.

Seeding and stacked smoothers

Exponential-smoothing is a recursive blend of the latest observation with the prior smoothed value, controlled by an alpha constant that can be fixed or derived from a chosen lookback N. Each exponential series is seeded with the first period's closing price, and recursive smoothing begins on the following period.

The first stage is a prefilter: a three-week exponential pass with a fixed alpha of 0.5 that uses the next period's close. Because that pass looks one period ahead, the zero-lag prefilter is available only after a one-period delay.

The second stage is a seven-week exponential smoother whose alpha equals 2 divided by N plus 1, with N supplied by the user and illustrated as 7.

Lead-lag compensation

The lead/lag centerline reuses that seven-week alpha and adds a gamma term. Gamma is defined as twice the quantity alpha minus 1 and is applied to the change in the second-stage smoother.

Lead-lag-compensation is that extra gamma term. It is used only in the lead/lag centerline update, so the centerline can offset lag introduced by ordinary exponential averaging.

Residual width and channel bands

The variance prefilter is the average of five squared residuals between the close and the lead/lag centerline. Modified-sigma is the square root of the average of those variance-prefilter values.

The price-channel bands sit 2.5 of those modified-sigma units above and below the lead/lag centerline. In the fixed sense used here, a price-channel is a pair of bands placed a fixed multiple of residual volatility around a lag-compensated smoothed centerline.

A slower permission overlay

A separate longer exponential series of closes, using alpha equal to 2 divided by N plus 1 with an illustrated N of 29, serves as the trading filter. Any N may be substituted.

That series is the trend-filter: a slower exponential series of closes used as a longer-horizon permission overlay rather than as the channel centerline.

Inspecting constants before reassembly

Editorial interpretation: once the prefilter, the mid-stage smoother, the gamma update, the modified-sigma envelope, and the slower filter are specified apart from one another, the constants can be inspected one at a time. Those constants are the fixed prefilter alpha, the user-chosen N values, gamma defined from alpha, and the 2.5 band multiple.

The archive then reassembles the pieces into a single channel-and-filter construction. It does not rank those constants or extend the construction beyond that assembly.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
12 of 55 in the Price channel track
19931-2 pp.Next on Price channelConstructing a lead-lag filter and price channel as one stackThe basic lead-lag filter starts with an exponential average of the close, then applies a second exponential average to a linear combination of that series and a one-bar delay of itself.
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
1993Lead-lag smoothing for weekly trend-channel construction1993Constructing a lead-lag filter and price channel as one stack1988Three-zone price channel from quadratic smoothing1989A variable-sensitivity stochastic built on three-sigma bounds1993Constructing zero-net-lag price channels