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2014issue C0860-61

Construct a dual quotient-copy trend filter under a frequency roof

After a supersmoother removes aliasing-band energy, the finished filter imposes a frequency-roof. Two quotient copies at different linearity-control settings then supply zero-cross rules for admission and exit, with a trailing-stop specified in parallel.

  • After higher-frequency content is isolated, a supersmoother removes remaining very high frequencies treated as aliasing noise, and the finished filter imposes a frequency-roof on what may remain.
  • In an upward-bias setting, the long-entry zero-cross-rule is the first quotient-copy crossing above zero, and the long-exit rule is a less sensitive second copy crossing below zero.
  • A trailing-stop is specified in parallel because the slower-copy exit can close a position before a larger directional move has finished.
  • With linearity-control set to negative values, the same stack is inverted: a short opens when the first copy falls through zero and closes when the second copy rises back through zero.
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Current trackTrailing stop87 readingsTrend filter137 readingsRule-based entry174 readings

Roof the frequencies that may remain

The finished filter is constructed to impose a frequency-roof on the band of frequencies that may remain in the output. After higher-frequency content is isolated, a supersmoother is applied so the remaining very high frequencies, treated as aliasing noise, are removed.

Pair two quotient copies as zero-cross rules

In an upward-bias setting, the long-entry rule is a first quotient-copy crossing above zero. A second quotient-copy is built with a slightly less sensitive linearity-control setting, and the long-exit rule is that second copy crossing below zero.

Each of those tests is a zero-cross-rule. Entry or exit is defined only by a named quotient-copy moving through zero in a specified direction. Linearity-control is the signed sensitivity setting that tilts each quotient-copy toward an upward or downward market bias.

Keep a trailing-stop as a parallel exit

The slower-copy exit can close a position before a larger directional move has finished, so a trailing-stop rule is specified as a parallel way to leave the trade. The trailing-stop is a separate exposure bound that can close a position even when the slower quotient-copy has not yet crossed back through zero.

Invert the same stack under a downward bias

In a downward-bias setting, linearity-control is set to negative values and the signal logic is inverted. Under the inverted rules, a short is opened when the first quotient-copy falls through zero and is closed when the second copy rises back through zero.

SPY with dual quotient-copy filters, upward bias

Daily SPY from late August 2012 through early October 2013, the Excel reconstruction of Ehlers’ upward-bias case. Price climbs from the mid-140s toward the high 160s while two quotient copies (K = 0.90 and K = 0.40, both 20/100) stay mostly above zero after the November 2012 dip; the less-sensitive copy crosses back below zero around 19 April 2013, the exit the tip uses as a caution against leaving a still-live trend. Values were read off the published Excel price pane, not taken from a table.
Daily SPY from late August 2012 through early October 2013, the Excel reconstruction of Ehlers’ upward-bias case. Price climbs from the mid-140s toward the high 160s while two quotient copies (K = 0.90 and K = 0.40, both 20/100) stay mostly above zero after the November 2012 dip; the less-sensitive copy crosses back below zero around 19 April 2013, the exit the tip uses as a caution against leaving a still-live trend. Values were read off the published Excel price pane, not taken from a table.SPDR S&P 500 (SPY) · Daily · 2012-08-29T00:00:00.000Z to 2013-10-09T00:00:00.000Z

Digitized from the Excel price pane (First 29 Aug 2012, Last 9 Oct 2013; reported window high 177.60, low 130.70). Quotient-copy levels are described in the caption but not plotted here because the oscillator pane cannot be read to honest price units without inventing precision. The 19 Apr 2013 zero-cross is stated in the accompanying text.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
21 of 36 in the Trailing stop track
201430-35 pp.Next on Trailing stopStop distance, size, and trailing swing invalidationProtective stops are treated as required even when a trend looks strong, because losses without a stop are described as likely to expand.
All readings on this track · 36 readings
  1. 1988Half-day bars, a midpoint gate, and a bar-based trail
  2. 1989Packaging two-bar reversals into testable entry and exit rules
  3. 1989Weekly high and low averages as stop-and-reverse levels
  4. 1991Constant false-alarm rate for dominant-cycle stops
  5. 1992Tick-index extremes as continuation and turn hypotheses
  6. 1993Constructing layered stops from equity and structure
  7. 1993Filter crossovers with moving-average slope
  8. 1993Precommit stop bounds from equity and structure
  9. 1998Evaluating a trendline barrier that can only tighten a capped stop
  10. 1999Constructing common-number support and resistance
  11. 2001Four-step opening-hour bias and trailing stops
  12. 2004Make the trading system the star
  13. 2005A beginner stock case: stop, trail, and the pre-trade checklist
  14. 2006Sell stops that trail support after the buy
  15. 2006Treat a wave-3 label as unfunded until the stop rails are written
  16. 2008Test medium-term divergence with a trendline break and a trailing stop
  17. 2010Rule-based forex entry, stop and trail
  18. 2012Precommitting stops when one currency range templates another
  19. 2012Cat-ears as a downtrend continuation hypothesis
  20. 2013Three-average swing entry and a trailing average exit
  21. 2014Construct a dual quotient-copy trend filter under a frequency roof
  22. 2014Stop distance, size, and trailing swing invalidation
  23. 2014Long-only RSI pullback, reversal-bar-entry, and staged-trail construction
  24. 2015Dual-average regime, trigger candle, and trail as one daily script
  25. 2015Three-gate trend system: filter, trigger, and trailing stop
  26. 2016Construct HHLLS crossover and breakout entry rules
  27. 2017An appointment-trade around a scheduled political close
  28. 2017Golden-cross breakout rules for a swing entry
  29. 2017Breakout confirmation above round numbers, with nines as sell shelves
  30. 2018Classify diamond geometry before the breakout
  31. 2019When trails and stops betray the support read
  32. 2019One-triggers-the-other pairs for preplanned swing entries
  33. 2019One-triggers-the-other orders for a breakout and its stop
  34. 2019When the second decision unbounds planned risk
  35. 2020Last-Hour Breakout With a Same-Session Flatten
  36. 2020Couple the slow period to stop-loss and trailing-stop settings
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