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2005issue C031

Constructing a z-score scored range-breakout filter

A range-exit filter in this construction first takes a longer base-window and a shorter confirmation-window, then scores only those exits that still show overlap-flatness. The published mark is a residual-z-score, or a zero triplet when the windows or the zero-sigma-guard block a stable fit.

  • The construction is defined as a quiet, range-bound interval followed by an accelerating move away from that interval.
  • The filter pairs a longer base-window with a shorter confirmation-window, with an example pairing of 20 and 3 observations, and returns a zero triplet when that short window is longer than the base-window or when fewer than one extra observation beyond the base-window is available.
  • A range-exit is raised only when the latest close sits above the base-window high or below the base-window low, and overlap-flatness then asks whether the left-side and right-side high-low bands of the base-window still overlap.
  • If both geometric tests pass, a helper fit on the ordered base-window closes supplies a sigma, an expected next close, and a slope. The residual-z-score is the latest close minus that expected next close, divided by the fitted sigma, unless the zero-sigma-guard returns a zero z-score when fitted sigma is smaller than 0.000001. The published output triplet is the prior close, the current close, and the residual z-score.
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Breakout confirmation2 readingsCurrent trackZ-score normalization11 readings

A quiet range then a move away

The construction is defined as a quiet, range-bound interval followed by an accelerating move away from that interval.

The filter takes a longer base-window and a shorter confirmation-window. An example pairing is 20 and 3 observations.

When the routine returns zeros

The routine returns a zero triplet when the confirmation-window is longer than the base-window or when fewer than one extra observation beyond the base-window is available.

Range-exit then overlap-flatness

A range-exit candidate is raised only when the latest close sits above the base-window high or below the base-window low.

After that exit test, overlap-flatness is checked by asking whether the left-side and right-side high-low bands of the base-window still overlap. Both geometric tests must pass before scoring begins.

Residual-z-score and the zero-sigma-guard

If both geometric tests pass, a helper fit on the ordered base-window closes supplies a sigma, an expected next close, and a slope.

The residual-z-score is the latest close minus that expected next close, divided by the fitted sigma.

If the fitted sigma is smaller than 0.000001, the zero-sigma-guard withholds a standardized residual and returns a zero z-score instead.

What the filter publishes

The published output triplet is the prior close, the current close, and the residual z-score.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
9 of 11 in the Z-score normalization track
20061-5 pp.Next on Z-score normalizationConstructing a trend system from Bollinger Bands and z-scoresPrices inside a one-standard-deviation band around a moving average are classified as range conditions, and prices outside that band are classified as trend conditions.
All readings on this track · 11 readings
  1. 1991Constructing standardized sentiment trend filters
  2. 1995Market z-score residuals for style pair construction
  3. 1995Constructing scaled z-score normalization for model inputs
  4. 1996Normalize price and volume onto a common scale
  5. 2001Constructing pair spreads with z-score triggers
  6. 2003Rebuilding band distance as a z-score crossover
  7. 2003Constructing price z-scores with dual averages and bands
  8. 2003Zigzag target zones from a normalized deviation oscillator
  9. 2005Constructing a z-score scored range-breakout filter
  10. 2006Constructing a trend system from Bollinger Bands and z-scores
  11. 2011How an adjustable-bands z-test resizes the no-trade zone
By fieldIndicators and filters56 readingsBy year20056 readings
All 11 readings tagged Z-score normalization
Also on Z-score normalization5 readings
1998The triangle is a waiting room until a two-touch line breaksBreakout confirmation1991Constructing standardized sentiment trend filters1995Constructing scaled z-score normalization for model inputs1995Market z-score residuals for style pair construction1996Normalize price and volume onto a common scale