Skip to main content
Track Bollinger Bands
8 / 45
Search the archiveLibrary
Library

1996issue C101-3

Dual-horizon ratio envelopes and regression error channels

A gold-mining index divided by a gold-bullion price is wrapped in long-horizon and short-horizon moving-average envelopes, then switched with four crossing tests. A second band is the smoothed fitted line plus and minus twice the smoothed residual-standard-error, with the close mapped as a percent-channel-location.

  • The ratio-series is a gold-mining index divided by a gold-bullion price, and it is formed before any envelope is drawn.
  • The long-horizon-envelope and the short-horizon-envelope use different lookbacks and standard-deviation offsets, and the mechanical-switch is four named crossings executed at the bar close.
  • The residual channel is the smoothed fitted value plus and minus twice the smoothed residual-standard-error, with the close also mapped as a percent-channel-location.
  • Editorial reading: an average-plus-dispersion band measures distance from a moving mean, while a fit-plus-error band measures distance from a local line.
Entries in this reading3 entries
Current trackBollinger Bands84 readingsLinear regression112 readingsMechanical trading system158 readings

A ratio before any envelope

The archive begins with a ratio-series. That series is the quotient of a gold-mining index and a gold-bullion price. The two envelopes and the later residual channel are written only after that quotient exists.

Editorial note: this article follows those writing steps as a construction lesson. It is not a view on metals and it does not rank one envelope style over the other.

Long and short deviation horizons

The long-horizon-envelope equals the 46-period average of the ratio-series plus or minus 2.3 times its 46-period standard deviation. That gives a long top edge and a long bottom edge.

The short-horizon-envelope equals the 4-period average of the same ratio-series plus or minus 1.6 times its 4-period standard deviation. That gives a short top edge and a short bottom edge. Both horizons are moving-average channels around one series. They differ in lookback and in how many standard deviations offset the edges.

K-ratio with 46-week standard-deviation envelopes

From 1992 through 1996 the miner-to-bullion K-ratio lives inside a 46-week moving-average envelope set 2.3 standard deviations out. The band widens after the 1992 slide and the ratio almost tags the upper rail on the late-1993 spike — the geometry the four crossing rules later switch on. Coordinates were read from the printed weekly MetaStock figure; they are approximate.
From 1992 through 1996 the miner-to-bullion K-ratio lives inside a 46-week moving-average envelope set 2.3 standard deviations out. The band widens after the 1992 slide and the ratio almost tags the upper rail on the late-1993 spike — the geometry the four crossing rules later switch on. Coordinates were read from the printed weekly MetaStock figure; they are approximate.K-ratio (Barron's GMI / Handy & Harman gold) · Weekly · 1992-01-01T00:00:00.000Z to 1996-12-31T00:00:00.000Z

Digitized from the printed weekly chart; y is good to about ±0.03. Long bands use the source’s 46-week window and 2.3σ offset. The figure also draws a 4-week, 1.6σ envelope that sits too close to the ratio to recover as its own series.

Four crossings as one switch

A buy signal is true when the ratio-series crosses upward through the long lower envelope or downward through the short upper envelope. A sell signal is true when the ratio-series crosses downward through the long upper envelope or upward through the short lower envelope.

Those four tests are the mechanical-switch. The mechanical procedure opens one long unit and later closes that long unit at the close of the bar that prints the matching signal.

A channel from fit and residual error

A second envelope is built from a fitted line rather than from a moving average. Residual-channel construction estimates the regression-slope of close versus bar index from a covariance-style summation divided by the variance of the bar index. The regression-intercept is then recovered from the mean close minus that slope times the mean bar index.

After the lookback is satisfied, residual-standard-error uses a divisor of length minus 2. The fitted value and the error width are then each smoothed. Published defaults are 21 for length and 3 for the smoother. The displayed residual channel is the smoothed fitted value plus and minus twice the smoothed standard error.

A companion reading, the percent-channel-location, maps the close onto that channel as one hundred times the distance from the lower band divided by the full band width.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
8 of 45 in the Bollinger Bands track
19971-9 pp.Next on Bollinger BandsRational group structure with a trend screen, RSI, and bandsA rational group structure first buckets firms by line of business, then drops members whose price path is a gross outlier versus the rest of the bucket.
All readings on this track · 45 readings
  1. 1992Constructing volatility-scaled bands with relative strength index confirmation
  2. 1994Implied volatility as a band-defined regime filter for index options
  3. 1995Constructing projection bands from least-squares slopes
  4. 1995Constructing regression projection bands and range oscillators
  5. 1996Constructing Bollinger bands, percent-b, and stochastics
  6. 1996Constructing mechanical rules from Bollinger Bands and stochastics
  7. 1996Constructing a standard-error envelope around a linear regression
  8. 1996Dual-horizon ratio envelopes and regression error channels
  9. 1997Rational group structure with a trend screen, RSI, and bands
  10. 1997Asymmetric volatility band construction
  11. 1998Constructing three-state filters from Bollinger band envelopes
  12. 1999Combination filters with Bollinger Bands and the relative strength index
  13. 1999Constructing stochastic timed exits and band-RSI reversals
  14. 1999Evaluating Bollinger Bands against fixed-width and range-based envelopes
  15. 2000Constructing a Bollinger Band target as a forward price
  16. 2001Numeric candlestick encoding with local size bands
  17. 2001Ranked candlestick sentiment to band-cross entries
  18. 2002Combining Bollinger Bands, RSI, and a stop-loss
  19. 2002Bollinger Bands remain filters, not forecasts
  20. 2002Constructing a stochastic RSI with Bollinger bands
  21. 2002Constructing a StochRSI and Bollinger mechanical system
  22. 2003Constructing volatility-scaled Bollinger envelopes
  23. 2003Why tick breadth fails as a market personality
  24. 2005Constructing Bollinger bands versus fixed trading bands
  25. 2006Squared versus absolute deviation in envelope construction
  26. 2006Confirming yen crossovers with implied volatility and bands
  27. 2006A daily candle reversal is a hypothesis until shorter sessions fail at the same zone
  28. 2008Rebuild the Relative Strength Index as price-scale bands
  29. 2008Reading Relative Strength Index extremes on one price axis with Bollinger Bands and moving averages
  30. 2011Three-filter confirmation for short-swing futures
  31. 2011Constructing an inverse Fisher stochastic with bands and averages
  32. 2012Constructing a Bollinger Band indicator suite
  33. 2012Stacking price extremes, crossovers, bands, and MACD
  34. 2012Adaptive Bollinger band impulse, trend, and momentum filters
  35. 2013Rescaling stochastic, percent-B, and wave-count parameters
  36. 2014Industry-group quartile pivots as a Bollinger Bands case study
  37. 2014Bollinger Bands as adaptive price envelopes: a 2014 classroom case
  38. 2016Trend-channel entry rules from stacked moving averages
  39. 2016A permission stack for Bollinger, RSI, and the 50-period average
  40. 2017Constructing weighted Bollinger bands and volume averages
  41. 2017Four swing-entry rules that share a timed exit
  42. 2017Two-wave monthly cycles as a regime filter
  43. 2019Constructing exponential-deviation-bands from a midline-average
  44. 2020Critiquing exponential variants of Bollinger Bands
  45. 2020Constructing selectable volatility and moving-average bands
By fieldIndicators and filters682 readingsBy year199680 readings
All 84 readings tagged Bollinger Bands
Also on Bollinger Bands5 readings
1995Constructing price envelopes from averages, volatility, and regression1995Constructing projection bands from least-squares slopes1995Constructing regression projection bands and range oscillators1996Constructing a standard-error envelope around a linear regression1996Standard-error bands, width gates, and weekday counts