Skip to main content
Track Bollinger Bands
4 / 45
Search the archiveLibrary
Library

1995issue C071-6

Constructing regression projection bands and range oscillators

Separate least-squares slopes from a 14-bar window of highs and a 14-bar window of lows project every bar in the lookback. The rails are the extrema of those projections, and bandwidth plus a 0-100 oscillator are normalizations of that same pair.

  • Separate least-squares slopes from a 14-bar window of highs and a 14-bar window of lows drive every later projection.
  • The upper rail is the largest value among the current high and each earlier high advanced by its lag times the high-side slope; the lower rail is the smallest matching value on the lows.
  • Projection bandwidth is 200 times the difference of the two rails divided by their sum, and the projection oscillator places the close on a 0-100 scale between those rails.
  • The rails belong on the price scale, while the oscillator is drawn in a separate pane, with optional 20 and 80 guides and lookback left as an input.
Entries in this reading3 entries
Current trackBollinger Bands84 readingsLinear regression112 readingsStochastic oscillator170 readings

Two slopes drive every projection

Separate least-squares slopes are taken from a 14-bar window of highs and a 14-bar window of lows, and those two slopes drive every later projection. Linear regression is used here only as that statistic: the least-squares slope of an ordered high or low series over a stated lookback. That slope is the only trend statistic needed to step each past extreme forward to the current bar.

A projection band is the current extreme among a family of highs or lows, each advanced by its bar lag times the matching regression slope. The upper rail is the largest value among the current high and each earlier high advanced by its lag times the high-side slope. The lower rail is the smallest value among the current low and each earlier low advanced by its lag times the low-side slope.

Bandwidth and oscillator restate the same pair

Projection bandwidth is the normalized width of the two rails, formed as 200 times their difference divided by their sum. The projection oscillator is the close expressed as a percentage of the gap between the lower and upper rails: it places the close on a 0-100 scale between those rails.

A slower companion series is an exponential smooth of that oscillator, using a 3-bar span in some recipes and a 4-bar span in another. Both series still point at the same two rails. Lookback is exposed as an input, with 14 as the suggested default, so the same construction can be rebuilt at other lengths.

Price pane and oscillator pane

The rails belong on the price scale because they are price projections, while the oscillator is a percentage and is drawn in a separate pane. Horizontal guides at 20 and 80 can be added so the oscillator is read with the same overbought and oversold framing used for a stochastic oscillator.

SOEX daily closes inside 14-bar projection bands

From early March through 4 May 1995 the SOEX daily close stays between the upper and lower 14-bar projection rails, then the early-May thrust tags the upper rail while the session still settles mid-envelope. Levels were read off the TradeStation plot; the final close 493.54 is the printed 4 May value.
From early March through 4 May 1995 the SOEX daily close stays between the upper and lower 14-bar projection rails, then the early-May thrust tags the upper rail while the session still settles mid-envelope. Levels were read off the TradeStation plot; the final close 493.54 is the printed 4 May value.SOEX · daily · 1995-03-01T00:00:00.000Z to 1995-05-04T00:00:00.000Z

Separate 14-bar least-squares slopes on highs and lows. Mid-sample points are approximate digitizations, to the nearest index point. The 4 May rails were cross-checked against the printed close 493.54, bandwidth 2.35 and oscillator 53.50.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
4 of 45 in the Bollinger Bands track
19961-3 pp.Next on Bollinger BandsConstructing Bollinger bands, percent-b, and stochasticsA Bollinger band pair is a 20-day simple moving average of closes plus and minus twice the 20-day standard deviation of those closes, with the same window used for the average and the spread.
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 year199575 readings
All 84 readings tagged Bollinger Bands
Also on Bollinger Bands5 readings
1995Constructing projection bands from least-squares slopes1995Constructing price envelopes from averages, volatility, and regression1996Dual-horizon ratio envelopes and regression error channels1996Constructing a standard-error envelope around a linear regression1996Standard-error bands, width gates, and weekday counts