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2003issue C041-14

Constructing finite-volume-element divergence with slope comparison

A finite-volume-element oscillator signs each bar only after a close-scaled money-flow cutoff, then compares 35-bar linear-regression slopes of the oscillator and of close so price-indicator divergence can be stated as a next-bar rule.

  • Typical price and a close-versus-midpoint money-flow term set each bar to +1, -1, or 0 only after a close-scaled money-flow cutoff, with a default cutoff of 0.003.
  • After a 22-bar window, signed volume is summed, divided by average volume times the sample length, and scaled by 100 so the oscillator can be compared with price.
  • Price-indicator divergence is operationalized as opposite 35-bar linear-regression slopes of the oscillator and of close, with an optional scale factor for a shared pane.
  • One mechanical construction buys the next bar when the oscillator crosses above -5 under that slope-sign pair, and exits on a negative 25-bar oscillator slope or a 50-session calendar-adjusted hold.
Entries in this reading3 entries
Current trackLinear regression112 readingsVolume-price analysis129 readingsPrice-indicator divergence142 readings

What the oscillator measures

The finite-volume-element is a bounded oscillator that assigns each bar a signed volume contribution after a money-flow cutoff, then scales the rolling signed-volume sum by average volume so the result can be compared with price.

The oscillator first forms typical price as the mean of high, low, and close, then builds a money-flow term from the close versus the bar midpoint plus the change in typical price. That pairing is volume-price-analysis: intra-bar location of the close and the change in typical price, together with volume, decide whether a bar adds to or subtracts from the oscillator.

Signing volume with a money-flow cutoff

A bar is signed +1, -1, or 0 only after that money-flow term is compared with a cutoff scaled by close. The money-flow-cutoff is a price-scaled threshold that classifies a bar as positive, negative, or neutral volume instead of treating every close-to-close move as signed flow. The default cutoff shown is 0.003.

After a 22-bar sample window, signed volume is summed, divided by average volume times the sample length, and scaled by 100 to produce the oscillator.

Divergence as opposite regression slopes

Price-indicator-divergence is a condition in which the linear-regression slope of the oscillator and the linear-regression slope of price have opposite signs. Divergence is operationalized by comparing a 35-bar linear-regression slope of the oscillator with a 35-bar linear-regression slope of close, with an optional scale factor so the two slopes can be plotted on one pane.

The linear-regression-slope is a fitted trend of an ordered series over a stated lookback, used here as a comparable baseline for oscillator trend versus price trend.

FVE on daily Manugistics (MANU), July–December 2002

Traders should see finite-volume-element (FVE) falling with price into August, then rising from about −54 at the early-September A low to about +8 at the late-October B spike while price still bases near 6–8; that positive oscillator slope against a flat close is the divergence, and the November price breakout follows as FVE runs toward +58. Points were read from the orange FVE pane of the AmiBroker screenshot (horizontal grid every 20 points); the last print is the platform label 31.44.
Traders should see finite-volume-element (FVE) falling with price into August, then rising from about −54 at the early-September A low to about +8 at the late-October B spike while price still bases near 6–8; that positive oscillator slope against a flat close is the divergence, and the November price breakout follows as FVE runs toward +58. Points were read from the orange FVE pane of the AmiBroker screenshot (horizontal grid every 20 points); the last print is the platform label 31.44.MANU (Manugistics Group) · daily · 2002-07-01T00:00:00.000Z to 2002-12-27T00:00:00.000Z

Except for the terminal FVE print of 31.4381, values are digitized from the raster and are only good to a few oscillator points. The screenshot does not print a year; the TradeStation MANU chart in the same tip, captured 17 February 2003, places this July–December span in 2002. AmiBroker does not label the FVE lookback on the pane; the accompanying BackTest EZ dialog uses a 21-bar FVE.

A next-bar entry and timed exit

One mechanical rule buys the next bar when the oscillator crosses above -5 while its 35-bar slope is positive and the 35-bar price slope is negative. The same construction exits when the oscillator’s 25-bar linear-regression slope is negative or the position has aged beyond a 50-session calendar-adjusted hold.

The same signed-volume oscillator, 35-bar slope-sign comparison, and cross of the oscillator through -5 appear as a coded long-entry test in more than one platform recipe.

A second volume-price pair and other detectors

A second volume-price pair updates a positive-volume series only on up-volume bars and a negative-volume series otherwise, each adding the close-to-close percent change. That pair can be computed as a running sum from the first bar or as a fixed-length window sum, with example windows of 200 bars and moving-average lengths of 12 or 127.

An alternative divergence detector normalizes successive oscillator peaks and successive price peaks over a lookback range, then subtracts the two normalized peak changes. A third detector uses a percent-B style comparison.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
32 of 43 in the Linear regression track
20041-1 pp.Next on Linear regressionBuilding a daily score from regression, retracement, and volumeThe lookback window is one plus the bars since the latest 20 percent close-based zigzag pivot, and a score is issued only when that window is between 10 and 60 trading days.
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  5. 1990Constructing least-squares polynomial smoothers
  6. 1991Endpoint growth rates versus linear-regression consistency
  7. 1991Out-of-sample checks for linear growth fits
  8. 1991Trend as persistence, not a straight line
  9. 1991Quadratic trend, residual oscillator, and a secondary cycle calendar
  10. 1991Time-origin offset and residual-price divergence on a quadratic least-squares fit
  11. 1991A least-squares trendline from ordered prices
  12. 1992Constructing log-linear growth and reliability screens
  13. 1992Constructing log-linear growth-rate baselines
  14. 1992Next-session high, low, and close from rolling linear regression
  15. 1993Auditing an index price-earnings multiple with short-rate regression
  16. 1994Regression-seeded nested exponential price filter
  17. 1994Constructing the double exponential average from lag cancellation
  18. 1994Evaluating money supply as a linear leading-index baseline
  19. 1995Constructing least-squares trend channels
  20. 1995Linear baseline holdout checks for annual bill-rate forecasts
  21. 1995Projection bands from high and low regression slopes
  22. 1995Evaluating a least-squares end-point moving average on a known test series
  23. 1996Constructing an endpoint moving average from a least-squares line
  24. 1996Scoring equity path consistency with a k-ratio overlay
  25. 1996Evaluating month-end yield gaps for equity regimes
  26. 1996Constructing session-indexed standard error bands
  27. 1998Evaluating linear regression baselines for index valuation
  28. 1998R-squared as a two-state trend filter from a price-time fit
  29. 2000Second-order moving-average lag correction
  30. 2002Price regression line versus beta for index tracking
  31. 2003Regression slope with an r-squared trend confidence gate
  32. 2003Constructing finite-volume-element divergence with slope comparison
  33. 2004Building a daily score from regression, retracement, and volume
  34. 2004Constructing least-squares trendlines from ordered prices
  35. 2007Rectangle breakout targets beyond height
  36. 2007Confirming a price trend with regression slope and r-squared
  37. 2008A linear-regression angle assembled as one trend filter
  38. 2010A two-state swing machine from four running extremes
  39. 2016Score oil-complex tightness before divergence or regression
  40. 2017Nikkei-yen intermarket divergence as a regime case study
  41. 2017Constructing Calmar ratio and linear regression baselines
  42. 2019Pair-trade layer construction versus average-spread management
  43. 2020A convolution slope built from nested linear regression
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