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2006issue C111-5

Constructing a log-change probability line for trend and range rules

A continuation probability is built from the average and root-mean-square of log price changes and rescaled to a 0-1 reading. That line is then used only through a precommitted trendline break, a range extreme, or a two-series confirmation.

  • A continuation probability divides the average log change of a price series by the root-mean-square of those log changes, then rescales the ratio so the reading sits on a 0-1 scale.
  • The same construction is applied without change to monthly index bars, monthly single-name bars, and daily bars, so the filter is specified as timeframe-agnostic.
  • A trendline on the probability series, highs and lows treated as support and resistance, or a second-series confirmation can be named in advance as the only event that may open, close, or skip a trade.
  • A reversal rule that buys below 0.2 or sells above 0.8 still requires a stop, because those extremes can persist rather than turn.
Entries in this reading3 entries
Current trackTrendline128 readingsSupport and resistance170 readingsRule-based entry174 readings

The archive forms a continuation probability by dividing the average log change of a price series by the root-mean-square of those log changes, then rescaling as ((average / RMS) + 1) / 2 so the reading sits on a 0-1 scale. The point of the construction is to put a continuation reading on the chart as something that can be drawn on, not only watched.

The same construction on any bar scale

The same construction is applied without change to monthly index bars, monthly single-name bars, and daily bars, so the filter is specified as timeframe-agnostic rather than tied to one chart scale.

On monthly Nasdaq-100 bars the probability line is presented as marking both multi-month advances and abrupt reversals that fixed-lookback oscillators such as RSI or stochastics often smear.

NASDAQ 100 monthly continuation probability

The 0–1 continuation reading stays weak through the 2000–02 NDX decline, then holds high during the 2003–04 advance and only briefly collapses on sharp monthly reversals. Traders can treat the line as a constructed probability, not a price overlay. Every point is the published P column from the source workbook, P = ((average log change / RMS of log changes) + 1) / 2.
The 0–1 continuation reading stays weak through the 2000–02 NDX decline, then holds high during the 2003–04 advance and only briefly collapses on sharp monthly reversals. Traders can treat the line as a constructed probability, not a price overlay. Every point is the published P column from the source workbook, P = ((average log change / RMS of log changes) + 1) / 2.NDX · monthly · 2000-05-01T00:00:00.000Z to 2006-04-03T00:00:00.000Z

P is first published in May 2000 after the workbook has enough monthly log-change history to form AVG and RMS. AVG is the mean of LN(close/prior close); RMS is (SUMSQ/COUNT)^0.5 of those log changes.

A trendline on the probability series

A trendline is a line drawn across successive lows or highs of the continuation-probability series so a later break of that line can falsify the active up or down hypothesis.

On daily Microsoft bars an upward trendline on the probability series is drawn from a low near 0.043 to a later mid-range point. That line is treated as broken on 15 March 2006, ending that uptrend hypothesis.

Highs and lows as support and resistance

Support and resistance means high and low extremes of the probability line, or of price read against that line, treated as barriers where a continuation reading is exhausted and a reversal hypothesis becomes testable.

On daily QQQQ bars the probability line's own highs and lows are paired with support and resistance to frame trades while price is moving sideways.

One reading, three precommitted procedures

A rule-based entry is a precommitted threshold or two-series confirmation that turns the same probability reading into buy, sell, or stand aside as one testable procedure.

One fully specified entry rule buys when the daily QQQQ probability crosses above 0.5 and sells when it crosses below 0.5.

A second rule anticipates reversals from readings below 0.2 (buy) or above 0.8 (sell) and requires a stop, because those extremes can persist rather than turn.

A two-series rule buys only when the S&P 100 probability is rising while the VIX probability is falling, and sells only when those conditions reverse. Otherwise the procedure does not fire.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
34 of 53 in the Trendline track
20071-4 pp.Next on TrendlineLinked cross breaks as dollar-pair filtersEvery listed major and commodity-pair shares a US dollar leg, so a directional call on those pairs also requires a view on dollar strength or weakness.
All readings on this track · 53 readings
  1. 1984Constructing the slow stochastic from a five-session range
  2. 1985Gold-proxy trendlines and a January support base
  3. 1988Construct a five-week new-highs total as a breadth chart
  4. 1988Stacked channel, trendline, and moving-average warnings in 1987
  5. 1989Auditing fifth-wave counts with equality, Fibonacci, and trendlines
  6. 1990Money-fund maturity as a companion Eurodollar chart
  7. 1990Constructing wave targets from ratios, triangles and trendlines
  8. 1992Nested time frames for trend and channel signals
  9. 1992A pre-trade checklist for trendline breaks and loss limits
  10. 1992Bond-fund timing inside trendlines, retracements, and dual averages
  11. 1992Two-point trendline construction from rise over run
  12. 1993Disposable chart ratings from confirmed level tests
  13. 1993When trend channels define fair value after dislocations
  14. 1993Valid trendline anchors for three-part reversals
  15. 1994Pairing stochastic divergence with trendline invalidation
  16. 1995Constructing measured targets after trendline breaks
  17. 1997A three-part pullback plan with RSI, Fibonacci retracements, and a tight trendline
  18. 1998Rule-based Trendline construction for testable entries
  19. 2000Constructing trendlines, breaks, and role reversal
  20. 2000Constructing speed resistance lines from trend extremes
  21. 2000Nasdaq tech cycle stages with a 15-day average and trendlines
  22. 2002Two-session candlesticks that test support, resistance, and trendlines
  23. 2002Constructing Fibonacci ratio grids from a peak and a trough
  24. 2002Evaluate trendline geometry before trusting a breakout
  25. 2002Trendline, volume, and breakout hypotheses versus cycle-end stories
  26. 2003Writing the long S&P 500 trendline and cycle junction as one hypothesis
  27. 2003A three-event trendline reversal checklist
  28. 2003Reverse-engineered Relative Strength Index price curves
  29. 2003Two-anchor trendline construction without cut-through
  30. 2004Treat a 15-minute e-mini stair-step as congestion under a daily lid
  31. 2005A 50-day average, a trendline break, and an open barrier flip
  32. 2005Matching a forty-day average to a crude trendline
  33. 2006Constructing a relative spread-strength oscillator for staged cycle confirmation
  34. 2006Constructing a log-change probability line for trend and range rules
  35. 2007Linked cross breaks as dollar-pair filters
  36. 2007A case study in support, resistance, and trendline role reversal on currency charts
  37. 2007Reading trendline breaks in a housing-sector case
  38. 2007Constructing replaceable trendlines for break signals
  39. 2007Reading trendline breaks before the mechanical signal
  40. 2007Trading choppy forex trends with channels and Fibonacci breaks
  41. 2007A stacked hypothesis from wave, trendline, ratio, and candle
  42. 2008Exit rules before entry: trendline, support, and stops
  43. 2008Capitulation headlines need trend confirmation
  44. 2008RSI divergence classes, ratio thresholds, and trendline tests
  45. 2010Support and resistance as falsifiable chart hypotheses
  46. 2012Reading a 2012 software directory as a breakout and channel case study
  47. 2013Treat a currency position as a regime, then map shared levels
  48. 2014Evaluating trendline swing size per market
  49. 2018Intermarket regime stress and the January 2018 trendline break
  50. 2018Weekly and daily Stochastic oscillator construction on a single daily chart
  51. 2018Constructing trendlines, support, and breakout targets from crowd exits
  52. 2019Trendline break and Fibonacci retracement as a falsifiable outlook check
  53. 2019Monthly S&P 500 false-break versus the decade trendline
By fieldIndicators and filters682 readingsBy year200683 readings
All 128 readings tagged Trendline
Also on Trendline5 readings
1985Gold-proxy trendlines and a January support base1988Constructing trend definitions with filters and lines1988Three-point curved trend channel construction1990Money-fund maturity as a companion Eurodollar chart1992Nested time frames for trend and channel signals