Evaluating hourly DJIA growth-rate and velocity attractors

The evaluation question

The study objectives were to inspect the fine statistical structure of hourly price changes and to test how far growth-rate and velocity variables could indicate the chance of daily and short-term DJIA changes.

Editorial reading: that aim is an evaluation question. A defined hourly lookback can be used to ask whether growth-rate counts and velocity basins behave like a quantitative baseline under Dominant cycle detection.

How the hourly sample was coded

Hourly DJIA observations from January 2, 1990 through February 15, 1991 were coded as up, down, or unchanged. Each day was treated as seven continuous hourly points. Changes of 2.5 points or less were labeled unchanged.

Editorial note: that coding fixes the sampling interval and the lookback on which later hour counts and basin summaries depend.

Labels before a theoretical model

Short-term DJIA moves in that sample were first labeled by visual inspection of closes as up, down, or sideways, without using a theoretical model to define the segments.

Editorial contrast: those visual labels come before Elliott wave analysis or Fibonacci retracement. The overlays do not define the segments being counted.

Aggregated hour ratios

Across all labeled advances, 428 up hours and 256 down hours produced an aggregated up-to-down hour ratio of 1.672.

Across all labeled declines, 198 up hours and 312 down hours produced an aggregated down-to-up hour ratio of 1.576.

Those two aggregated hour ratios were noted as close to the Fibonacci ratio of 1.618. Sideways segments totaled 143 up hours and 127 down hours for a ratio of 1.126, nearer even occurrence of up and down hours.

Growth-rate and velocity basins

Growth-rate dynamics were summarized as two attractor basins near the golden mean. Time mediated the link between growth rate and DJIA change, so the length of a decline was related to how long down hours exceeded up hours.

Hourly velocity showed several attractor basins and a nonlinear, non-constant link to DJIA change. That link included stiffening that limited move size, softening that enlarged it, and a region of roughly linear velocity-to-magnitude behavior.

The October 13, 1989 DJIA break was presented as an exit from a linear uptrend into a non-proportional snap. Market action around October 10, 1989 was modeled as a broken-spring case of extreme softening.

What stays conceptual

Editorial practice: keep the hourly coding, the visual labels, and the growth-rate and velocity basins as the quantitative baseline. A later sample is the place for an out-of-sample check.

Elliott wave analysis and Fibonacci retracement can sit on the chart afterward as conceptual overlays. They should not replace the defined lookback or rewrite the segments after the counts are made.