A fractal-dimension regime-gate for mechanical breakout entries

Start with the regime class

The historical workflow first measures how space-filling the recent price path has been. Fractal dimension supplies a fractional label for that window: trending, random, or cyclic, rather than a Euclidean line, plane, or solid.

That class is then available to a mechanical entry as market state. The breakout remains a price-structure condition. The label is what allows the condition to become a signal, or what withholds it.

How fractal dimension becomes a label

A price path with fractal dimension near 1 behaves like a line and is treated as trend-like. A value near 1.5 is treated as random or Brownian. A value nearer 2 is treated as a more space-filling, cyclic figure.

The Hurst exponent is a persistence statistic related to fractal dimension by D = 2 - H. Values of H away from one-half imply memory or anti-persistence in the path. A Hurst estimate can be converted directly into a regime label.

An arbitrary band on one window

On a 64-day window ending May 26, 2017, an arbitrary band of 1.45 to 1.55 classified S&P 500 names as random. Values below 1.45 were labeled trending. Values above 1.55 were labeled cyclic.

Under those same cutoffs, about 30 percent of S&P 500 stocks were labeled trending, 50 percent random, and 20 percent cyclic. Most names were not in a trend class.

The same date can hold several regimes

Whether a given stock looks random or partially predictable depends on the fractal-dimension estimator, the length of the time window, and the asset. Different names can sit in different regimes at the same calendar date.

Estimators that a rule engine can refresh

Classical rescaled-range analysis estimates the Hurst exponent by breaking logarithmic daily returns into successively larger non-overlapping power-of-two segments, averaging R/S, and taking the slope of log(R/S) versus log(segment length).

A two-segment high-low slope method and a finer true-range method both estimate fractal dimension from OHLC structure. The true-range-slope-estimator substitutes mean true range times n for summed segment slopes and the window range over n for the full-window slope.

Those shortcuts exist because full rescaled-range work is laborious at a single date and does not readily produce a moving daily Hurst or fractal-dimension series for a live rule engine.

Double confirmation and the no-trade zone

A mechanical entry procedure can require double confirmation of a breakout with the regime direction. The price-structure breakout and the regime-gate must agree before a signal is issued.

Conflicting colors or classes are treated as an explicit no-trade zone rather than forced into a signal.

Editorial: TradersWeek treats that no-trade zone as abstention inside the same testable procedure as the entry, not as a missing signal.