Financial fractals · interactive experiment
Explore market
turbulence.
How does concentrating activity into short bursts change a market path? Adjust the activity clock and compare it with a uniform-clock baseline.
Read Fractals and Financial Risk: What Averages Hide →Change a parameter. Keep the comparison.
Pin a result, then adjust λ or H while keeping the seed fixed. Charts compare the current and pinned paths on shared scales. Clear the pin to return to the uniform-clock reference.
Activity concentration λ redistributes activity through time: the clock changes when activity concentrates. Both models retain the same end-of-year log-price variance.
Return dependence H changes dependence between underlying increments. H is not a correlation coefficient. With an uneven clock, observed calendar-time correlations also depend on the clock. Try changing H with concentration at zero first.
The H presets are scenarios, not calibrated market presets. The uniform-clock reference uses the current H. A pinned result retains its own H, concentration, and seed.
Studies find persistence in some markets and periods, but evidence depends on the data and estimation method. Return dependence is different from volatility persistence. Read the evidence and qualifications →
Uniform-clock reference: GBM (H = ½).
Where activity accumulates
Taller bars mean more activity in that interval. Steeper parts of the cumulative clock show the same concentration.
Quiet stretches and bursts
Log returns, aligned in time and shown on the same vertical scale. A faster clock increases the scope for movement in either direction.
The resulting price paths
Both start at 100. With a pin, their difference reflects the settings shown in the control bar. Without a pin, the reference isolates the clock’s effect.
Generating the experiment…
Simulated teaching paths, not calibrated market data. 512 intervals over one model year. End-of-year log-price standard deviation: 20%; marginal mean price growth: 4%. Realized volatility can differ between samples.
Inspect the statistics
These describe the current sample. A non-zero estimate can occur by chance, and a broad estimated spectrum does not by itself establish multifractality.
| Measure | Current path | Uniform clock |
|---|
Current-path counts and a fitted Gaussian. When pinned, both histograms share bins.
Absolute-return autocorrelation at lags 1–24.
Raw-return autocorrelation at lags 1–24. Compare with absolute returns above to distinguish direction from size.
An exploratory estimate of varying local roughness; sensitive to sample length and method.
Activity concentration is the cascade parameter λ; current value: 0.06. The uniform-clock reference uses the selected H and is GBM only at H = ½. A pinned reference preserves its saved settings. The CSV includes both prices, log returns, activity increments, and model settings.
Does the pattern survive another sample?
One path can be misleading. Compare 100 paired realizations at the current λ and H against uniform clocks. This ensemble uses fresh realizations, independently of the single pinned result.
How fractals repeat across scales
This geometric cartoon replaces each segment with a smaller zigzag. It illustrates recursive construction; it is a separate experiment from the activity clock above.
Edit the generator
Time and height scale separately. Peak time must precede trough time; the controls keep them apart.