Hawkes Process
stochastic-process · 37 views
stochastic-processpoint-process
What It Is
Self-exciting point process --- events trigger more events, creating clustered bursts
Interpretation
Standard analysis sees: low-complexity (predictable, not noise-like); time-irreversible (sharp rises, slow decay). The atlas additionally detects Time Reversibility:ordinal_reversal_distance.
What standard analysis sees
tail heaviness0.80
asymmetry0.79
occupancy0.38
short-range corr0.62
long-range memory0.63
spectral colour0.37
periodicity0.36
complexity0.14
time-irreversibility0.95
volatility clustering0.63
multifractality0.82
dimensionality0.59
nonstationarity0.63
What the atlas adds
Time Reversibility:ordinal_reversal_distance+2.5z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
Laplacian:gradient_curvature_anticorrelation | +2.4z | bank-miss 2.7σ |
Visibility Graph:assortativity | +2.1z | bank-miss 2.4σ |
Composition
dtypefloat64
range[1.064, 10.06]
unique values16384 / 16384
mean ± std9.07 ± 1.16
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Hawkes_Process.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Hawkes_Process.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Hawkes_Process.png)
Inflation (Substitution) > barcode
/d_curve/Hawkes_Process.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Hawkes_Process.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Hawkes_Process.png)
Ulam Spiral (Sacks) > default
/default/Hawkes_Process.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Wind Speed | 3.90 | cross-origin |
| Solar Wind IMF | 3.90 | cross-origin |
| Collatz Trajectory | 4.06 | cross-origin |
Which Geometries Light Up
Laplacian › Laplacian:gradient_curvature_anticorrelation | rank 5/306 | 0.9969 |
Level Statistics › Level Statistics:wd_classification | rank 5/306 | 0.2680 |
Visibility Graph › Visibility Graph:assortativity | rank 5/306 | 0.5315 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 5/306 | 0.8354 |
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