BTC Returns
financial · 36 views
financial
What It Is
Bitcoin hourly log-returns --- heavy tails (kurtosis ~18), volatility clustering, and leverage effects. The canonical non-Gaussian financial time series
Interpretation
Standard analysis sees: heavy-tailed; aperiodic / broadband; high-complexity (noise-like); time-irreversible (sharp rises, slow decay). The atlas finds no named structure, but the source is distinctively extreme on Level Statistics:wd_classification (-2.2z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.93
asymmetry0.17
occupancy0.27
short-range corr0.20
long-range memory0.42
spectral colour0.83
periodicity0.08
complexity0.86
time-irreversibility0.90
volatility clustering0.46
multifractality0.56
dimensionality0.58
nonstationarity0.81
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Level Statistics:wd_classification | -2.1z | bank-miss 1.0σ |
Composition
dtypefloat64
range[-0.05516, 0.0645]
unique values16382 / 16384
mean ± std6.61e-05 ± 0.00514
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/BTC_Returns.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/BTC_Returns.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/BTC_Returns.png)
Inflation (Substitution) > barcode
/d_curve/BTC_Returns.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/BTC_Returns.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/BTC_Returns.png)
Ulam Spiral (Sacks) > default
/default/BTC_Returns.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Nikkei Returns | 2.67 | |
| S&P 500 Returns | 2.73 | |
| NASDAQ Returns | 3.11 |
Which Geometries Light Up
Cayley › Cayley:growth_exponent | rank 2/298 | 2.0677 |
Cayley › Cayley:spectral_gap | rank 2/298 | 0.0371 |
Cayley › Cayley:saturation_radius | rank 298/298 | 0.0080 |
Fisher Information › Fisher Information:geodesic_velocity | rank 5/298 | 1.4666 |
Gottwald-Melbourne › Gottwald-Melbourne:angular_spectral_structure | rank 294/298 | 0.4360 |
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