S&P 500 Returns
financial · 36 views
financial
What It Is
S&P 500 daily close-to-close log returns (^GSPC, 1928+). The canonical U.S. equity benchmark; heavy tails, volatility clustering, leverage effects.
Interpretation
Standard analysis sees: heavy-tailed; left-skewed; aperiodic / broadband; time-irreversible (sharp rises, slow decay). The atlas finds no named structure, but the source is distinctively extreme on Nonstationarity:ac1_trend (-3.0z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.96
asymmetry0.02
occupancy0.25
short-range corr0.37
long-range memory0.40
spectral colour0.66
periodicity0.11
complexity0.82
time-irreversibility0.93
volatility clustering0.45
multifractality0.51
dimensionality0.63
nonstationarity0.81
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Nonstationarity:ac1_trend | -3.0z | bank-miss 1.1σ |
Mostow Rigidity:distance_rigidity | -3.0z | bank-miss 1.6σ |
Wasserstein:self_similarity | -2.7z | bank-miss 1.8σ |
Composition
dtypefloat64
range[-0.229, 0.1096]
unique values16286 / 16384
mean ± std0.000273 ± 0.0101
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/S&P_500_Returns.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/S&P_500_Returns.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/S&P_500_Returns.png)
Inflation (Substitution) > barcode
/d_curve/S&P_500_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/S&P_500_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/S&P_500_Returns.png)
Ulam Spiral (Sacks) > default
/default/S&P_500_Returns.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Nikkei Returns | 2.66 | |
| BTC Returns | 2.73 | |
| NASDAQ Returns | 3.45 |
Which Geometries Light Up
Catch24 › Catch24:CO_trev_1_num | rank 4/298 | 2.2070 |
Cayley › Cayley:spectral_gap | rank 4/298 | 0.0320 |
Cayley › Cayley:growth_exponent | rank 5/298 | 2.0550 |
Cayley › Cayley:saturation_radius | rank 294/298 | 0.0083 |
G2 Root System › G2 Root System:kurtosis_differential | rank 296/298 | -4.0114 |
Wasserstein › Wasserstein:self_similarity | rank 295/298 | 0.8372 |
← Nikkei Returnsin chaos
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources