S&P 500 Returns
financial · 37 views
financialstochastic
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 Wasserstein:self_similarity (-2.7z) — 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
dimensionality0.64
nonstationarity0.81
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Wasserstein:self_similarity | -2.7z | bank-miss 1.7σ |
Mostow Rigidity:distance_rigidity | -2.7z | bank-miss 1.6σ |
Nonstationarity:ac1_trend | -2.3z | bank-miss 1.6σ |
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 > free_plate_nodal
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 | 2.88 | |
| BTC Returns | 2.97 | |
| MFPT Inner Unloaded | 3.07 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:CO_trev_1_num | rank 4/307 | 2.2184 |
Catch24 › Catch24:DN_HistogramMode_10 | rank 304/307 | -1.0352 |
Catch24 › Catch24:DN_HistogramMode_5 | rank 304/307 | -1.0158 |
Cayley › Cayley:growth_exponent | rank 4/307 | 2.0601 |
Cayley › Cayley:spectral_gap | rank 4/307 | 0.0316 |
Cayley › Cayley:saturation_radius | rank 306/307 | 0.0080 |
Wasserstein › Wasserstein:distributional_stationarity | rank 304/307 | 0.8328 |
← Nikkei Returnsin continuous-flows
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources