Structural geometry for noisy markets
Markets are noisy. Structure is not.
A geometric engine that exposes deterministic structure hidden inside volatile, high-dimensional markets.
Patent pending — Switzerland · Independent research at the intersection of geometry and finance.
Most quantitative models explain how much a series moves: volatility, correlations, regimes, carry. SNAP2D focuses on why it moves: how much of the behaviour is still governed by persistent deterministic structure once linear and volatility baselines have been removed.
The engine does not propose trades, factors or forecasts. It measures how “signal-rich” a time series remains after your own models have done their job — exposing when your stack stands on solid structure, and when it stands on noise.
Residual structure is the last layer of truth in any model. SNAP2D measures it.
Beyond measuring structure, SNAP2D can
certify it. A run is marked
PASS when the residual geometry remains
stable across multiple aggregation scales,
producing a strong z_min margin — a rigorous
indication that the detected structure is not a
single-window artefact.
Certification is currently available on weekly horizons, where multi-scale invariance is statistically meaningful.
Quantify how much of a time series remains explainable after AR, GARCH or ML baselines, across assets, horizons and feature sets.
SNAP2D sits beside your stack. You keep your forecasts, risk engines and execution — it simply tells you what is still structurally there.
See when structure tightens, collapses or shifts across regimes, helping research and risk stay aligned with how the market actually behaves.
When enabled, SNAP2D verifies that detected residual structure is multi-scale invariant. The console returns a simple PASS/FAIL status plus a minimum z-score margin.
Financial time series are not globally linear. They exhibit local, state-dependent geometry that AR, GARCH and machine-learning models tend to smooth away.
SNAP2D introduces a nonlinear surface jointly adaptive to state and volatility over the residuals, measuring the structural curvature that conventional models leave behind. The result is a new class of market diagnostic: a structural readout of how much deterministic behaviour the market is still carrying in a given window.
At a high level, SNAP2D takes:
and learns a smooth two-dimensional structural surface over this space. This surface captures the deterministic curvature that conventional models leave behind. The structural gain R_fin quantifies how much this geometry reduces residual uncertainty relative to the baseline — a direct measure of the market’s remaining deterministic structure. Model internals and operators are never exposed — only the structural diagnostics.
A certification run evaluates whether the same residual geometry persists when the data is re-aggregated across multiple time scales. SNAP2D reports: Status (PASS/FAIL), a conservative minimum z-score margin (z_min), and the list of scales tested. Only the certificate is exposed — no internal operators.
Residual geometry
Volatility models can make a series look well-behaved, but residuals often tell a different story. SNAP2D measures how much structure survives after a linear baseline and a GARCH volatility model, and pushes residual autocorrelation close to white-noise levels — without touching your forecasting stack.
The chart shows residual ACF for the same instrument under three treatments:
For quant teams, it draws the line between modelling volatility and certifying that the residual no longer carries exploitable structure.
SNAP2D’s proprietary residual gain metric R_fin summarises this improvement as a single structural efficiency score against AR and GARCH baselines. Values around 1 indicate noise-dominated regimes; values above 1 indicate nonlinear structure, and values significantly above 1.5 mark strong structural coherence.
Alongside R_fin, SNAP2D also computes R_fin_IQR, a robustness variant that looks only at the central 50% of residuals. High R_fin_IQR means the structural gain is not just driven by tail events, but by the core of the distribution.
SNAP2D can optionally run a
multi-scale certification step.
When the residual geometry remains coherent across the
tested scales, the run is marked PASS
together with a minimum margin z_min and the
list of scales.
Certification is currently calibrated for weekly horizons, where invariance is statistically meaningful.
Residual autocorrelation collapses under SNAP2D even after AR and GARCH baselines have been applied.
SNAP2D quantifies how much deterministic structure remains in a time series after removing linear baselines and standard volatility models. The examples below use weekly data and identical parameters across assets. These are not forecasts, but structural readings.
R_fin ≈ 1.54 — moderate but persistent nonlinear structure, with a surprisingly strong core (R_fin_IQR ≈ 3.02). Residual curvature drops materially under SNAP2D, revealing periods where the index behaves far from pure noise even after AR(2) and GARCH.
R_fin ≈ 1.79 — higher structural content than the ETF, helped by a longer historical window. Residual structure remains stable across horizons, indicating a non-trivial degree of underlying coherence in a broad benchmark.
R_fin ≈ 1.63 — a noisy, event-driven market with clear pockets of nonlinear determinism (R_fin_IQR ≈ 2.28). SNAP2D reduces residual curvature from roughly 0.63–0.66 (AR / GARCH) to about 0.04.
R_fin ≈ 1.82 — strong macro-driven structural content. Residual curvature collapses to C ≈ 0.0014, with episodes of very high determinism (R_fin_IQR ≈ 2.86) consistent with regime-driven behaviour in rates.
R_fin ≈ 2.34 — a rare case of pronounced nonlinear determinism in a major index. Baseline AR(2) and GARCH leave substantial residual structure (A ≈ 1.59, B ≈ 1.50), while SNAP2D collapses it to C ≈ 0.037. Structural regimes are clearly visible (R_fin_IQR ≈ 2.62).
Why teams add SNAP2D
SNAP2D does not compete with your models; it interrogates the geometry of their residuals instead. The goal is not to replace your stack, but to show what it is really standing on.
Flag periods where geometry says “there is something there” before you commit research time. Focus alpha search on assets and windows where structural indicators and R_fin are strongest.
Compare strategy performance against SNAP2D structural indicators. See when P&L came from persistent structure versus backtest artefacts or transient inefficiencies.
When structure collapses and residuals whiten, SNAP2D shows it. Use it as an additional lens alongside VaR, correlation and volatility metrics to understand when your risk is standing on signal versus noise.
SNAP2D adds a rare capability: not only measuring residual structure, but certifying multi-scale invariance when it holds.
Built for teams who already live inside noisy data and care about what their models are truly capturing — not just how nicely they fit the past.
Filter research by structure. Prioritise alpha exploration on windows and assets where geometry says “there is something there”, rather than where backtests merely look best.
Add a structural layer to VaR, correlation and vol metrics. Track when cross-asset structure tightens or disappears and adjust risk accordingly.
Test non-price datasets — flows, options surfaces, microstructure, macro and alternative data — for structural persistence before integrating them into production pipelines.
Cross-asset and cross-horizon
Equities · Rates · FX · Commodities · Futures · Options surfaces · Microstructure · Alternative signals
Deployment
SNAP2D is designed to respect existing controls, workflows and regulatory constraints, giving you structural insight without forcing architectural change.
SNAP2D is designed to operate within controlled research environments without exposing internal operators or proprietary implementation details.
A compiled, encrypted SNAP2D engine running inside your environment (on-prem or VPC). Your data never leaves your infrastructure; the algorithm is delivered as a binary with no access to internal operators or source.
Suitable for certifying structure on proprietary time series under existing governance and controls.
SNAP2D can be integrated into research and risk pipelines as a structural diagnostic, with support for custom feeds, features and monitoring.