Paper: arXiv 2610.05740

Authors: Anjali Thawait

Abstract

Market-regime models typically assume a finite set of discrete latent states. We examine whether high frequency limit-order-book dynamics exhibit distinct regime separation or apparent regimes result from discretising an underlying continuum, analysing deep limit-order book data for EURO STOXX 50 index futures across 987 clean trading days from 2022 to 2025 using 30, 45 and 60-second aggregation windows. Market states are represented by symmetric positive definite covariance matrices and analysed under Log-Euclidean and affine-invariant geometries; the resulting state cloud has an effective dimension of approximately 1.4. A causal anomaly layer filters statistical, calendar and rollover contamination, while label-free economic validation evaluates market-state separation independently of volatility-based proxy labels. A 17-method zoo spanning conventional and Riemannian representations, reinforced by full-cloud geometric certificates, consistently favours a continuum over a discrete regime structure. A dominant latent coordinate captures between 83.66% and 85.27% of variation in the covariance-state geometry and tracks VSTOXX without regime labels, remaining stable across years although its average level shifts with market conditions, indicating that conventional regimes are coarse quantisations. A divisive hierarchy spanning macro, macro-subregime, micro and micro-subregime tiers is evaluated using expanding-year walk-forward tests, with out-of-sample performance strongest at the macro tier while finer tiers fail to generalise; continuous fine-scale information nonetheless remains predictive, and its discretisation causes the performance loss. Forecasting performance peaks near ten minutes, reaching a maximum pooled R2_OOS of 0.7483. Overall, the latent stress coordinate defines a stable, low-dimensional geometric continuum that captures market stress and its predictive dynamics.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 9.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly rigorous empirical analysis of LOB dynamics using advanced mathematical concepts like Riemannian geometry. Its central finding of a continuous stress continuum rather than discrete regimes is novel and well-supported. The methodology is thoroughly detailed, and the provision of a GitHub repository enhances reproducibility.

Research Flowchart

  flowchart TD
    A[Research Goal: Discrete Regimes vs. Latent Continuum in LOB Dynamics?] --> B{Data: EURO STOXX 50 Futures LOB (2022-2025)}
    B --> C[Methodology: Covariance Matrices (Log-Euclidean/Affine-Invariant Geometry) & Anomaly Filtering]
    C --> D{Computational Process: 17-Method Zoo (Conventional & Riemannian) & Geometric Certificates}
    D --> E[Outcome 1: Effective Dimension ~1.4; Consistent Favoring of Continuum Over Discrete Regimes]
    E --> F[Outcome 2: Dominant Latent Coordinate (83.66%-85.27% Variance) Tracks VSTOXX, Stable Across Years]
    F --> G[Outcome 3: Divisive Hierarchy Fails at Finer Tiers; Continuous Information Predictive; Forecasting R2_OOS=0.7483]