发表机构
Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过分析欧洲斯托克50指数期货的深度限价订单簿数据，发现市场状态更可能是连续谱而非离散状态，并提出了一个稳定的低维潜在压力坐标，其预测性能在十分钟时最优。
AI 中文摘要
市场状态模型通常假设存在一组有限的离散潜在状态。我们研究了高频限价订单簿动态是否表现出明显的状态分离，或者看似存在的状态实际上是对潜在连续体进行离散化的结果。我们分析了2022年至2025年间987个干净交易日的欧洲斯托克50指数期货的深度限价订单簿数据，采用了30秒、45秒和60秒的聚合窗口。市场状态由对称正定协方差矩阵表示，并在对数欧几里得几何和仿射不变几何下进行分析；由此产生的状态云的有效维度约为1.4。一个因果异常层过滤了统计、日历和展期污染，而无标签的经济验证则独立于基于波动率的代理标签评估市场状态分离。一个包含17种方法的组合，涵盖传统表示和黎曼表示，并辅以全云几何证书，一致地支持连续体而非离散状态结构。一个主导的潜在坐标捕获了协方差状态几何中83.66%至85.27%的变化，并在无状态标签的情况下跟踪VSTOXX，且在不同年份间保持稳定，尽管其平均水平随市场条件变化，这表明传统状态是粗略的量化。一个涵盖宏观、宏观子状态、微观和微观子状态层级的划分层次结构通过扩展年份的滚动前向测试进行评估，样本外表现最强的是宏观层级，而更细的层级无法泛化；然而，连续的细尺度信息仍然具有预测性，其离散化导致了性能损失。预测性能在接近十分钟时达到峰值，最大汇总R2_OOS为0.7483。总体而言，潜在压力坐标定义了一个稳定的、低维的几何连续体，能够捕捉市场压力及其预测动态。
英文摘要
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.
Comments45 pages, 16 figures, 18 tables
