Non-parametric online market regime detection and regime clustering for multidimensional and path-dependent data structures

Paper: arXiv 2306.15835

Authors: Zacharia Issa, Blanka Horvath

Abstract

In this work we present a non-parametric online market regime detection method for multidimensional data structures using a path-wise two-sample test derived from a maximum mean discrepancy-based similarity metric on path space that uses rough path signatures as a feature map. The latter similarity metric has been developed and applied as a discriminator in recent generative models for small data environments, and has been optimised here to the setting where the size of new incoming data is particularly small, for faster reactivity. On the same principles, we also present a path-wise method for regime clustering which extends our previous work. The presented regime clustering techniques were designed as ex-ante market analysis tools that can identify periods of approximatively similar market activity, but the new results also apply to path-wise, high dimensional-, and to non-Markovian settings as well as to data structures that exhibit autocorrelation. We demonstrate our clustering tools on easily verifiable synthetic datasets of increasing complexity, and also show how the outlined regime detection techniques can be used as fast on-line automatic regime change detectors or as outlier detection tools, including a fully automated pipeline. Finally, we apply the fine-tuned algorithms to real-world historical data including high-dimensional baskets of equities and the recent price evolution of crypto assets, and we show that our methodology swiftly and accurately indicated historical periods of market turmoil.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10 (capped from 7.5: no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a mathematically sophisticated framework combining rough path signatures with Maximum Mean Discrepancy for online regime detection. It provides robust theoretical grounding alongside empirical validations across synthetic data, high-dimensional equity baskets, and crypto assets. The methodology effectively addresses non-Markovian dynamics and path-dependency in market data.

Research Flowchart

  flowchart TD
    A["Research Goal: Online Market Regime Detection & Clustering for Multidimensional Data"] --> B["Data Inputs: Synthetic Datasets, Equity Baskets, & Crypto Assets"]
    B --> C["Core Methodology: Rough Path Signatures & Maximum Mean Discrepancy (MMD)"]
    C --> D["Computational Process: Path-Wise Non-Parametric Two-Sample Testing"]
    D --> E["Automated Pipeline: Online Regime Change & Outlier Detection"]
    E --> F["Outcomes: Swift & Accurate Identification of Historical Market Turmoil"]