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

arXiv: https://arxiv.org/abs/2306.15835 · HTML: https://mlsanity.com/paper/2306.15835/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 69 references that are in the map.
- First posted on arXiv 27 Jun 2023.

## Builds on (most cited first, 24 of 24)

- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Understanding Failures in Out-of-Distribution Detection with Deep Generative Models](https://mlsanity.com/paper/2107.06908/) (2021)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [The Signature Kernel is the solution of a Goursat PDE](https://mlsanity.com/paper/2006.14794/) (2020)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [Statistical Inference for Generative Models with Maximum Mean Discrepancy](https://mlsanity.com/paper/1906.05944/) (2019)
- [Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distance](https://mlsanity.com/paper/1906.04516/) (2019)
- [Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions](https://mlsanity.com/paper/1604.05251/) (2016)
- [Non-adversarial training of Neural SDEs with signature kernel scores](https://mlsanity.com/paper/2305.16274/) (2023)
- [A Data-driven Market Simulator for Small Data Environments](https://mlsanity.com/paper/2006.14498/) (2020)
- [Distribution Regression for Sequential Data](https://mlsanity.com/paper/2006.05805/) (2020)
- [A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data](https://mlsanity.com/paper/1306.4933/) (2013)
- [Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes](https://mlsanity.com/paper/2109.03582/) (2021)
- [Deep Hedging: Learning to Simulate Equity Option Markets](https://mlsanity.com/paper/1911.01700/) (2019)
- [Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence](https://mlsanity.com/paper/1912.05737/) (2019)
- [On the Convergence of Gradient Descent in GANs: MMD GAN As a Gradient Flow](https://mlsanity.com/paper/2011.02402/) (2020)
- [Random Forests for Change Point Detection](https://mlsanity.com/paper/2205.04997/) (2022)
- [On the Use of Random Forest for Two-Sample Testing](https://mlsanity.com/paper/1903.06287/) (2019)
- [Selective review of offline change point detection methods](https://mlsanity.com/paper/1801.00718/) (2018)
- [Dimensionless Anomaly Detection on Multivariate Streams with Variance Norm and Path Signature](https://mlsanity.com/paper/2006.03487/) (2020)
- [Clustering Market Regimes using the Wasserstein Distance](https://mlsanity.com/paper/2110.11848/) (2021)
- [Graph-based multiple change-point detection](https://mlsanity.com/paper/2110.01170/) (2021)

## Built on by (most cited first, 2 of 2)

- [Random Fourier Signature Features](https://mlsanity.com/paper/2311.12214/) (2023)
- [Automated regime classification in multidimensional time series data using sliced Wasserstein k-means clustering](https://mlsanity.com/paper/2310.01285/) (2023)

## Abstract (arXiv)

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.