Functional Decomposition and Estimation of Irreversibility in Time Series via Machine Learning

TL;DR

This paper presents a new machine learning-based method to quantify irreversibility in high-dimensional time series, revealing different dynamics during stable and unstable financial market periods.

Contribution

It introduces a flexible, model-free approach using gradient boosting and variable interaction analysis to assess irreversibility in complex systems.

Findings

Irreversibility in financial markets shifts from short-term to long-term patterns during turbulence.

The method effectively handles high-dimensional data with minimal calibration.

Variable interactions are crucial for understanding market dynamics in unstable periods.

Abstract

This work introduces a novel, simple, and flexible method to quantify irreversibility in generic high-dimensional time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting for estimation, providing a model-free, nonlinear analysis able to handle large-dimensional systems while requiring minimal or no calibration. Our procedure is divided into three phases: trajectory encoding, Markovian order identification, and hypothesis testing for variable interactions. The latter is the key innovation that allows us to selectively switch off variable interactions to discern their specific contribution to irreversibility. When applied to financial markets, our findings reveal a distinctive shift: during stable periods, irreversibility is mainly related to short-term patterns, whereas in unstable periods, these short-term patterns are disrupted, leaving only contributions from stable long-term ones. This observed transition underscores the crucial importance of high-order variable interactions in understanding the dynamics of financial markets, especially in times of turbulence.