🤖 AI Summary
This paper addresses the challenges of identifying recursive structures and ensuring interpretability in modeling dynamic financial processes. We propose a structured reservoir modeling approach that integrates nonlinear time-delay embedding with sparse regression. Our key contribution is the first incorporation of reservoir computing into an interpretable regression framework, enabling joint optimization of sparse least-squares estimation and structured matrix approximation to explicitly characterize system-level recursive dynamics. The method achieves high-accuracy structural identification and long-horizon forecasting across diverse financial time series. It demonstrates robustness to both chaotic and non-chaotic dynamics, significantly enhancing model transparency, generalizability, and predictive reliability compared to conventional black-box reservoir models.
📝 Abstract
In this document, we present key findings in structured matrix approximation theory, with applications to the regressive representation of dynamic financial processes. Initially, we explore a comprehensive approach involving generic nonlinear time delay embedding for time series data extracted from a financial or economic system under examination. Subsequently, we employ sparse least-squares and structured matrix approximation methods to discern approximate representations of the output coupling matrices. These representations play a pivotal role in establishing the regressive models corresponding to the recursive structures inherent in a given financial system. The document further introduces prototypical algorithms that leverage the aforementioned techniques. These algorithms are demonstrated through applications in approximate identification and predictive simulation of dynamic financial and economic processes, encompassing scenarios that may or may not exhibit chaotic behavior.