Dynamic financial processes identification using sparse regressive reservoir computers
This work addresses the challenge of modeling complex financial systems for researchers and practitioners, though it appears incremental as it builds on existing reservoir computing and approximation techniques.
The paper tackles the problem of identifying dynamic financial processes by developing sparse regressive reservoir computers that use structured matrix approximation and sparse least-squares methods to approximate output coupling matrices, enabling predictive simulation of financial systems with or without chaotic behavior.
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.