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Stochastically Structured Reservoir Computers for Financial and Economic System Identification

Lendy Banegas, Fredy Vides

TL;DR

SSRCs address the problem of identifying financial and economic dynamics by enforcing structure through graph-informed coupling and stochastic embeddings. The approach couples a reduced stochastic embedding $\tilde{\eth}_{s,p,r}$ with a graph-constrained output matrix $W$, solved as a structured nonnegative least squares problem to yield $\hat{W}$. Through two case studies—a nonlinear stochastic dynamic model and regional inflation networks—the method demonstrates nonlinear pattern capture, interdependence discovery, and interpretable predictive capability under uncertainty. The contributions include (i) introducing stochastic matrix structures for economic behavior, (ii) a constrained optimization framework ensuring structural compliance, and (iii) practical insights for policy-relevant dynamics.

Abstract

This paper introduces a methodology for identifying and simulating financial and economic systems using stochastically structured reservoir computers (SSRCs). The framework combines structure-preserving embeddings with graph-informed coupling matrices to model inter-agent dynamics while enhancing interpretability. A constrained optimization scheme guarantees compliance with both stochastic and structural constraints. Two empirical case studies, a nonlinear stochastic dynamic model and regional inflation network dynamics, demonstrate the effectiveness of the approach in capturing complex nonlinear patterns and enabling interpretable predictive analysis under uncertainty.

Stochastically Structured Reservoir Computers for Financial and Economic System Identification

TL;DR

SSRCs address the problem of identifying financial and economic dynamics by enforcing structure through graph-informed coupling and stochastic embeddings. The approach couples a reduced stochastic embedding with a graph-constrained output matrix , solved as a structured nonnegative least squares problem to yield . Through two case studies—a nonlinear stochastic dynamic model and regional inflation networks—the method demonstrates nonlinear pattern capture, interdependence discovery, and interpretable predictive capability under uncertainty. The contributions include (i) introducing stochastic matrix structures for economic behavior, (ii) a constrained optimization framework ensuring structural compliance, and (iii) practical insights for policy-relevant dynamics.

Abstract

This paper introduces a methodology for identifying and simulating financial and economic systems using stochastically structured reservoir computers (SSRCs). The framework combines structure-preserving embeddings with graph-informed coupling matrices to model inter-agent dynamics while enhancing interpretability. A constrained optimization scheme guarantees compliance with both stochastic and structural constraints. Two empirical case studies, a nonlinear stochastic dynamic model and regional inflation network dynamics, demonstrate the effectiveness of the approach in capturing complex nonlinear patterns and enabling interpretable predictive analysis under uncertainty.

Paper Structure

This paper contains 9 sections, 24 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Notation
  3. Methodology
  4. Algorithms
  5. Interpretation
  6. Computational simulations
  7. Modeling Preference Evolution in Investment Coalitions with SSRCs
  8. Regional Inflation Network Dynamics
  9. Conclusion and Future Work

Figures (5)

  • Figure 1: Structured coupling matrix (left) and relational graph (right) of the investment preference evolution model.
  • Figure 2: Estimated short-term evolution (left) and long-term evolution (right) of investment preference allocations.
  • Figure 3: Regional Inflation Network Graph
  • Figure 4: Contribution between the inflation networks and the US federal funds rate
  • Figure 5: US inflation signal (top left). Honduran inflation signal (top right). Salvadoran inflation signal (bottom left). Guatemalan inflation signal (bottom right).