Financial empirical dynamic modeling: a parameter-free sufficient approach for price model

Abstract

This paper presents a parameter-free, sufficient approach for financial price modeling, grounded in Empirical Dynamic Modeling (EDM) theory. Unlike conventional time series models that depend on restrictive parametric assumptions, EDM reconstructs system dynamics directly from data, capturing nonlinear, non-stationary, and chaotic behaviors inherent in financial markets. However, EDM's reliance on large-scale state-space reconstruction, neighbor search algorithms, and iterative multi-scale decomposition imposes substantial computational demands. To address this, we develop a high-performance computing (HPC) framework that leverages parallel and distributed architectures to accelerate embedding, decomposition, and forecasting steps. The proposed framework not only scales efficiently to massive financial datasets but also supports real-time forecasting, a critical requirement in high-frequency trading and risk management where millisecond-level responsiveness is essential. Empirical evaluations across diverse financial assets demonstrate superior predictive accuracy, robustness, and computational scalability compared to ARMA, ARIMA, GRU, LSTM, and 2DSL models. By integrating supercomputing resources with EDM's parameter-free methodology, this work establishes a computationally sufficient paradigm for financial forecasting that bridges dynamical systems theory and large-scale financial analytics.