<div> <div> A mathematical theory is presented for the dynamic modeling of multivariate economic systems composed of "n" structurally dependent events, based on the Acceleration Balance Equation (ABE). This third-order differential equation describes the temporal evolution of economic events x(t), incorporating observed acceleration, internal potential acceleration, and, when relevant, external accelerations. The parameters “μ” and “m” represent structural damping and the weighting of each phenomenon’s relative importance, while the term proportional to the jerk captures delayed and oscillatory effects characteristic of economic dynamics. </div> <div> The “ABE” model is an extension or generalization of the Navier–Stokes equations; it represents a significant breakthrough because it makes it possible to extend fluid-dynamics concepts to economic time series. </div> <div> <br> </div> <div> The ABE model extends to coupled multivariate systems, where vectors of economic variables interact through coupled differential equations. The T-Metric, derived from a Hamiltonian functional, is introduced to interpret temporal trajectories as geodesics within a space endowed with a potential field. Empirical validation demonstrates the model’s ability to infer latent structures and predict future dynamics with higher accuracy than traditional linear approaches, including complex phenomena such as synchronization, shock propagation, and systemic stability. </div> <div> <br> </div> <div> The model captures the natural dynamics of the economy, satisfying the principle of minimum energy and Lagrangian, while allowing for both joint and independent analysis of time series. Each series exhibits its own internal dynamics, suggesting a new perspective: time series are systems with individual identity as well as interactive relationships. On this basis, the ABE model enables the derivation of quantitative and quantum metrics, as well as the representation of parameter spaces through various diagrams, facilitating comparative analysis and characterization of relationships between variables. </div> <div> <br> </div> <div> The model identifies optimal investment periods, anticipates phases of instability, detects equilibrium states, and locates sensitive variables to guide economic outcomes. The combination of ABE and the T-Metric, through geodesics (n-Geodesics-ABE model) and level curves, provides a rigorous analytical tool for studying stable, unstable, or turbulent equilibria, evaluating policies, and exploring counterfactual scenarios. The Isolated-ABE, n-Joint-ABE, n-Lagrangian-ABE and n-Geodesics-ABE variants allow both trend prediction and precise quantitative forecasting, consolidating ABE as a comprehensive platform for modeling and predicting economic dynamics, incorporating probability measures through wave function and Bayes. </div> </div>