Residual Waves of War: A Novel Model for Economic Shock and Recovery Using Oscillating F-Distribution Functions

As we observe serious rise in global crises like frontal and civil conflicts, natural disasters, global pandemics etc. economic systems (commodity, money and labor market equilibriums) are highly prone to disruptions and shocks. The shocks travel vast distances, both temporally and spatially, and the path or trajectory of both the impact and the recovery are very difficult to predict or model. Traditional economic models frequently fail to capture the nonlinear and residual dynamics of such events. Thus, policy-makers too find it difficult to foresee or mitigate long-term damages, because there are hardly any reliable tool for such forecasts. This paper proposes a unique theoretical model that conceptualizes economic shocks as wave-like phenomena. We draw principles from traditional wave interference and statistical distribution theory, too simulate the economic shock behavior. Specifically, we consider the sinusoidal interference function to define any economic shock, then integrate it within an F-distribution envelope. This enables us to predictably represent both immediate impact and residual oscillations of such ripples over time. The magnitude and duration of the shock are encoded into the degrees of freedom of the F-distribution, while the embedded sinusoidal component captures the constructive and destructive interferences that projects multi-layered economic disturbances. We propose empirical validation (fit) of the model on Russia’s GDP over their invasion in Ukraine. The findings reveal that such hybrid models not only enhance predictive accuracy but also provide a meaningful foundation for designing dynamic policy responses post-shock. This framework, while currently applied to war-related disruptions, is designed for broader adaptability to other economic shocks, offering a powerful new tool for economic diagnostics and forecasting.