Quantifying USA tariffs effect: machine learning, entropy and fractal insights into the stock markets

Abstract This study presents a multiscale econometric framework to evaluate the impact of the USA tariff announcement of 2 April 2025 on the S&P 500 (USA) and S&P/ASX 200 (AUS) stock indices. We employ normalized permutation entropy (PE) to characterise the evolution of ordinal-pattern complexity and compute fractal-dimension estimates (Higuchi, Katz, Sevcik) to assess geometric scaling behaviour across different time-windows. Post-event PE remains uniformly high across windows, with values ranging from 0.666 to 0.913 for the USA and 0.690 to 0.923 for AUS, implying stable distributional entropy and no significant alteration of underlying symbolic dynamics. Fractal dimension estimates exhibit small but systematic changes: the Higuchi dimension increases (USA: 1.507 $$\rightarrow $$ 1.561; AUS: 1.524 $$\rightarrow $$ 1.533), indicating a marginal rise in high-frequency roughness, while Katz and Sevcik dimensions decline (USA Sevcik: 1.337 $$\rightarrow $$ 1.229), consistent with smoother medium-scale structure. Across all measures, the shock does not generate a statistically meaningful structural break. Additionally, machine-learning models (kNN, SVR, Random Forest, XGBoost, Neural Network) demonstrate strong cross-market predictability, with ensemble methods achieving out-of-sample $$R^2>0.98$$ . Overall, the results suggest that both markets absorbed the tariff shock rapidly, exhibiting stable multiscale dynamics despite heightened geopolitical uncertainty. A model-agnostic XAI framework combining SHAP attribution and permutation-based diagnostics is used to isolate robust and independent information content.