Mathematical Modeling and Predictive Analytics for International Trade and Business Performance

International trade flows and the performance of internationally active firms are shaped by an interacting set of economic, geographic, institutional and financial forces. This study develops and evaluates an integrated mathematical modeling and predictive analytics framework that links three layers of analysis: (i) structural gravity models of bilateral trade, estimated by log-linear ordinary least squares (OLS) and Poisson pseudo-maximum likelihood (PPML); (ii) time-series models for forecasting aggregate export values, including Holt–Winters exponential smoothing, a seasonal autoregressive model and a gradient-boosting learner; and (iii) supervised machine-learning models of firm-level export performance. Because the true data-generating process of real trade data is unknown, the framework is evaluated on a calibrated simulation design in which all structural parameters are known in advance. The design comprises a panel of 13,920 directed country-pair-year observations (30 economies, 2008–2023, 14.8% zero flows), a monthly export index for 2010–2024, and a cross-section of 1,500 exporting firms. Results show that PPML recovers the true trade elasticities with a mean absolute error of 0.074, less than half that of log-linear OLS (0.158), confirming that heteroskedasticity and zero flows bias the conventional estimator. In out-of-sample forecasting, a parsimonious seasonal autoregressive model achieved the lowest error (MAPE 1.51%), outperforming both Holt–Winters (3.13%) and a lag-based gradient-boosting model (7.24%). For bilateral trade prediction, tree-based ensembles modestly improved on gravity regressions, while for firm performance, regularised linear models and neural networks performed comparably to boosted trees (test R² ≈ 0.70–0.72). Export-market concentration, productivity and exposure to trade-policy uncertainty emerged as the dominant predictors of firm export growth. Counterfactual simulations indicate that a ten-percentage-point tariff increase would reduce total trade by 16.4%, while improved logistics performance would raise it by 25.9%. The study concludes that theory-consistent structural models and flexible machine-learning tools are complements rather than substitutes, and it offers practical guidance for analysts, managers and policymakers.