Lorentz-Inspired Density Forecasting Across Economic Systems: Mathematical Foundations and Cross-Country Evidence

This research investigates Lorentz-inspired probability distributions and their applications to macroeconomic density forecasting across different economic systems. The study develops and examines three related mathematical frameworks: an interior-weighted Lorentz density model, a generalized Lorentzian heavy-tail distribution, and a Lorentz–Leibniz temporal-memory extension. The mathematical analysis addresses probability normalization, distributional regularity, identification conditions, predictive log-score properties, and conditional forecast-loss bounds. The empirical investigation includes cross-country macroeconomic comparisons, a six-country fixed-protocol validation, and reproducible reduced-model inflation experiments involving eight economies, including Türkiye, China, the United States, Germany, Japan, Poland, Hungary, and Vietnam. Two economic hypotheses are investigated: Lorentz-only models may be particularly applicable to established capitalist economies. Lorentz–Leibniz temporal-memory models may offer additional predictive value in economies undergoing market-oriented transitions. The empirical findings indicate heterogeneous forecasting performance across countries and economic conditions. Improvements in some reduced-model experiments are concentrated around the 2022 inflation shock, while the fixed-protocol validation does not establish aggregate predictive superiority. The study presents these economic-system relationships as hypotheses requiring further empirical validation rather than established economic laws. The manuscript includes mathematical propositions, detailed proofs, country-level analyses, and supplementary computational materials. It aims to contribute to probabilistic macroeconomic forecasting, economic risk analysis, and the mathematical study of economic uncertainty. Author: Mahir SogutAffiliation: Independent Researcher, Çankırı, TürkiyeFunding: No external fundingCompeting interests: None declared Research status: Manuscript submitted to SN Business & Economics for editorial consideration. The findings have not yet undergone completed journal peer review.