Lie Algebra-Based Modeling of Nonlinear Macroeconomic Dynamics Under Fractal Structures
Fractal and Fractional, cilt.10, sa.7, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 10 Sayı: 7
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/fractalfract10070492
- Dergi Adı: Fractal and Fractional
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: chaos, fractal, inflation, interest rate, Lie method
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
Regression methods are widely used to investigate macroeconomic relationships; however, they are generally estimated without first examining whether the underlying variables exhibit fractal structures, persistence, and chaotic dynamics. Although nonlinear regression models relax the assumption of linearity, they rarely account for the complex geometric, long-memory, and dynamical properties that characterize macroeconomic time series. Motivated by this limitation, this study proposes a fractal-oriented Lie regression framework that integrates fractional persistence and Lie algebra to model nonlinear macroeconomic interactions within a unified analytical structure. For Türkiye, the empirical analysis employs monthly data on inflation, interest rates, exchange rates and oil prices covering the period 2000M1–2026M1, encompassing major economic crises and structural breaks. Prior to model estimation, the dynamical characteristics of the variables are examined using entropy measures, long-range dependency analysis, Lyapunov exponents and attractors. The results reveal persistent fractal structures, significant fractional dependence and chaotic behavior, indicating that macroeconomic variables evolve within a complex nonlinear dynamical system rather than around a conventional equilibrium. Based on these results, the variables are represented within a Lie algebra framework in which nonlinear transformation matrices preserve the underlying geometric structure while simultaneously capturing both self-dynamics and cross-variable interactions. The proposed Lie regression model demonstrates substantial improvements over standard regression methods in both model adequacy and forecasting performance. Oil prices emerge as the dominant transmitter of shocks by generating pronounced asymmetric effects on inflation, exchange rates and overall macroeconomic stability. The model achieves remarkable forecasting accuracy by reducing RMSE, MAE, and MAPE from 18.58, 13.61, and 69.92 under a standard regression model to 0.27, 0.22 and 16.4, respectively. Finally, the estimated Lie transformation matrix is employed as a policy-simulation mechanism to evaluate the transmission of alternative oil-price shocks. Scenarios based on 5%, 10%, and 20% increases in oil prices quantify the resulting adjustments in inflation, interest rates, and exchange rates by providing forward-looking assessments of macroeconomic vulnerability. The proposed framework extends standard regression analysis by explicitly incorporating fractional persistence and chaotic dynamics into a Lie algebra representation, thereby offering a more accurate and theoretically consistent approach for modeling complex macroeconomic systems.