Exploring the food-energy inflation relationship through Fourier methods: Asymmetric and nonlinear causality

This study investigates the long-run relationship and Granger-type predictive causality between food and energy inflation in T?rkiye, with a particular focus on asymmetric transmission, price stickiness, and structural changes. Monthly data covering the period from January 2003 to February 2025 are employed. The analysis begins with linearity testing, followed by the application of Fourier-based unit root and cointegration tests to account for structural shifts. Long-run coefficients are estimated using Dynamic OLS, Fully Modified OLS, and Canonical Cointegration methods. In addition, Hatemi-J asymmetric causality tests are conducted within a Granger framework to examine the direction and nature of shocks. The findings reveal that a 1% increase in energy inflation leads to a 1.13% increase in food inflation in the long run. Bidirectional Granger-type causality is detected for positive shocks, whereas negative shocks exhibit weaker and asymmetric linkages. These results support the presence of price stickiness and nonlinear transmission mechanisms. Overall, the study provides a comprehensive framework for understanding energy-food inflation dynamics and highlights the importance of accounting for asymmetries in policy design.