The Dynamics of Producer Food Prices: a Fourier–Wavelet Analysis of Exchange Rates and Agricultural Inputs

This study is motivated by the persistent nature of food inflation in Türkiye, driven by exchange rate volatility and dependence on imported inputs, as well as the tendency of the existing literature to address these dynamics mostly within a linear framework. The analysis explores the long-term relationships, nonlinear structures, and time–frequency co-movements between the Food Producer Price Index (Food PPI), Agricultural Input Price Index (GFE), and exchange rates (USD/TRY, EUR/TRY). Monthly data covering the 2015:01–2025:05 period are used; the relevant series are seasonally adjusted and logarithmically transformed. Methodologically, the study applies the LR and Hansen (1999) tests to detect nonlinearity, while the Harvey–Mills (2002) and Kapetanios–Shin–Snell (2003) tests are employed to determine integration orders. The Fourier cointegration test examines long-term relationships; DOLS estimates capture the degree of exchange rate pass-through; and Wavelet Coherence (WTC) analysis reveals time–frequency interactions. The findings indicate that the Food PPI and exchange rates are I(1), while the GFE is I(2). Hence, cointegration analysis includes only exchange rates as explanatory variables. DOLS estimates the pass-through coefficients as 1.13 (USD) and 1.14 (EUR). WTC results highlight strong synchronization (→) and occasional exchange rate and GFE leadership (↗/↘), particularly after 2018. Structural breaks identified by the HM test align with exchange rate shocks (2016–2019), the 2020 pandemic, and post-2022 energy price surges. The study provides an original contribution by combining nonlinear tests, Fourier, and WTC analyses to examine the food PPI–exchange rate nexus in Türkiye.