Fourier Cointegration Analysis of the Relationship Between Interest and Noninterest Income in Banks: The Case of Azer Turk Bank

This study investigates the dynamic relationship between interest and noninterest income at Azer Turk Bank using quarterly data from 2016Q1–2024Q3. Unit root tests including Augmented Dickey–Fuller (ADF), Kwiatkowski–Phillips–Schmidt–Shin (KPSS), and Fourier–KPSS indicate that both variables are non-stationary in levels but become stationary after first differencing. The Hylleberg–Engle–Granger–Yoo (HEGY) test further shows that both series contain a unit root at the non-seasonal (0) frequency, while no unit roots are detected at the seasonal frequencies (π/2 and 3π/2). Johansen cointegration and the Fourier Autoregressive Distributed Lag (Fourier–ADL) framework confirm the existence of a stable long-run equilibrium. As a key methodological contribution, the study derives explicit Fourier-based Vector Error Correction Model (VECM) equations, enabling the modeling of cyclical deviations around nonlinear trends. Fourier Toda–Yamamoto and Breitung–Candelon frequency-domain causality tests reveal asymmetry: interest income consistently drives noninterest income in the short and medium run, whereas the reverse effect is weak. The results also confirm mean reversion, with deviations from equilibrium corrected within 5.9; 2.5 quarters. Overall, the findings highlight the limited diversification potential of noninterest income and the decisive role of lending in bank revenues, offering both methodological advances and practical guidance for macroprudential policy.