This study examines Time-Varying Granger Causality Tests used to determine dynamic relationships between time series variables, and specifically addresses the Recursively Evolving Window (REW) approach developed by Shi, Phillips, and Hurn (2018, 2020), one of the most recent and widely used approaches in this field. Traditional causality tests assume that relationships remain constant throughout the entire period, which can lead to misleading causality results during periods of global crises, policy changes, and structural breaks. To overcome this limitation, the proposed REW algorithm can accurately determine the exact dates when the causality relationship begins and ends with high precision, thanks to its flexible window structure. Within the methodological framework, the FEW, ROW, and REW algorithms were compared, and the theoretical basis of the algorithm was presented. In the application section of the study, the relationship between the VIX (Fear Index) and BIST100 was examined using weekly data covering the period 2005-2025. The analysis revealed that the VIX has a non-stationary, time-varying predictive power over BIST100 returns. It has been proven that the causal relationship significantly strengthened during periods of external shocks, such as the 2008 Global Crisis, the 2013 Fed Taper Tantrum process, and the 2020 COVID-19 pandemic. Consequently, this methodology reveals temporary causality periods that static models overlook, providing policymakers and investors with an important decision-making mechanism.