Econometric analysis of BIST Bank Index determinants with Fourier approach

This study aims to reveal the development and performance of the BIST Banking Index traded on Borsa Istanbul by examining the determinants of the index using econometric methods developed with the Fourier approach. In the theoretical framework section, the role of the banking sector in financial markets is discussed and financial variables that could affect the index are examined. When determining the variables, the model with the lowest Akaike Information Critterion (AIC) was selected and the analysis was conducted using the variables of bond interest rate, credit default sawp (CDS) spread, Exchange rate (USD/TRY), industrial production index and BIST100 index. Within the scope of time series analysis, Fourier ADF unit root tests, Fourier ARDL cointegration tests and Fourier Toda Yamamoto causality tests were applied by including Fourier terms in traditional approaches. Fourier approaches have been preferred for their ability to deliver stronger and more reliable results by taking into account the structural breaks in indicators following financial, political, geopolitical, etc. shocks. In particular, the Turkish economy experienced numerous shocks between 2015 and 2024, leading to structural breaks in financial indicators. Traditional time series methods may be insufficient in producing sound and reliable results because they cannot account for such structural breaks. For this reason, causality and cointegration tests developed using Fourier terms were preferred, thus creating a model that takes into account the nonlinear dynamics and structural breaks that emerge in the series. Thanks to its ability to capture structural breaks resulting from high volatility during the period, it has revealed both the direction and level of the relationship between the BIST Bank Index and financial indicators in a more consistent manner. In the Fouirer ARDL cointegration test, the model with the lowesr value of -369.379 was selected from 2500 models based on the Akaike Information Criterion (AIC). As a result of the cointegration test, a long term relationship was found between the BIST Banking Index and the variables of CDS, bond interest rate, exchange rate (USD/TRY), BIST100 index and industrial production index. The analysis results indicate that only sin2.L0 is significant at the %5 level among the Fourier components, suggesting that during the analyzed period, the BIST Banking Index series was exposed not only to economic indicators but also to low frequency structural fluctuations over time. No meaningful relationship was detected in the other Fouirer component (cos(2πt/51)) either in the current period or in the period lagged by one period. This indicates that the characteristic structure of the change in the waveform is asymmetric or unidirectional and that there are shocks in the bank index that recur at regular intervals but are not symmetric. In this study, according to the Fourier Toda Yamamoto causality test, it was found that there is a unidirectional causality relationship from the CDS and USD/TRY variables, which are determinants of the BIST Banking Index, to the BIST Banking Index and also a unidirectional causality relationship from the BIST Banking Index to the bond interast rate. Based on the empirical results obtained, it reveals that financial market Dynamics in Turkey have a fragile structure and that the banking sector is sensitive to financial shocks.