## 4 Results and Discussion  
### Basic Statistical Analysis  
This section presents the empirical results of the analysis. In time series econometrics, testing for unit roots or stationarity is a critical preliminary step to avoid spurious regression results and to ensure the selection of the appropriate estimation method. Accordingly, before proceeding with the estimation of the FARDL model, unit root tests were conducted to determine the order of integration for each variable. Traditional unit root tests, such as the augmented Dickey-Fuller (ADF) test and the Phillips-Perron (PP) test, are commonly employed in this context. However, these conventional methods do not account for structural breaks, which can lead to misleading conclusions in the presence of such breaks. To address this limitation and enhance the robustness of the analysis, the Fourier-ADF and Fourier-LM tests were utilized. These tests incorporate Fourier transformations, which effectively capture structural breaks by identifying smooth shifts in the data without requiring prior knowledge of the breakpoints. The use of Fourier-based unit root tests allows for a more reliable assessment of stationarity, accommodating potential non-linearities and discontinuities in the data. As a result, this approach yields more robust and accurate empirical findings. The results from the Fourier-ADF and Fourier-LM tests, presented in Table 2, provide a comprehensive overview of the stationarity properties of the variables under investigation, ensuring a solid foundation for subsequent model estimation and policy analysis. The null hypothesis H\({}_{0}\) for both the Fourier-LM and Fourier-ADF tests posits the presence of a unit root, while the alternative hypothesis H\({}_{1}\) suggests stationarity. As shown in Table 2, the results indicate that H\({}_{0}\) cannot be rejected at the level I(0) for either test, signifying that the dataset exhibits non-stationarity at levels. However, upon differencing the data, H\({}_{0}\) is rejected at I(1), confirming that the variables become stationary after the first difference. This finding implies that the series is integrated of order one, I(1), and thus suitable for further analysis using the FARDL framework. The decision to employ the FARDL approach in this study is particularly justified by its ability to account for structural breaks, a feature that traditional cointegration methods often overlook. As highlighted in the methodology, the FARDL method outperforms conventional approaches by incorporating Fourier terms, which capture smooth structural shifts without prior \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{2}{c}{**Fourier-ADF Test**} & \multicolumn{2}{c}{**Fourier-LM Test**} \\ \cline{2-5}  & **I(0)** & **I(1)** & **I(0)** & **I(1)** \\ \hline CO\({}_{2}\) & 0.137 & \(-\)5.796 *** & \(-\)4.489 ** & \(-\)6.357 *** \\ tp & \(-\)2.652 & \(-\)6.771 *** & \(-\)1.635 & \(-\)6.856 *** \\ ee & \(-\)1.972 & \(-\)6.132 *** & \(-\)1.838 & \(-\)6.538 *** \\ eg & \(-\)0.723 & \(-\)5.856 *** & \(-\)4.502 ** & \(-\)5.924 *** \\ ur & \(-\)1.745 & \(-\)5.003 ** & \(-\)1.136 & \(-\)5.399 *** \\ in & \(-\)1.593 & \(-\)6.782 *** & \(-\)4.131 ** & \(-\)6.898 *** \\ fdi & \(-\)2.474 & \(-\)5.515 *** & \(-\)1.098 & \(-\)6.146 *** \\ gt & \(-\)1.041 & \(-\)5.619 *** & \(-\)1.283 & \(-\)6.395 *** \\ \hline \hline \end{tabular} Note: ** 5% significance level. *** 1% significance level.  
\end{table} 
Table 2: Results of unit root test. knowledge of their timing. This flexibility is crucial for improving the robustness of the empirical results, especially in the context of time series data with potential breaks. The results of the FARDL bounds testing, as summarized in Table 3, provide further evidence of the long-run relationships between the variables under study, offering insights into the dynamic interactions that govern the model.