## 4 Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Indicator** & \(CO_{2}\) & **GDP** & **RENC** & **ACEL** & **FDI** \\ \hline Mean & 0.15885 & 6.950086 & 3.716281 & 4.25389 & \(-\)0.108199 \\ Median & 0.127473 & 6.945961 & 3.745767 & 4.256014 & 0.308696 \\ Maximum & 0.691487 & 7.713896 & 3.970292 & 4.601162 & 1.286619 \\ Minimum & \(-\)0.409446 & 6.270796 & 3.48124 & 3.908242 & \(-\)3.6036 \\ Std. Dev. & 0.356628 & 0.459706 & 0.169379 & 0.237885 & 1.083264 \\ Skewness & 0.039307 & 0.084788 & 0.005215 & \(-\)0.01467 & \(-\)1.578133 \\ Kurtosis & 1.565627 & 1.677821 & 1.3829 & 1.637362 & 5.211024 \\ Jarque–Bera & 2.923441 & 2.517294 & 3.704757 & 2.63166 & 21.0384 \\ Probability & 0.231837 & 0.284038 & 0.156864 & 0.268252 & 0.000027 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Descriptive statistics. Figure 1: The evolution of \(CO_{2}\), GDP, RENC, ACEL, and FDI in India (1990–2023). The Phillips-Perron (PP) unit root test [40] indicates that all variables are integrated to order 1, as shown in Table 4. From the PP test results, all variables (except for FDI) are integrated to order I (1), suggesting that they are non-stationary at level I(1) but become stationary at first difference. The FDI variable is stationary at level I(0), highlighting its distinct behavior compared to the other variables analyzed. According to Table 5, four of the % criteria (LR, FPE, SC and HQ) suggest that a lag length of 3 is the most favorable selection for the ARDL model. LR denotes the sequential modified likelihood ratio test statistic (with each test conducted at a 5% significance level), FPE stands for the final prediction error, AIC refers to the Akaike information criterion, SC is the Schwarz information criterion, and HQ represents the Hannan-Quinn information criterion. This selection is essential for capturing the short- and long-term dynamic effects of the analyzed variables, while also preventing residual autocorrelation. The obtained model is ARDL (3, 2, 3, 3, 3, 3, 3). Table 6 indicates that the F-statistic values computed for the ARDL bounds test exceeds the upper bound I (1). This outcome supports rejection of the null hypothesis of no cointegration at the 5% level. In other words, the F-statistic value (45.50) clearly exceeds the upper bound I (1) at the 1% significance level, confirming the presence of a cointegration relationship among the variables. This indicates the existence of a stable long-term relationship between \(CO_{2}\) emissions and the economic factors analyzed. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Statistic** & **Value** & **K (Number of Regressors)** \\ \hline F-statistic & 45.50 & 6 \\  & Critical value bounds & \\ Significance & I (0) & I (1) \\
10\% & 2.25 & 3.38 \\
5\% & 2.68 & 3.96 \\
1\% & 3.71 & 5.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of the ARDL cointegration bounds test. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Variables**} & **Level** & **First Difference** & **Order of Integration** \\ \cline{2-4}  & **T-Statistics** & **T-Statistics** & **at 5\% L.O.S.** \\ \hline CO\({}_{2}\) & 1.05 (0.72) & \(-\)5.26 *** (0.00) & 1 (1) \\ \hline GDP & 1.17 (0.99) & \(-\)6.55 *** (0.00) & 1 (1) \\ \hline GDP2 & 1.84 (0.999) & \(-\)5.90 *** (0.00) & 1 (1) \\ \hline GDP3 & \(-\)2.51 (0.999) & \(-\)5.49 *** (0.00) & 1 (1) \\ \hline RENC & \(-\)1.24 (0.645) & \(-\)4.10 *** (0.00) & 1 (1) \\ \hline ACEL & \(-\)0.19 (0.929) & \(-\)7.68 *** (0.00) & 1 (1) \\ \hline FDI & \(-\)3.33 ** (0.021) & \(-\)6.37 *** (0.00) & 1 (0) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PP unit root test results.