## 3 Results and Discussion
The subsequent positions are occupied by other well-performing methods, GB and RF. These rankings remain consistent for both forward and backward interpolation (Table 2). To address the challenge of evaluating imputation methods in scenarios lacking reference data, we have developed an innovative assessment metric. The methodology involved a strategic approach: starting with the original dataset containing missing values, we identi \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Forward** & **Backward** \\  & **Imputation** & **Imputation** \\ \hline R & 98.64\% & 92.82\% \\ K & 99.37\% & 93.91\% \\ CB & 99.75\% & 95.94\% \\ GB & 99.54\% & 95.22\% \\ XGB & 99.37\% & 94.21\% \\ RF & 99.48\% & 94.58\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Percentage of cases with preserved temporal correlation for different imputation methods. Figure 9: Performance index of different imputation methods. fied an equivalent number of adjacent time points surrounding these gaps. The underlying hypothesis suggested that error magnitudes resulting from applying identical imputation methods to newly created gaps would closely approximate errors observed in the original imputation process. The proposed methodology combines the results of forward imputation (applied to the original dataset with missing values) and backward imputation (applied to newly created adjacent gaps). An imputation method was considered effective if the errors from both approaches aligned with a linear function originating at zero and maintaining a 45-degree slope. This alignment indicates equal contributions of errors from both interpolations, reflecting the method's consistency regardless of the scenario. Symmetry along the 45-degree line minimizes biases, as deviations would suggest a method's overfitting or underfitting in specific cases. This criterion ensures robustness and generalizability, avoiding disproportionate sensitivities to initial conditions or subsequent adjustments. By aligning error points along the 45-degree line, the interpolation method demonstrates balanced performance, reliability, and accuracy, making it optimal for applications requiring consistent data estimation. We have performed backward imputation using the ratio method, ARIMA-based Kalman filter, and P variants of machine learning imputation methods, calculating for each case the slope and intercept of regression equations derived from original and backward-imputed value pairs. The R function collecting the basic statistical metrics of evaluation are publicly available on GitHub at [[https://github.com/zsmagyari/SelfImpute](https://github.com/zsmagyari/SelfImpute)]([https://github.com/zsmagyari/SelfImpute](https://github.com/zsmagyari/SelfImpute)). Our analysis provides robust substantiation for the initial research hypotheses. Across the four monitoring stations, the CB method demonstrated the highest performance, consistently exhibiting low deviation from the 45-degree reference line and presenting the lowest intercept values, as illustrated in Figure 10.  
A predictable correlation emerged, revealing that higher percentage gap variations corresponded directly to more pronounced statistical divergences. The CB method's performance was particularly compelling, with the RF method and, in certain instances, the Kalman filter closely approximating its precision. The proposed self-assessment efficiency methodology found strong empirical validation through this approach. A significantly high correlation coefficient of 0.95 was observed between the performance index and the linear regression slope's deviation from the 45-degree reference line obtained through backward interpolation. This statistically significant correlation (Figure 11) fundamentally substantiates our methodological framework. The proximity to a perfect correlation suggests considerable reliability and reproducibility of our self-assessment technique across diverse data interpolation scenarios.