## 1 Introduction  
Data integrity represents a critical foundation for scientific research, operational decision-making, and predictive modelling. Nonetheless, real-world datasets--especially those requiring continuous monitoring--frequently exhibit incompleteness. Missing data not only reduce statistical power but potentially introduce significant analytical bias if not meticulously addressed, thereby compromising research reliability and subsequent interpretative conclusions. Imputation strategies for hydrological and climatological datasets demonstrate considerable variability in their treatment of correlation, autocorrelation, and periodicity [1, 2]. The original ratio method emerges as a versatile technique [3], leveraging proportional relationships and has been used especially in environmental sciences [4] but also in sociology [5] and economics [6]. In hydrological contexts, this method proves especially valuable for reconstructing missing rainfall [7, 8] or river flow data [9] by exploiting relationships between nearby monitoring stations or historical trends. However, its primary constraint lies in its dependence on external data sources, which may not always be available. In climatology and hydrology, widely utilized gap-filling methods often rely on data from nearby stations. To differentiate these approaches from the methods explored in the current research, the term \"self-imputation\" was introduced, signifying that the imputation process and its evaluation are conducted exclusively using the incomplete dataset itself, without incorporating external reference data. To circumvent the methodological limitations in the absence of reference data, our research introduces a novel self-imputation approach. This innovative method capitalizes on the intrinsic periodic and autocorrelative properties of hydroclimatic systems, enabling data reconstruction without relying on external predictors. The approach presents a robust alternative for addressing data challenges in sparse observational networks, potentially enhancing the ability to manage incomplete environmental datasets. ARIMA (AutoRegressive Integrated Moving Average) models represent a widely used imputation methodology for stationary time series analysis [10; 11]. Despite their widespread application, these models present significant computational challenges when confronted with incomplete datasets. The presence of data gaps fundamentally disrupts the calculation of critical lagged terms and error correction mechanisms [12], thereby limiting their direct applicability in scenarios with substantial missing information. Complementary approaches, such as Kalman Filter techniques and their sophisticated extensions, including the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), have demonstrated remarkable versatility across diverse domains [13]. These methodological frameworks have proven particularly effective in dynamic data imputation, with applications spanning robotics [14], econometrics [15], and climate science [16]. Machine Learning (ML) has emerged as a transformative methodology in addressing data imputation challenges within hydrology and climatology, demonstrating unprecedented capabilities in extracting intricate patterns from incomplete environmental datasets [17; 18; 19]. Researchers have increasingly developed hybrid methodological frameworks that ingeniously integrate deterministic seasonal trend analysis with stochastic fine-tuning techniques, thereby enhancing predictive accuracy and computational resilience [20]. Ensemble methodological approaches, integrating deterministic models with machine learning-based stochastic techniques, represent a promising strategy for substantially enhancing imputation robustness [21]. This sophisticated approach enables more precise reconstruction of datasets characterized by complex periodicity and inherent measurement noise.