## 1 Introduction  
Time series analysis is a fundamental aspect of numerous scientific disciplines, including economics and engineering. At its core, a time series is a sequence of data points, typically comprising successive measurements made over a specific time interval. The importance of time series data lies in its ability to predict future phenomena based on the correlation between previous observations and future values. This forecasting process is not merely an extrapolation; it involves a comprehensive understanding of intricate patterns, trends, and seasonality within the data. For instance, in economics, time series analysis facilitates distinguishing long-term trends from short-term variations, ensuring that economic policies are not misguided by transient fluctuations [1]. Nevertheless, time series analysis presents several challenges. The data can exhibit diverse patterns, including seasonal, cyclical, and chaotic behavior patterns. Furthermore, the data's non-stationarity can lead to unreliable forecasting outcomes if not properly addressed. In addition to these analytical challenges, external factors can introduce noise into data patterns, complicating the prediction process. Thus, the rigorous preprocessing of time series data is imperative for effective analysis. In our previous work [2], we explored the use of positional self-attention mechanisms integrated into autoencoders for preprocessing time series data. This study demonstrated that positional encodings could effectively capture short-term temporal dependencies, leading to significant improvements in model performance over traditional statistical preprocessing methods. The key findings highlighted a reduction in the Mean Squared Error (MSE), Mean Absolute Error (MAE), and other performance metrics across various regression models, including Linear Regression, Support Vector Regression (SVR), and K-Nearest Neighbors (KNN). However, the previous study also identified several limitations. The positional self-attention mechanism, while effective for short-term dependencies,struggled to adequately capture longer-term cyclical patterns in the data [3]. Additionally, the method exhibited sensitivity to the choice of hyperparameters and showed limited improvements in datasets with pronounced cyclical behaviors, such as seasonal or periodic time series. Our paper underscores the importance of addressing and mitigating various issues that arise from improper data preprocessing methods. Capturing intricate temporal dependencies within data that exhibit periodic features is a significant challenge in data analysis, particularly in the context of time series and spatiotemporal data. A primary difficulty lies in the tendency of most existing approaches to overlook the long-term dependencies inherent to the data. These approaches often fail to consider the comprehensive mechanisms required to model these long-term dependency issues [4]. Alternatively, they employ batch techniques that fragment long sequences into numerous short ones, which inadequately capture the dependencies between sequences, a problem known as sequence fragmentation [5]. Additionally, the shifting of long-term periodic dependencies needs to be addressed in current studies [6]. The objective of this paper is to capture periodic features effectively using weather coefficient data. Addressing these challenges necessitates innovative techniques specifically designed for time series data. This paper proposes a pioneering approach to tackle the complexities of preprocessing time series data. The central aspect of this approach involves replacing traditional positional encoding techniques with a personalized cycling technique integrated into self-attention mechanisms. The significance of this issue is further highlighted by existing research that emphasizes the limitations of positional models in accurately capturing these dependencies.