## 4 Result and Discussion
### Regression Model Performance
[24] applied LSTM networks to forecast climate data, achieving improved accuracy for short-term predictions but struggling with longer-term dependencies. [PERSON] et al. [25] combined LSTM and Prophet models to capture daily cycles effectively, yet this approach required significant computational resources. [PERSON] et al. [26] employed advanced RNNs to model temporal relationships, demonstrating good performance in handling sequential data but with limited capacity to capture cyclical patterns. Unlike these methods, our proposed approach introduces a cycling layer to better capture both short-term and long-term cyclical patterns, resulting in lower error rates and faster model fitting times. Furthermore, the sensitivity of the model's performance to various hyper-parameters, such as the cycling period and the choice of activation functions, also plays a crucial role in determining its effectiveness. The cycling period defines how well the model captures repetitive patterns in time series data. We set 12 h or 24 h per cycling in the experiment. If the period is too short, the model may focus only on short-term dependencies, missing out on long-term trends. Conversely, a period that is too long might overlook shorter, important fluctuations. Similarly, the choice of activation functions impacts how the model handles non-linearities in the data. Functions like ReLU can speed up training but may suffer from issues like \"dead neurons,\" while tanh or sigmoid activations may better capture smooth cyclic patterns but could be prone to the vanishing gradient problem. The paper does not provide a detailed exploration of how these hyper-parameters influence model performance, particularly in terms of the forecast accuracy and model fitting speed. While the results are encouraging, several limitations of the testing process should be acknowledged. The models were evaluated using a narrow set of metrics, and critical factors, such as computational efficiency, robustness to outliers, and scalability, were not addressed. Additionally, the performance of the cycling layer may vary with different parameter configurations, and a more comprehensive hyperparameter search could potentially yield different outcomes. Moreover, the findings are constrained to the specific conditions of the tests that were conducted. The observed improvements with the cycling \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Linear** & **Polynomial** & **Support Vector** & **KNN** & **LSTM** & **GRU** \\  & **Regression** & **Regression** & **Regression** & **Regression** & **LSTM** & **GRU** \\ \hline
**MAE** & **0.0001487 (24 h)** & 0.00159 (12 h) & 0.1068 (12 h) & 0.0077 (24 h) & 0.00238 & 0.00226 \\ \hline
**MSE** & 3.978 (24 h) & 2.0274 (24 h) & 0.1071 (12 h) & **0.0150 (24 h)** & 1.2093 & 1.1162 \\ \hline \hline \end{tabular} Note: The bold marks the best MSE and MAE scores.  
\end{table} 
Table 4: Four regression models with cycling layer preprocessing against LSTM and GRU. layer may not be universally applicable across all datasets or problem domains. It is also important to recognize that the cyclical patterns examined--specifically the 12 h and 24 h cycles--were selected based on specific assumptions that might not be relevant to other temporal patterns or phenomena.