# A Predictive Method for Temperature Based on Ensemble EMD with Linear Regression
## 3 Methodology  
In this section, we present the foundational theory behind our proposed EEMD-LSTM and EEMD-LR prediction methods. Initially, we provide a brief overview of the EEMD, LSTM, and LR techniques discussed earlier. Subsequently, we delve into the basic structure of prediction methods for EEMD-LSTM and EEMD-LR, establishing the theoretical framework for our prediction methodologies [44]. Our approach involves decomposing complex wind speed sequences into low complexity sub-sequences using EEMD. These sub-sequences are then individually predicted by employing LR, LSTM, EEMD-LSTM, and EEMD-LR methodologies. The ultimate forecast for the initial sequence is obtained by aggregating the prediction values from multiple sub-sequences. The models for EEMD-LSTM and EEMD-LR are depicted in Figures 8 and 9, respectively. Additionally, Figure 10 illustrates the the proposed EEMD-LR. This approach aims to simplify complex problems by breaking them down into simpler ones, solving each to address the overall complexity. The fundamental operational process of EEMD-LR involves decomposing the problem into manageable subproblems and solving them individually to attain the overarching solution. Figure 8: Schematic diagram of EEMD-LSTM. Figure 9: Schematic diagram of EEMD-LR. Below are schematic diagrams of the models for the EEMD-LSTM and EEMD-LR methods. The models encompass five distinct steps: collect and prepare data, employ EEMD to decompose and to create various sub-sequences, train machine learning models separately for forecasting, aggregate prediction results from all sub-sequences, and evaluate the model. Figure 10 is a concise overview of the fundamental operational process of the EEMD-LR method. In short, Figure 10 illustrates the end-to-end workflow of the proposed EEMD-LR method: raw Signal \(\rightarrow\) EEMD \(\rightarrow\) IMFs \(\rightarrow\) parallel LR models \(\rightarrow\) ensemble prediction. The novelty of combining EEMD with LR lies in leveraging EEMD's ability to decompose complex time series into intrinsic mode functions, which can capture underlying patterns and trends more effectively. This decomposition enhances LR's predictive accuracy by providing cleaner, more relevant features for regression analysis. By integrating these methods, our approach addresses limitations of traditional regression models, achieving an improved prediction performance on non-stationary or noisy data. This novel combination offers a more robust and accurate framework for time-series forecasting, which sets it apart from conventional methods that rely solely on linear regression or simpler decomposition techniques. To clarify the EEMD-ML interaction, further explanation is provided on the relationships between important modules. After decomposing the raw temperature signal into IMFs via EEMD, each IMF (and residual) is treated as an independent input channel for the ML model. For linear regression (LR), each IMF component is fitted with a separate LR sub-model. Predictions from all sub-models are aggregated (summed) to produce the final output. Decomposition reduces nonlinearity in sub-signals, simplifying the modeling complexity. LR is applied to each IMF to capture linear trends at different frequency scales, which avoids the need for complex nonlinear architectures. Below is a detailed description of the proposed method:  
Figure 10: Diagram outlining the proposed EEMD-LR. 1. Simulation data are generated alongside the collection of real-world data, both of which undergo preprocessing to align with formatting requirements for the EEMD. This ensures the formation of the input data \(X\) for the EEMD;
2. The EEMD divides the input data \(X\) into \(n\) sub-sequences, adhering to the regulations of the decomposition for time series. Typically, the final sub-sequence is termed the residual sub-sequence \(S_{R}\). Hence, the \(n\) sub-sequences comprise \(n-1\) IMF sub-sequences and one residual sub-sequence \(S_{R}\), which is denoted as (\(S_{1}\), \(S_{2}\), \(\ldots\), \(S_{n-1}\), \(S_{R}\)).