## 4 Experiments
### Experimental Results
#### 4.4.7 Ablation Results  
To further validate the rationality and effectiveness of the RPM-ETC model design, a series of ablation experiments were conducted, particularly examining the model's performance in the absence of the Self-temporal Compression Mechanism. This mechanism is crucial for the model, as it enhances the model's ability to process time series data through iterative compression. The specific results of the ablation study are presented in Table 14, where the accuracy, frames per second (FPS), and quantity of model parameters (in millions) served as the primary evaluation metrics. The outcomes of the ablation study reveal several key findings. First and foremost, the adoption of the Self-temporal Compression Mechanism significantly improved the model's efficiency in recognizing patterns, owing to its capacity to distill essential information from time series data. Specifically, the inclusion of this mechanism not only elevated the accuracy from 79.3% to 86.3% but also markedly increased the processing speed, as the Self-temporal Compression Mechanism reduced the length of the time series iteratively with each input, thus enhancing the FPS from 280.9 to 386.3. Additionally, we also investigated the performance of the model in the absence of the partial autocorrelation function (PACF). Experimental results revealed that without the PACF, the model exhibited lower accuracy. This could be attributed to the lack of consideration for the temporal dependencies among different features. The PACF aids the model in more accurately understanding and capturing the dependencies within time series data. Hence, its absence might hinder the model from fully utilizing temporal information, thus affecting its accuracy. This further validates the significance of PACF in the model \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Comparison Group** & **t-Value** & **Degrees of Freedom (df)** & **\(p\)-Value** \\ \hline RPM-ETC vs. Transformer & 14.27 & 5.55 & \(p\) \(<\) 0.001 \\ RPM-ETC vs. LSTM & 40.11 & 4.40 & \(p\) \(<\) 0.001 \\ RPM-ETC vs. RNN & 17.58 & 4.31 & \(p\) \(<\) 0.001 \\ RPM-ETC vs. MiniRocket & 36.58 & 4.31 & \(p\) \(<\) 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Statistical comparison of RPM-ETC with other methods. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model Configuration** & **Accuracy (\%)** & **FPS** & **Parameters (M)** \\ \hline RPM-ETC w/o Enhanced PE & 81.3 & 351.7 & 20.08 \\ RPM-ETC w/o PACF & 76.3 & 346.3 & 20.07 \\ RPM-ETC w/o Self-temporal Compression & 79.3 & 280.9 & **17.88** \\ RPM-ETC & **86.3** & **386.3** & 20.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Results of ablation experiment. Bold values represent the best performing data for each column. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **Values** & **Mean** & **Standard Deviation (SD)** \\ \hline RPM-ETC & [86.3, 85.9, 86.3, 86.2, 84.3] & 85.80 & 0.85 \\ Transformer & [80.1, 79.2, 80.0, 79.7, 80.1] & 79.82 & 0.38 \\ LSTM & [70.3, 70.1, 69.8, 70.0, 70.2] & 70.08 & 0.19 \\ RNN & [79.1, 78.9, 78.7, 79.0, 79.1] & 78.96 & 0.17 \\ MiniRocket & [71.7, 71.5, 71.6, 71.3, 71.7] & 71.56 & 0.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Accuracy data description of different methods. and underscores the necessity of considering temporal dependencies among features in time series modeling. Meanwhile, we investigated the performance of the model without an enhanced PE. The experimental results demonstrate that an enhanced PE significantly mitigated the issue of positional information decay, improving the overall performance of the model. Specifically, an enhanced PE provided additional positional information support in deep networks, enabling the model to capture temporal relationships more accurately and enhance prediction accuracy. This validated the effectiveness of our proposed method in preserving and strengthening positional information, proving its advantage in boosting the performance of Transformer-based time series models.