## 4 Discussion  
As the results show in Table 6 and Figure 8, MLP, as the first proposed model among the above models, has MAE, MSE, MAPE, and \(R^{2}\) values of 3.0191, 16.9058, 0.0202, and 0.9717. Despite its simplicity--comprising only a few linear layers--MLP achieves reasonable performance in long-sequence modeling due to its straightforward architecture. And it is the most time-saving model among them. BP is currently one of the most widely used neural network models. Its learning rule is to use the steepest descent method, which continuously adjusts the weights and thresholds of the network through BP to minimize the sum of squared errors of the network. Compared to MLP, BP has a better result in our experiments, and the values of the four metrics are 2.8884, 16.0640, 0.0192, and 0.9731. Due to the unique design structure, LSTM is suitable for processing and predicting important events with very long intervals and delays in time series. Compared to the previous two models, its metrics were significantly better, being 2.6428, 13.2309, 0.0173, and 0.9779. The hyperparameters of the SNN are chosen according to the following rules: with twice the number of iterations of ICS-SNN, adjust the hyperparameters based on experience, and then select the hyperparameter with the smallest metrics. The SNN model with manually tuned hyperparameters achieves MAE, MSE, MAPE, and R\({}^{2}\) values of 2.7351, 13.2958, 0.0184, and 0.9790, respectively. Although LSTM excels in capturing long-term dependencies, the ICS-SNN model surpasses it by leveraging optimized hyperparameters and temporal dynamics inherent to spiking neurons. The SNN has manually adjusted parameters, which means there is a long and tedious training process. Most numbers in people's lives do not exceed two decimal places, so when researchers need to change the hyperparameter, they prefer to choose integers and numbers with no more than two decimal places. But the optimal solution is obviously randomly distributed, so there is a long way to go if we adjust the hyperparameters manually. Without hyperparameter optimization, SNNs demonstrate inferior performance compared to LSTM, highlighting the necessity of automated parameter tuning. In order to see the improvement effect of ICS clearly, we conducted the CS-SNN experiments at the same time. The values of the four metrics are 2.4709, 11.2242, 0.0163, and  
Figure 8: The results of each model and metric. 0.9812. The traditional CS algorithm can help the SNN achieve a small improvement. By automatically transforming hyperparameters, a greater chance of approaching the optimal solution is obtained. The piecewise mapping in ICS ensures a more uniform initial population distribution, reducing the risk of local optima. Additionally, the adaptive discovery probability mimics natural cuckoo behavior, balancing exploration and exploitation. ICS-SNN obtains values of the four metrics of 2.3571, 10.4675, 0.0156, and 0.9822. Meanwhile, compared with SNN, ICS-SNN reduced MAE by 13.82%, MSE by 21.27%, and MAPE by 15.21%, and R^2 increased from 0.9790 to 0.9822. The final hyperparameter values of ICS-SNN, CS-SNN, and SNN are shown in Table 7. These hyperparameters work together on the results. The results obtained by individually modifying one parameter and simultaneously modifying multiple parameters may have significant differences. Figure 9 is the pictorial result of 300 data to the reciprocal of actual and predicted values. It can be clearly seen from the figure that the two lines of ICS-SNN are closer together, which means its experimental results are the best among the six models. Considering that the ICS-SNN model enhances its global search capability by introducing an ICS algorithm and uses RLIF to better process time series data, theoretically the model should be able to capture short-term market dynamics more effectively. Based on the 1-min K-line data we used, it is expected that the optimal prediction range of ICS-SNN may be concentrated within a few minutes to a few hours.