# A Hybrid Deep Learning Model Based on FFT-STL Decomposition for Ocean Wave Height Prediction
## 3 Experimental Results and Analysis
### Data Analysis and Modeling
In the initial stage (0 to 5 iterations), the training loss reflected by the mean square error (MSE) shows a rapid downward trend, rapidly decreasing from approximately 0.035 to approximately 0.010. At this stage, the model quickly learns the main features of the data. As training progresses, the training loss continues to decrease at a relatively slow rate and eventually stabilizes at about 0.005. This shows that the model constantly optimizes the parameters and gradually converges to a relatively stable state, as shown in Figure 8. From the trend of changes in training loss and validation loss, both are on a downward trend throughout the training process. This phenomenon intuitively shows that the model is effectively learning the characteristics of the data. It should be noted that the validation loss is lower than the training loss in most iterations. This result strongly shows that the model shows good performance in the validation set, there is no obvious overfitting problem, and it has strong generalization ability. During model training, the loss curves in Figure 8 show a special pattern. For most of the training time, the validation set loss is always lower than the training set loss. This phenomenon is due to the use of dropout, a regularization technique used to alleviate overfitting. Dropout encourages the model to learn more generalizable features by randomly deactivating some neurons during training. As a result, the model may perform better on the validation set, resulting in a lower loss in the validation set than loss in the training set. The training results are shown in the Figure 9.  
In this study, the SARIMAX model is used to predict the seasonal component of the decomposed significant wave height data. The model is based on 16,427 observation samples and is targeted at seasonal difference series. The parameter estimation results show that the non-seasonal autoregressive coefficient is \(-0.3845\) and the non-seasonal moving average coefficient is \(-0.9578\); the seasonal autoregressive coefficient and moving  
Figure 8: The changing remainder of training loss and validation loss for bilstm. Figure 9: Predicted results of BiLSTM. average coefficient are 0.2010 and 0.5145, respectively. The variance of the disturbance term is estimated to be \(\sigma^{2}\) = 0.0002. All parameter estimates are statistically significant at the 0.1% level. The model evaluation indicators show that the model has a high goodness of fit, with a log-likelihood value of 47,580.405, and information criterion values of AIC = -95,150.81, BIC = \(-\)95,112.28, and HQIC = \(-\)95,138.08, indicating that the model has a high degree of fit. The residual diagnostics rejected the null hypothesis of residual independence at the 5% significance level, indicating the presence of autocorrelation. The Jarque-Bera test statistic reaches 965,897.14 (\(p<0.001\)), the skewness is \(-\)0.13, and the kurtosis is 40.58, indicating that the residuals have obvious characteristic of a peak and a thick tail. The heteroskedasticity White test yields a \(p\)-value \(<0.001\) and the heteroskedasticity coefficient H = 0.87, indicating the existence of conditional heteroskedasticity. In order to further improve the impact of residual autocorrelation, the weighted least squares method is used to assign lower weights to observations with larger residual variances, thereby improving the robustness of parameter estimation. The SARIMAX model effectively captures the seasonal pattern and short-term dynamics of the wave height series. For the remainder, we used an improved deep convolutional neural network model to predict the data. The convolution model consists of five sequentially connected modules. At the front end of the network, the first-layer module performs preliminary feature extraction on the input signal through a trainable one-dimensional convolution kernel.