Big scallop price

**Figure 5.** The outcome of VMD for each aquatic product price dataset.

From the above figure we can see that the IMF components in the upper layers are strongly non-linear and unstable during the decomposition of EMD and VMD. Therefore, it is extremely crucial to predict the IMF components in the upper layers precisely. In addition, the EMD algorithm has the problem of modal mixing in the decomposition process, which greatly affects the subsequent prediction accuracy, while the application of the VMD algorithm can effectively tackle this problem.

#### *4.3. Aquatic Product Price Forecasting Results Based on VMD-IBES-LSTM Model*

The parameter settings of the improved bald eagle search algorithm are as follows: the number of bald eagles is 5, the dim is 4, the range of learning rate is [0.001, 1], the number of neurons is [10, 500], and the maximum number of iterations is 100. Set the first 367 groups as the training set and the last 41 groups as the test set. The fitting results of each IMF price component are shown in the Figures 6–10 below.

**Figure 7.** Fitting results of IMF components of crucian carp price dataset.

**Figure 8.** Results of fitting each IMF component to the carp price dataset.

**Figure 9.** Fitting results for each IMF component of the white chub price dataset.

**Figure 10.** Fitting results for each IMF component of the big scallop price dataset.

After summarizing each IMF, the regression images of each dataset are as follows (Figure 11):

**Figure 11.** *Cont*.

It can be seen from the above figure that the goodness of fit of the VMD-IBES-LSTM model on Grass carp, crucian carp, carp, white chub, and big scallop price is 0.99767, 0.99764, 0.99665, 0.98873, and 0.97522, respectively, which indicated that the VMD-IBES-LSTM model fits best on the grass carp price dataset, while the fit is relatively average on the big scallop price dataset.

The error analysis of each IMF component is shown in the Table 3 below.


**Table 3.** Error analysis table.


**Table 3.** *Cont.*

*4.4. Comparative Results and Discussion*

To test and validate the effectiveness and superiority of the model that is proposed in this study. In this research, we selected the EMD-VMD-LSTM model [8], VMD-LSTM model [11], CEEMD-CNN-LSTM [12] model, MOGWO-LSSVM model [42], and the model that was proposed in this paper for comparison


**Table 4.** Comparison of various models in prediction performance.


## **5. Discussion**

The fitting images of VMD-IBES-LSTM model and other models that were proposed in this study are as follows (Figure 12).

**Figure 12.** *Cont*.

**Figure 12.** *Cont*.

**Figure 12.** Fitting images of each model.

In the beginning, the models fit well because the fluctuations in grass carp, crucian carp, carp, and chub prices were small. However, with the passage of time, the fit of the single model (LSTM) becomes progressively worse, especially at the extremes. Taking the grass carp and carp price dataset as an example, it is clear that the prediction accuracy of the single model (LSTM) is poor at the extremes, which indicates the limitations of the single model in dealing with highly non-linear and non-stationary time series. Models that are based on the "decomposition-prediction-integration" idea such as the VMD-IBES-LSTM model, VMD-LSTM model, and EMD-VMD-LSTM model are less affected and have a better overall fit to the original dataset. To a higher degree, this indicated that compared to traditional single models (LSTM, BPNN, BiLSTM) and models that are based on the "feature extraction-prediction" idea (CNN-LSTM model, CNN-BiLSTM model), models that are based on the "decomposition-prediction-integration" models showed significant improvements in robustness and model accuracy.

In addition, from the above data results, it can be seen that the hybrid models that are based on the idea of "decomposition-prediction-integration" (e.g., VMD-LSTM) have better performance in terms of *MSE*, *RMSE*, and *RMSE* for each dataset. The *MSE*, *RMSE*, *MAPE*, and *MAE* of these hybrid models (e.g., NAR, LSTM, BPNN) are all smaller than those of the individual models (e.g., LSTM, BPNN), demonstrating that these hybrid models are significantly more accurate in prediction than the individual models. The reason for this analysis may lie in the fact that signal decomposition techniques can effectively solve problems such as prediction difficulties that are caused by the non-smoothness of time series data, significantly reducing the complexity of the data, and providing the possibility of improving the prediction accuracy of the models.

From the above figure, it can be seen that the VMD-IBES-LSTM model proposed in this study outperforms VMD-LSTM, CNN-BiLSTM, Bayes-BiLSTM and other models on each dataset. The improvement in the accuracy of the model is mainly in the following aspects.


Based on the above model and results, we would like to make the following policy recommendations.


However, the method that was proposed in this study can be improved in the following aspects:


## **6. Conclusions**

As an essential resource, the price trend of aquatic products has a crucial impact on economic and social development. To address the non-linear and non-stationary characteristics of aquatic product prices, this paper proposes a new hybrid VMD-IBES-LSTM model for fish price forecasting and compares with VMD-LSTM and other models. The results indicated that the VMD-IBES-LSTM model outperforms the other listed models in *MSE*, *RMSE*, *MAE*, and *MAPE* indicators. Ultimately, based on the above model, we put forward three policy recommendations.

However, the model that was proposed in this study can still be improved in the following aspects. (1) Consider other improved versions of the LSTM, such as Bi-LSTM and GRU, for comparison testing. (2) It can be combined with other optimization algorithms to verify whether the accuracy of the model has been improved. (3) The inclusion of factors that are closely related to aquatic product prices can be considered to further improve the prediction accuracy of the model. On 31 January 2020, the World Health Organization listed the epidemic situation of novel coronavirus as a public health event of international concern. Cities in China adopted the strategy of "closing cities" and isolation. The aquatic product trade fell into a stagnant state. Changes in the external factors in the short-term led to a decline in the prediction accuracy of this model. Some studies also show that the prediction accuracy of the SARIMA model decreases with time, which is more accurate when predicting the values of the next three to six periods, but when the prediction range exceeds six periods, the simulation effect becomes worse, and the prediction error gradually increases. The same conclusion has been reached in the actual prediction process in this paper. It can be seen from the comparison between the actual value and the predicted value in Table 4 that the relative error of prediction gradually increases with the passage of time. The short-term changes of the internal and external factors also need to re-evaluate their parameters regularly according to the constantly updated data, so as to improve the accuracy of model prediction.

**Author Contributions:** J.W.: Writing—original draft, investigation, visualization, writing—review & editing. Z.Y.: Methodology, supervision, validation. Y.H.: Writing—original draft, diagram and flowchart preparation, writing-review & editing. D.W.: Conceptualization, formal analysis, resources. Z.Y.: Investigation, visualization. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the China Education Ministry of Humanities and Social Science Research Youth Fund project (No. 18YJCZH192). Ministry of Finance and Ministry of agriculture and rural areas: national special fund for the construction of modern agricultural industrial technology system "Industrial Economic Research on national marine fish industrial technology system" (No. CARS-47-G29). Major project of National Social Science Fund "Research on the development strategy of China's deep blue fishery under the background of accelerating the construction of a marine power" (No. 21 & ZD100).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All experimental data in this paper come from Price information system of national agricultural products wholesale market in China: http://pfsc.agri.cn/#/indexPage (accessed on 4 April 2022).

**Acknowledgments:** Thanks to the computing science center of Shanghai Ocean University for its support for scientific research.

**Conflicts of Interest:** The authors declare no conflict of interest.
