Price Forecasting of Aquatic Products Based on Weight Allocation Intelligent Combinatorial Modelling

Price Forecasting of Aquatic Products Based on Weight Allocation Intelligent Combinatorial Modelling | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Price Forecasting of Aquatic Products Based on Weight Allocation Intelligent Combinatorial Modelling Daqing Wu, Binfeng Lu, Zinuo Xu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3966059/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The price prediction of aquatic products is of great significance to the socio-economic development and fisheries industry. However, due to the complexity and uncertainty of the aquatic product market, traditional forecasting methods often struggle to accurately predict price fluctuations. Therefore, this study adopts a intelligence combination model to enhance the accuracy of aquatic product price prediction. Firstly, three decomposition methods, namely empirical wavelet transform, singular spectrum analysis, and variational mode decomposition, are applied to decompose the complex original price series. Secondly, a combination of bidirectional long short-term memory artificial neural network, extreme learning machine, and exponential smoothing prediction methods is used for cross-prediction on the decomposed results. Subsequently, these predicted result are input into the PSO-CS intelligence algorithm for weight allocation and generating combined prediction results. Empirical analysis is conducted using the data of daily sea purchase price of larimichthys crocea in Ningde City. The combination prediction accuracy with PSO-CS weight allocation is found to be higher than that of single model predictions, yielding superior results. Based on the weight allocation intelligent combinatorial modelling, the prediction of aquatic product prices demonstrates higher accuracy and stability, enabling better adaptation to market changes and price fluctuations. Price Forecasting Aquatic Products Intelligent Combinatorial Modelling Neural Network Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1 Introduction With the rapid economic development and the increase in disposable income, there has been a continuous upgrading of consumption structure, with residents placing greater emphasis on dietary health and protein intake. As a rich source of protein, aquatic products play a significant role in the daily diets of people worldwide and hold an important position globally. The evolving consumer mindset has led to a significant increase in demand for aquatic products [ 1 ]. However, as the demand for healthy diets continues to rise, the volatility of aquatic product prices has also attracted widespread attention. In recent years, there has been frequent fluctuation in aquatic product prices, which has had a severe impact on people's lives and national economic stability. For instance, in the Ningde area of Fujian Province, there have been substantial price fluctuations in artificially farmed larimichthys crocea. In the period leading up to the Spring Festival in 2020, fish farmers urgently sold off large quantities of larimichthys crocea to recoup their investments, resulting in a significant increase in supply and a subsequent depression in prices, which fell below 22 yuan/kg. Before the Mid-Autumn Festival, the supply was severely inadequate, leading to a substantial increase in acquisition prices, reaching over 40 yuan/kg [ 2 ]. The price volatility of aquatic products affects the decision-making processes of producers, consumers, governments, and other stakeholders. Therefore, accurately predicting changes in aquatic product prices has become an urgent need for decision-makers and relevant stakeholders. Establishing an efficient and accurate aquatic product price forecasting model is crucial in preventing adverse impacts on people's lives caused by unforeseen events. This measure plays a significant role in addressing issues related to agriculture, rural areas, and farmers and promoting agricultural informatization. The concept of "food systems thinking" emphasizes the importance of healthy diets and the complexity of relationships between foods. In this study, we will apply this concept, integrating aquatic product price forecasting into a broader food system [ 3 ]. Through this approach, we aim to establish a predictive system for aquatic product prices, providing decision-makers with more accurate information and promoting sustainable development and precise agricultural management. Predicting prices of aquatic products is a focal issue in the field of aquatic product price research, and research methods exhibit diversification. The price of aquatic products demonstrates complex volatility and nonlinear characteristics, representing a typical complex time series that poses significant challenges for accurate forecasting. Traditional econometric methods commonly employed in price forecasting include Autoregressive Integrated Moving Average (ARIMA) [ 4 ] and Exponential Smoothing (ETS) [ 5 ]. These methods have been widely used in the field of price forecasting, where they have been adapted to various agricultural product price characteristics, gradually improving the predictive capacity of models as historical data becomes more abundant and precise [ 6 , 7 ]. Machine learning (ML) methods possess powerful data-driven attributes and adaptive learning capabilities, enabling them to effectively extract hidden factors that traditional methods fail to capture. Models such as Extreme Learning Machine (ELM) [ 8 ] and Long Short-Term Memory (LSTM) networks [ 9 ] are employed to output results. Compared to traditional econometric methods, these models exhibit higher accuracy, robustness, and generalization, allowing for more precise prediction of agricultural product prices. On one hand, when dealing with high-dimensional and large-scale prediction problems, shallow machine learning algorithms like Support Vector Machines (SVM) and Backpropagation Neural Networks (BPNN) face significant limitations, including the curse of dimensionality and ineffective feature representation [ 10 ]. On the other hand, although individual model prediction errors fluctuate greatly, overall precision decreases as the prediction horizon lengthens. However, not all artificial intelligence models outperform traditional econometric forecasting methods in practical predictions [ 11 , 12 ]. Hence, appropriate prediction models should be selected based on the characteristics of the data and task at hand. Combination models, by integrating the advantages of traditional statistical methods, intelligent optimization algorithms, and artificial intelligence techniques, set prior assumptions and perform data processing for prediction problems, thereby reducing learning biases and significantly enhancing the fitting ability of predictive models [ 13 ]. In terms of research methodology, scholars have gradually developed a "decompose-integrate" hybrid model, which has improved predictive performance to some extent. Unlike general hybrid models, the decompose-integrate framework first decomposes agricultural product prices into multiple components and then predicts each component using corresponding forecasting methods. Since its inception, this approach has been applied in various fields such as commodity prices and energy, yielding favorable results [ 14 ]. In the field of complex time series forecasting modeling, the decompose-integrate methodology is considered an effective strategy for improving prediction accuracy. Its core idea is to use signal decomposition algorithms to break down complex time series into a series of relatively simple and stationary sub-sequences, thereby reducing the complexity of prediction modeling tasks [ 15 ]. Techniques such as Empirical Wavelet Transform (EWT), Empirical Mode Decomposition (EMD) [ 16 ], and Singular Spectrum Analysis (SSA) [ 17 ] have been adopted to decompose the original data sequence and eliminate noise in the time series. By separately modeling the decomposed components such as trend, seasonality, and residuals, and recombining them to obtain the predicted values of the original time series, more accurate forecasting results can be achieved compared to directly modeling the original time series. However, a substantial amount of theory and practice have demonstrated that it is impossible for a single model to capture both linear and nonlinear patterns in agricultural product price sequences. Therefore, scholars have introduced hybrid models for price prediction. A hybrid model combines the prediction results of different forecasting methods to form new predictions. The most commonly used combination strategy is to use statistical methods to determine weights, such as the mean method, median method, minimum error method, and more complex Bayesian averaging method [ 18 ]. This strategy achieves complementarity among individual models, thereby capturing the underlying patterns in the sequence more accurately [ 19 ]. This conclusion has been proven in previous time series literature [ 20 ]. In the field of swarm intelligence optimization algorithms, research has shown that the Cuckoo Search (CS) algorithm has stronger comprehensive advantages in terms of parameter number, versatility, global optimization ability, and can flexibly combine with other algorithms such as PSO, demonstrating wider applicability [ 21 ]. The research findings presented above indicate that time series decomposition exhibits high accuracy and wide applicability in predicting water product prices. However, single-model predictions have disadvantages such as limited adaptability, inadequate precision, and poor robustness. Building upon previous research, this study proposes a weight allocation method based on Particle Swarm Optimization with Cuckoo Search Algorithm (PSO-CS) .This paper presents several novel contributions: We introduce a Weight Allocation Intelligent Combinatorial Modelling Forecasting Framework, which strategically assigns weight distribution across distinct models. This framework exhibits marked superiority in terms of flexibility, precision, and robustness. In our approach, prior to forecasting, we employ various decomposition techniques to partition the original dataset into multiple sub-series. This method accentuates intricate details within the time series, thereby rendering sub-series fluctuations smoother relative to the initial series, subsequently improving predictive accuracy. Leveraging the innate capabilities of self-learning and social learning introduced by the PSO-CS algorithm enables an enhancement in global search efficiency. The remainder of this paper is organized as follows. Section 2 briefly introduces the constructs the PSO-CS algorithm. Section 3 presents a Weight Allocation Intelligent Combinatorial Modelling Forecasting Framework. Section 4 provides an overview of the data context. In Section 5, the results of the experiments are analyzed. Finally, the conclusion is given in Section 6. 2 Fish price prediction framework based on PSO-CS weight allocation algorithm The basic idea of the particle swarm iteration-based cuckoo hybrid search optimization algorithm is in the iterative process of n particle swarms, the PSO algorithm is used to update the velocity and position of the particles in each generation to obtain the optimal position of a group of particles, and then the optimal particle position is entered into the CS algorithm to continue to iteratively update. Based on the number of iterations of the original algorithm, each particle swarm adds 1 update and calculation of the CS algorithm, and there is little change in the running time. Given \(m\) individual forecasting models, each assigned a corresponding weight denoted as \({w}_{i}（\text{1,2},\dots ,m）\) , the combined forecast can be expressed as $$\begin{array}{c}{\widehat{y}}_{\text{combined }}={\widehat{y}}_{1}*{w}_{1}+{\widehat{y}}_{2}*{w}_{2}+\cdots +{\widehat{y}}_{m}*{w}_{m} \left(1\right)\end{array}$$ For optimal weight assignment of combined models, determining the weights of each individual prediction model is critical. In this study, the corresponding weights for each individual model are estimated by constructing an optimisation problem that minimises the error between the combined predicted and observed values. Thus, an optimization problem estimating the reasonable weight of each individual model is construed as below: $$\begin{array}{c}Min G\left(y-{\widehat{y}}_{\text{combined }}\right) s.t.\sum _{i=1}^{m}{w}_{i}=1 \left(2\right)\end{array}$$ where \(G\) is a predetermined function such as sum squared (SSE),mean squared (MSE), sum absolute (SAE), mean absolute (MAE),etc., \(y\) is observed value. The proposed PSO-CS weight assignment method is based on an improved CS algorithm, namely the PSO-CS algorithm. The CS algorithm, inspired by cuckoo’s brood parasitic behavior, is a new population-based search paradigm. Cuckoos seek out nests of other hosts and then lay their eggs, which may be found and discarded by the hosts. To enhance the survival rate of their eggs, cuckoos can imitate the host’s eggs, or even take them out. The CS algorithm is efficient, robust, and relatively simple in comparison with other evolutionary computing algorithms due to its few control parameters. Furthermore, the levy flight instead of standard random walk is applied in CS, this helps to explore the huge solution space compared to the linear relationship, due to its infinite mean and variance, as well as nonlinear relationship. However, the huge exploration space of the CS algorithm may lead to poor convergence and accuracy of solutions, so the PSO algorithm is introduced to optimize the CS algorithm. The proposed PSO-CS weight assignment method can be expressed as follows: Define the objective function \(F\left(w\right)={\sum }_{i=1}^{n} y-\left|{\stackrel{\prime }{y}}_{n}\text{*}{x}_{n}\right|\) , where \({x}_{n}\) is the value of the weight coefficient, \({\stackrel{\prime }{y}}_{n}\) is the \(n\) th individual forecasting model, and \({\sum }_{i=1}^{n} {x}_{i}=1\) . Parameters such as population size \(N\) Maximum number of iterations \(T\) , minimum weighing value \({w}_{\text{m}\text{i}\text{n}}\) Maximum weight \({w}_{\text{m}\text{a}\text{x}}\) , acceleration coefficients \({c}_{1}\) and \({c}_{2}\) , maximum discovery, and probability \({p}_{a}\in \left[\text{0,1}\right]\) . A set of randomly generated host nests \({X}_{i}=\left\{{x}_{i1},{x}_{i2},\dots ,{x}_{iD}\right\}\) and the corresponding velocities \({V}_{i}=\left\{{v}_{i1},{v}_{i2},\dots ,{v}_{iD}\right\}\) and host nests \({X}_{i}(i=\text{1,2},\dots ,N)\) to its location in the \(D\) -dimensional space is a potential solution to the problem. In the \(t\) iteration, the update speed of the first \(i\) The first nest is built by optimizing the location of the first \(i\) The first nest. $$\begin{array}{c}{pbes\text{t}}_{i}^{\left(t\right)}=\left\{{pbest}_{i1}^{\left(t\right)},\dots ,{pbest}_{i,D}^{\left(t\right)}\right\} \left(3\right)\end{array}$$ and the optimal position for the entire population \(gbes{t}^{\left(t\right)}\) , and then update the nested positions. $${v}_{ij}^{\left(t+1\right)}=w\times {v}_{ij}^{\left(t\right)}+{c}_{1}\times {rand}\left(\text{0,1}\right)\times \left[pbes{t}_{ij}^{\left(t\right)}-{x}_{ij}^{\left(t\right)}\right]$$ $$\begin{array}{c}+{c}_{2}\times {rand}\left(\text{0,1}\right)\times \left[gbes{t}_{j}^{\left(t\right)}-{x}_{ij}^{\left(t\right)}\right] \left(4\right)\end{array}$$ $$\begin{array}{c}{x}_{ij}^{\left(t+1\right)}={x}_{ij}^{\left(t\right)}+{v}_{ij}^{\left(t+1\right)} \left(5\right)\end{array}$$ These are \({v}_{i,j}^{(t+1)}\) and \({x}_{ij}^{(t+1)}\) are \((t+1)\) of \(w={w}_{\text{m}\text{a}\text{x}}-\frac{{w}_{\text{m}\text{a}\text{x}}-{w}_{\text{m}\text{i}\text{n}}}{T}\times t\) are the inertia weights. Let \({x}_{ij}^{\left(t\right)}=pbes{t}_{ij}^{\left(t\right)}\) update the \({x}_{ij}^{(t+1)}\) , \(L\left(\lambda \right)\sim u={t}^{-\lambda }(1<\lambda \le 3)\) is \({x}_{ij}^{(t+1)}={x}_{ij}^{\left(t\right)}+\alpha ⊛L\left(\lambda \right)\) where \(\alpha\) is the step size that should be proportional to the size of the optimization problem. This \({x}_{ij}^{(t+1)}\) will change randomly, with probability \({p}_{a}\) . replacements \({x}_{ij}^{(t+1)}\) is defined by the \({x}_{ij}^{\left(t\right)}\) If the fitness value \(F\left({x}_{ij}^{(t+1)}\right)>F\left({x}_{ij}^{\left(t\right)}\right)\) . Then, it finds the list of nests by sorting the list of \(t\) generations of the best nests. The PSO-CS hybrid optimization algorithm combines the search capability of PSO and the global search capability of CS to improve the optimization capability of the algorithm in general. Experimentally, it is proved that the accuracy of the PSO-CS hybrid optimization algorithm is significantly better than that of the PSO algorithm, and it is more stable [ 22 ]. 3 Forecasting framework This article proposes an optimal combination framework for predicting the prices of aquatic products based on the PSO-CS weighted aggregation model, as shown in Fig. 1 . The framework consists of five steps: Step 1: Data decomposition. The price data of aquatic products is decomposed into multiple sub-sequences using EWT, VMD, and SSA decomposition techniques, aiming to identify the main sequences. Step 2: Individual prediction. The selected sub-sequence components are sequentially inputted into various prediction models, including LSTM, ELM, and ETS models, to obtain predictions for each component. Step 3: Removal of large errors. An error analysis is performed on the predicted results of the components. Components with significant errors are removed, and the original sequence of the removed component is merged with the residual sequence. Step 4: Combination. The predicted results of each group of components are summed to obtain the final prediction result for that group. Step 5: Prediction aggregation. The PSO-CS weight allocation method is employed to determine the optimal weights for different individual predictions. Then, the predictions of each component are weighted accordingly to obtain the final aggregated prediction result. 4 Empirical Analysis 4.1 Data description In 2020, the annual aquaculture production of larimichthys crocea in China reached 254,000 tons, accounting for 14.5% of the total marine fish aquaculture production in the country [ 23 ]. The larimichthys crocea aquaculture industry has become one of the distinctive pillar industries in the eastern Fujian Province. This research data comes from the WeChat official account platform of "Ningde Larimichthys Crocea" operated by the Fishery Association of Ningde City, Fujian Province, and selects the daily reference price for sea surface purchase of larimichthys crocea of 400-500g published by the platform as the research object. The selected time period ranges from May 13th, 2015 to May 24th, 2023, and missing values are filled using the backward filling method. A total of 2,948 daily price data points were collected, as shown in Fig. 2 − 1. The sample data is divided into three subsets: the training set consists of the first 80% of the price series, totaling 2,358 data points; the validation set consists of the remaining 20% of the series, totaling 590 data points. Table 1 Descriptive statistics of the reference price of the sea surface purchase of Ningde's larimichthys crocea Norm Average Maximum Minimum Upper quartile Standard deviation Skewness Kurtosis 14.7436 26.0000 11.5000 14.5000 2.1167 2.3174 8.3753 4.2 Evaluation indicators To accurately evaluate the prediction ability of different models, this paper uses four indicators to evaluate the models: mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and absolute percentage error (MAPE). $$\begin{array}{c}MSE=\frac{1}{N}\sum _{i=1}^{N} {\left({\widehat{x}}_{t}-{x}_{t}\right)}^{2} \left(6\right)\end{array}$$ $$\begin{array}{c}RMSE=\sqrt{\frac{1}{N}\sum _{i=1}^{N} {\left({\widehat{x}}_{t}-{x}_{t}\right)}^{2}} \left(7\right)\end{array}$$ $$\begin{array}{c}MAE=\frac{1}{N}\sum _{i=0}^{N-1}\left|{\widehat{x}}_{t}-{x}_{t}\right| \left(8\right)\end{array}$$ $$\begin{array}{c}MAPE=\frac{1}{N}\sum _{i=1}^{N}\left|\frac{{\widehat{x}}_{t}-{x}_{t}}{{x}_{t}}\right|\times 100\text{%} \left(9\right)\end{array}$$ 5 Results 5.1 Decomposition result In VMD decomposition, the parameter K represents the number of decomposed modes. A value of K that is either too large or too small can result in excessive noise or loss of information, which adversely affects the accuracy of subsequent predictions. Therefore, when selecting VMD parameters, it is necessary to balance the relationship between the value of K and prediction accuracy. Generally, the optimal value of K can be determined through methods such as cross-validation to ensure that VMD effectively extracts the important oscillatory patterns from the data and establishes accurate models for subsequent data analysis and prediction. After conducting experiments, the final decision was made to set the value of K in VMD decomposition as 5. The decomposed IMF components are shown in the following figure. In this study, the EWT (Empirical Wavelet Transform) algorithm is employed to decompose the original sequence. Subsequently, seven empirical mode components (EMCs) can be obtained, as shown in the figure. It can be observed that the EWT decomposition results exhibit a characteristic shift from low frequency to high frequency. The original sequence was subjected to embedding, decomposition, grouping, and recombination steps through Singular Spectrum Analysis (SSA), resulting in the extraction of six distinct component sequences, as illustrated in the figure below. 5.2 Single-model prediction results After decomposing the original sequence, each component was subjected to combined predictions using LSTM, ELM, and ETS models. The predictive performance of individual models is evaluated and presented in Table 2 . The corresponding MAPE accuracies for different single models are illustrated in Fig. 6 . Table 2 Assessment of the results of the single-model prediction of the sea surface purchase price of greater amberjack (Lepomis macrocephalus) Models MSE RMSE MAE MAPE LSTM Single model 0.0256 0.1599 0.0693 0.4846 EWT 0.0246 0.1569 0.0658 0.4525 VMD 0.0231 0.1518 0.0748 0.5217 SSA 0.0159 0.1259 0.0428 0.2989 ELM Single model 0.0136 0.1165 0.0479 0.3282 EWT 0.0137 0.1170 0.0551 0.3770 VMD 0.0081 0.0902 0.0481 0.3307 SSA 0.0006 0.0240 0.0113 0.0775 ETS Single model 2.4673 1.5708 1.1937 8.8844 EWT 1.9050 1.3802 1.1124 7.5960 VMD 6.3686 2.5236 2.0953 17.5228 SSA 1.8503 1.3603 1.0969 7.6466 Ave 1.0597 0.6481 0.4928 3.7101 Firstly, in most cases, the predictive accuracy of the non-decomposition model is higher than that of the models using EWT, VMD, and SSA decomposition techniques. However, the predictive accuracy of the ETS model based on VMD decomposition is lower than that of other decomposition models. In ETS prediction, errors in the VMD decomposition results are amplified. Secondly, it can be observed that the predictive accuracy of the models based on LSTM and ELM is higher than that of the ETS model. The main reason for this is that LSTM and ELM are artificial intelligence algorithms that excel in handling information contained in different components after decomposition. Generally speaking, they have stronger adaptability compared to linear models. Prediction models based on artificial intelligence algorithms are more suitable when combined with decomposition techniques. On the other hand, the ETS model is a complex nonlinear prediction model that is more suited for short-term trend forecasting. These findings indicate that the performance of decomposition techniques and prediction models tends to be diverse. Therefore, the combination of models is particularly important for mitigating the risk of model selection. Regarding decomposition techniques, the predictive model using the SSA decomposition technique yields better results in predicting the acquisition price of Spanish Mackerel on the sea surface compared to the predictive models using EWT, VMD decomposition, and no decomposition. The MAPE values are reduced by 37.57%, 58.54%, and 42.88% respectively, indicating that the SSA decomposition technique effectively discovers hidden factors behind price fluctuations in this dataset. 5.3 Combined model prediction results This section presents the performance of PSO-CS weight allocation for combined prediction. Table 3 showcases the weight allocation results for the combined prediction of the acquisition price of larimichthys crocea in the sea. Table 3 Results of the prediction weight allocation for the combination of the sea surface purchase price of greater amberjack Models Weight 1 Weight 2 Weight 3 Mini fitness EWT 0.97762 0.017449 0.054719 5.4956 VMD 0.45978 0.20007 0.39683 4.7631 SSA 0.3202 0.56079 0.16737 5.5289 LSTM 0.27499 0.69521 0.081055 5.5193 ELM 0.54832 0.31219 0.19195 5.5163 ETS 0.13105 0.90177 0.022209 8.0085 Tables 4 and 5 present the evaluation of the predicted results and the reduction in prediction error for the PSO-CS weighted combination forecasting of larimichthys crocea's sea surface purchase price. In most cases, the performance of the PSO-CS weighted combination method is superior to that of the single-model forecasting methods. PSO-CS overcomes the limitations of linear methods by adaptively optimizing weights instead of directly classifying weights based on the performance of individual models, resulting in better performance. Compared to single-model forecasting methods, the PSO-CS approach reduces MSE, RMSE, MAE, and MAPE by 44.43%, 22.69%, 12.21%, and 22.88%, respectively. However, it exhibits poor performance in the ETS-based forecasting method. This may be due to the larger errors in the ETS during the single-model forecasting process, which hinders the effective utilization of PSO-CS in the weight allocation stage, leading to inferior results. Similarly, the VMD-ETS-based forecasting already yields significant errors in the single-model forecasting stage, making it challenging for the PSO-CS weighted combination model to demonstrate its performance in the weight allocation stage. Table 4 Assessment of the results of the forecasting of the sea level purchase price combinations for greater amberjack Models MSE RMSE MAE MAPE based on EWT 0.01857427 0.13628745 0.09340442 0.65263831 based on VMD 0.92698336 0.96279975 0.79625986 5.37405448 based on SSA 0.04924591 0.22191419 0.1785835 1.2566242 based on LSTM 0.00845136 0.09193128 0.05254116 0.36355915 based on ELM 0.00692352 0.08320768 0.03967529 0.27210333 based on ETS 5.16845769 2.27342422 1.91025014 12.9420506 Ave 1.02977268 0.62826076 0.51178573 3.47683835 Table 5 Reduction rate of assessment error for the combination of forecasting results of the sea surface purchase price of greater amberjack (Lepomis macrocephalus) Models MSE RMSE MAE MAPE based on EWT 0.97132576 0.75282352 0.77280464 0.76762124 based on VMD 0.56545996 -0.0443994 -0.0768843 0.12261747 based on SSA 0.92085782 0.55914784 0.5345503 0.53012071 based on LSTM 0.62066388 0.38158246 0.16872412 0.17270049 based on ELM 0.22984798 0.04248147 0.02329428 0.02244412 based on ETS -0.6419242 -0.3304881 -0.3896967 -0.2429374 Ave 0.44437186 0.22685796 0.17213207 0.2287611 Figure 8 illustrates the reduction in average error of the PSO-CS method compared to single-model predictions. Considering the aforementioned, the experimental results effectively demonstrate the robustness of the proposed PSO-CS hybrid model. 6 Conclusion The prediction of aquatic product prices holds significant importance in the fields of agriculture and fisheries. It is crucial for decision-makers, producers, and consumers alike. Decision-makers can utilize price forecasts to formulate rational policies and strategies that promote sustainable development and maximize benefits. These aids regulatory bodies in market supervision by maintaining a fair competitive environment [ 24 ]. Producers can devise reasonable production plans and supply chain management based on the forecast results, thereby meeting market demand and enhancing efficiency. Consumers can better plan their purchasing behavior through price predictions, avoiding economic burdens resulting from future price increases. To address the limitations of existing models, this paper proposes a water product price prediction framework based on a Weight Allocation Intelligent Combinatorial Modelling. By utilizing daily purchase prices of larimichthys crocea in Ningde City, Fujian Province as data, the following conclusions are derived within the sample interval: Firstly, the decomposed-ensemble prediction model significantly improves the predictive performance compared to direct prediction models. Secondly, the accuracy of the SSA-ELM prediction model was 46.33% lower than the other three models on average, which is better than the other individual models. Thirdly, the combination prediction model based on PSO-CS weight allocation exhibits significantly superior performance compared to single-model predictions. In conclusion, the water product price prediction framework based on Weight Allocation Intelligent Combinatorial Modelling holds significant importance in the agricultural and fisheries sectors. Our research provides a scientific basis for decision-making and business operations in related fields, offering beneficial insights for future research and practical applications. Declarations Data availability statement The datasets generated during the current study are available from the corresponding author on reasonable request. The data of this study comes from the Fisheries Association of Ningde City, Fujian Province, China. CRediT authorship contribution statement Daqing Wu: Supervision, Conceptualization, Methodology, Writing – review & editing. Binfeng Lu: Data curation, Software, Writing – original draft, Writing – review & editing. Zinuo Xu: Formal analysis, Validation. Funding Statement This research was supported by the Major Social Science Projects in China (Evaluation of the Development Potential of the Deep Blue Fisheries Industry under Climate Change, No.21&ZD100) Declaration of Competing Interest The authors declare that they have no conflicts of interest to report regarding the present study. References QI W, KONG L, LI J and X. YANG (2023) Research on the Relationship between Youth Consumer Lifestyle and Attitude towards Fresh Agricultural Products:Based on Netnography Theory. J Agro-Forestry Econ Manage : 1–13 HUA J, SU G and Y. JIA (2022) Research on Pork Price Forecasting and Risk Early Warning Under Impact of Swine Epidemic. Agricultural Econ Manage (06): 101–113 Jia B (2014) Sales price forecast of major agricultural products in China. Stat Decis (20): 100–102 Wu Y and x., Wen (2016) Short-term stock price prediction based on ARIMA model. 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Proceedings of the CSU-EPSA 30(02): 66–70 + 78 Liao J (2023) Research on Artificial Intelligence Prediction of International Crude Oil Prices Based on VMD-LSTM-ELMAN Model. J Chengdu Univ Technol (Natural Sci Edition) (08): 21–24 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3966059","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":273615047,"identity":"c01fa3dc-5bdc-4cd6-8796-917bc4604a24","order_by":0,"name":"Daqing Wu","email":"","orcid":"","institution":"Shanghai Ocean University","correspondingAuthor":false,"prefix":"","firstName":"Daqing","middleName":"","lastName":"Wu","suffix":""},{"id":273615048,"identity":"b36c49b1-09ef-424d-91f4-263700f61fe6","order_by":1,"name":"Binfeng Lu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFklEQVRIie2OMUvDQBTH33GQLsauLzj0K1wQUgvSfpULASdxESRTOClkKrgq6HfIVHR75SAuV+dsrWStGOiogklHaUJHh/sNb/jzfu//ACyWf4h4nZL++cbxRGlqArmLjzqUkcnDtavOIsFyCXSIMikuT4WrYpZxIw5TApIBes/Ih47ZbitIrvoo2fojhcGwVaEL9A0ej2bLORLoa+9ecv8pBf9FtSgLlaN0kEOxnNePUZgV0jlxU5CC9itCsxTJQaZWm7IiSBql99Wp5Jz7tymyjAzUj/FdC+9UjMNKMBh5Kg/QCB0+zN6n3uMb+lmbsvqsNMTJuA+6rOI4Ce960aLa3JwP2lr+XmgGU/XAg/YtFovFsp9f1m9oTkzOEMYAAAAASUVORK5CYII=","orcid":"","institution":"Shanghai Ocean University","correspondingAuthor":true,"prefix":"","firstName":"Binfeng","middleName":"","lastName":"Lu","suffix":""},{"id":273615049,"identity":"dcfdc6a3-914c-456f-8a6b-585250c87332","order_by":2,"name":"Zinuo Xu","email":"","orcid":"","institution":"Xi'an Jiaotong-Liverpool University","correspondingAuthor":false,"prefix":"","firstName":"Zinuo","middleName":"","lastName":"Xu","suffix":""}],"badges":[],"createdAt":"2024-02-18 06:14:43","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3966059/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3966059/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51365202,"identity":"61d9a770-581a-4e13-8d7e-59cafc4a08a9","added_by":"auto","created_at":"2024-02-20 09:54:32","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":53307,"visible":true,"origin":"","legend":"\u003cp\u003eDiagram of the combined forecasting framework\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-3966059/v1/f17fc94d74131f2eb3ab8a3b.png"},{"id":51365196,"identity":"1f4cde37-d277-48a0-b294-bc2c436bc87b","added_by":"auto","created_at":"2024-02-20 09:54:31","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":82729,"visible":true,"origin":"","legend":"\u003cp\u003ePrice Trend of larimichthys\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-3966059/v1/3076a5070264dbdd3e44b263.png"},{"id":51365572,"identity":"3e12dc32-e08c-48ff-968e-e340e56f2481","added_by":"auto","created_at":"2024-02-20 10:02:32","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":97842,"visible":true,"origin":"","legend":"\u003cp\u003eVMD decomposition\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-3966059/v1/4643ddefc6110f4f0cc380a2.png"},{"id":51365199,"identity":"d25eb324-8251-4ab5-9916-1d711f8d1e2e","added_by":"auto","created_at":"2024-02-20 09:54:32","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":119199,"visible":true,"origin":"","legend":"\u003cp\u003eEWT decomposition\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-3966059/v1/caeccd1f7f9fae85ef6f08d0.png"},{"id":51365200,"identity":"7ec80b30-a1a9-4154-81a9-c329407bbb33","added_by":"auto","created_at":"2024-02-20 09:54:32","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":90271,"visible":true,"origin":"","legend":"\u003cp\u003eSSA decomposition\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-3966059/v1/37fbcdbb45da9333ad626a49.png"},{"id":51365197,"identity":"4a765e36-1d41-4da7-be00-b6af46dd207f","added_by":"auto","created_at":"2024-02-20 09:54:31","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":13999,"visible":true,"origin":"","legend":"\u003cp\u003eMAPE values for each single model of the sea surface purchase price of greater amberjack (Lepomis macrocephalus)\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-3966059/v1/56fc953342885f2baeb46fc3.png"},{"id":51365203,"identity":"67857155-769e-49c4-83e8-07f090d8c56f","added_by":"auto","created_at":"2024-02-20 09:54:32","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":151861,"visible":true,"origin":"","legend":"\u003cp\u003eResults of different combinations of prediction models for greater amberjack\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-3966059/v1/ded35c3b2763e64052a2d0eb.png"},{"id":51365198,"identity":"70b852eb-4073-4bdb-b819-c446b152fad3","added_by":"auto","created_at":"2024-02-20 09:54:32","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":11547,"visible":true,"origin":"","legend":"\u003cp\u003eAverage error reduction of PSO-CS method relative to single model\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-3966059/v1/a18da5da17c0786c1bc99bc1.png"},{"id":51537620,"identity":"6d8a28c1-a75a-458c-b393-7a6321f1e11c","added_by":"auto","created_at":"2024-02-23 10:10:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":939663,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3966059/v1/1b794b72-7caa-4cba-ad83-a1699c60cebb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Price Forecasting of Aquatic Products Based on Weight Allocation Intelligent Combinatorial Modelling","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eWith the rapid economic development and the increase in disposable income, there has been a continuous upgrading of consumption structure, with residents placing greater emphasis on dietary health and protein intake. As a rich source of protein, aquatic products play a significant role in the daily diets of people worldwide and hold an important position globally. The evolving consumer mindset has led to a significant increase in demand for aquatic products [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. However, as the demand for healthy diets continues to rise, the volatility of aquatic product prices has also attracted widespread attention.\u003c/p\u003e \u003cp\u003eIn recent years, there has been frequent fluctuation in aquatic product prices, which has had a severe impact on people's lives and national economic stability. For instance, in the Ningde area of Fujian Province, there have been substantial price fluctuations in artificially farmed larimichthys crocea. In the period leading up to the Spring Festival in 2020, fish farmers urgently sold off large quantities of larimichthys crocea to recoup their investments, resulting in a significant increase in supply and a subsequent depression in prices, which fell below 22 yuan/kg. Before the Mid-Autumn Festival, the supply was severely inadequate, leading to a substantial increase in acquisition prices, reaching over 40 yuan/kg [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The price volatility of aquatic products affects the decision-making processes of producers, consumers, governments, and other stakeholders. Therefore, accurately predicting changes in aquatic product prices has become an urgent need for decision-makers and relevant stakeholders. Establishing an efficient and accurate aquatic product price forecasting model is crucial in preventing adverse impacts on people's lives caused by unforeseen events. This measure plays a significant role in addressing issues related to agriculture, rural areas, and farmers and promoting agricultural informatization. The concept of \"food systems thinking\" emphasizes the importance of healthy diets and the complexity of relationships between foods. In this study, we will apply this concept, integrating aquatic product price forecasting into a broader food system [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Through this approach, we aim to establish a predictive system for aquatic product prices, providing decision-makers with more accurate information and promoting sustainable development and precise agricultural management.\u003c/p\u003e \u003cp\u003ePredicting prices of aquatic products is a focal issue in the field of aquatic product price research, and research methods exhibit diversification. The price of aquatic products demonstrates complex volatility and nonlinear characteristics, representing a typical complex time series that poses significant challenges for accurate forecasting. Traditional econometric methods commonly employed in price forecasting include Autoregressive Integrated Moving Average (ARIMA) [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] and Exponential Smoothing (ETS) [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. These methods have been widely used in the field of price forecasting, where they have been adapted to various agricultural product price characteristics, gradually improving the predictive capacity of models as historical data becomes more abundant and precise [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Machine learning (ML) methods possess powerful data-driven attributes and adaptive learning capabilities, enabling them to effectively extract hidden factors that traditional methods fail to capture. Models such as Extreme Learning Machine (ELM) [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] and Long Short-Term Memory (LSTM) networks [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] are employed to output results. Compared to traditional econometric methods, these models exhibit higher accuracy, robustness, and generalization, allowing for more precise prediction of agricultural product prices. On one hand, when dealing with high-dimensional and large-scale prediction problems, shallow machine learning algorithms like Support Vector Machines (SVM) and Backpropagation Neural Networks (BPNN) face significant limitations, including the curse of dimensionality and ineffective feature representation [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. On the other hand, although individual model prediction errors fluctuate greatly, overall precision decreases as the prediction horizon lengthens. However, not all artificial intelligence models outperform traditional econometric forecasting methods in practical predictions [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Hence, appropriate prediction models should be selected based on the characteristics of the data and task at hand.\u003c/p\u003e \u003cp\u003eCombination models, by integrating the advantages of traditional statistical methods, intelligent optimization algorithms, and artificial intelligence techniques, set prior assumptions and perform data processing for prediction problems, thereby reducing learning biases and significantly enhancing the fitting ability of predictive models [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. In terms of research methodology, scholars have gradually developed a \"decompose-integrate\" hybrid model, which has improved predictive performance to some extent. Unlike general hybrid models, the decompose-integrate framework first decomposes agricultural product prices into multiple components and then predicts each component using corresponding forecasting methods. Since its inception, this approach has been applied in various fields such as commodity prices and energy, yielding favorable results [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. In the field of complex time series forecasting modeling, the decompose-integrate methodology is considered an effective strategy for improving prediction accuracy. Its core idea is to use signal decomposition algorithms to break down complex time series into a series of relatively simple and stationary sub-sequences, thereby reducing the complexity of prediction modeling tasks [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Techniques such as Empirical Wavelet Transform (EWT), Empirical Mode Decomposition (EMD) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], and Singular Spectrum Analysis (SSA) [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] have been adopted to decompose the original data sequence and eliminate noise in the time series. By separately modeling the decomposed components such as trend, seasonality, and residuals, and recombining them to obtain the predicted values of the original time series, more accurate forecasting results can be achieved compared to directly modeling the original time series.\u003c/p\u003e \u003cp\u003eHowever, a substantial amount of theory and practice have demonstrated that it is impossible for a single model to capture both linear and nonlinear patterns in agricultural product price sequences. Therefore, scholars have introduced hybrid models for price prediction. A hybrid model combines the prediction results of different forecasting methods to form new predictions. The most commonly used combination strategy is to use statistical methods to determine weights, such as the mean method, median method, minimum error method, and more complex Bayesian averaging method [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. This strategy achieves complementarity among individual models, thereby capturing the underlying patterns in the sequence more accurately [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. This conclusion has been proven in previous time series literature [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. In the field of swarm intelligence optimization algorithms, research has shown that the Cuckoo Search (CS) algorithm has stronger comprehensive advantages in terms of parameter number, versatility, global optimization ability, and can flexibly combine with other algorithms such as PSO, demonstrating wider applicability [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe research findings presented above indicate that time series decomposition exhibits high accuracy and wide applicability in predicting water product prices. However, single-model predictions have disadvantages such as limited adaptability, inadequate precision, and poor robustness. Building upon previous research, this study proposes a weight allocation method based on Particle Swarm Optimization with Cuckoo Search Algorithm (PSO-CS) .This paper presents several novel contributions:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eWe introduce a Weight Allocation Intelligent Combinatorial Modelling Forecasting Framework, which strategically assigns weight distribution across distinct models. This framework exhibits marked superiority in terms of flexibility, precision, and robustness.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIn our approach, prior to forecasting, we employ various decomposition techniques to partition the original dataset into multiple sub-series. This method accentuates intricate details within the time series, thereby rendering sub-series fluctuations smoother relative to the initial series, subsequently improving predictive accuracy.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eLeveraging the innate capabilities of self-learning and social learning introduced by the PSO-CS algorithm enables an enhancement in global search efficiency.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe remainder of this paper is organized as follows. Section 2 briefly introduces the constructs the PSO-CS algorithm. Section 3 presents a Weight Allocation Intelligent Combinatorial Modelling Forecasting Framework. Section 4 provides an overview of the data context. In Section 5, the results of the experiments are analyzed. Finally, the conclusion is given in Section 6.\u003c/p\u003e"},{"header":"2 Fish price prediction framework based on PSO-CS weight allocation algorithm","content":"\u003cp\u003eThe basic idea of the particle swarm iteration-based cuckoo hybrid search optimization algorithm is in the iterative process of n particle swarms, the PSO algorithm is used to update the velocity and position of the particles in each generation to obtain the optimal position of a group of particles, and then the optimal particle position is entered into the CS algorithm to continue to iteratively update. Based on the number of iterations of the original algorithm, each particle swarm adds 1 update and calculation of the CS algorithm, and there is little change in the running time.\u003c/p\u003e \u003cp\u003eGiven \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(m\\)\u003c/span\u003e\u003c/span\u003e individual forecasting models, each assigned a corresponding weight denoted as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{i}（\\text{1,2},\\dots ,m）\\)\u003c/span\u003e\u003c/span\u003e, the combined forecast can be expressed as\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}{\\widehat{y}}_{\\text{combined }}={\\widehat{y}}_{1}*{w}_{1}+{\\widehat{y}}_{2}*{w}_{2}+\\cdots +{\\widehat{y}}_{m}*{w}_{m} \\left(1\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFor optimal weight assignment of combined models, determining the weights of each individual prediction model is critical. In this study, the corresponding weights for each individual model are estimated by constructing an optimisation problem that minimises the error between the combined predicted and observed values.\u003c/p\u003e \u003cp\u003eThus, an optimization problem estimating the reasonable weight of each individual model is construed as below:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}Min G\\left(y-{\\widehat{y}}_{\\text{combined }}\\right) s.t.\\sum _{i=1}^{m}{w}_{i}=1 \\left(2\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\)\u003c/span\u003e\u003c/span\u003e is a predetermined function such as sum squared (SSE),mean squared (MSE), sum absolute (SAE), mean absolute (MAE),etc., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(y\\)\u003c/span\u003e\u003c/span\u003e is observed value.\u003c/p\u003e \u003cp\u003eThe proposed PSO-CS weight assignment method is based on an improved CS algorithm, namely the PSO-CS algorithm. The CS algorithm, inspired by cuckoo\u0026rsquo;s brood parasitic behavior, is a new population-based search paradigm. Cuckoos seek out nests of other hosts and then lay their eggs, which may be found and discarded by the hosts. To enhance the survival rate of their eggs, cuckoos can imitate the host\u0026rsquo;s eggs, or even take them out. The CS algorithm is efficient, robust, and relatively simple in comparison with other evolutionary computing algorithms due to its few control parameters. Furthermore, the levy flight instead of standard random walk is applied in CS, this helps to explore the huge solution space compared to the linear relationship, due to its infinite mean and variance, as well as nonlinear relationship. However, the huge exploration space of the CS algorithm may lead to poor convergence and accuracy of solutions, so the PSO algorithm is introduced to optimize the CS algorithm. The proposed PSO-CS weight assignment method can be expressed as follows:\u003c/p\u003e \u003cp\u003eDefine the objective function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F\\left(w\\right)={\\sum }_{i=1}^{n} y-\\left|{\\stackrel{\\prime }{y}}_{n}\\text{*}{x}_{n}\\right|\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{n}\\)\u003c/span\u003e\u003c/span\u003e is the value of the weight coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\stackrel{\\prime }{y}}_{n}\\)\u003c/span\u003e\u003c/span\u003e is the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e th individual forecasting model, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sum }_{i=1}^{n} {x}_{i}=1\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eParameters such as population size \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N\\)\u003c/span\u003e\u003c/span\u003e Maximum number of iterations \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(T\\)\u003c/span\u003e\u003c/span\u003e, minimum weighing value \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{\\text{m}\\text{i}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e Maximum weight \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{\\text{m}\\text{a}\\text{x}}\\)\u003c/span\u003e\u003c/span\u003e, acceleration coefficients \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({c}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({c}_{2}\\)\u003c/span\u003e\u003c/span\u003e, maximum discovery, and probability \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{a}\\in \\left[\\text{0,1}\\right]\\)\u003c/span\u003e\u003c/span\u003e. A set of randomly generated host nests \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{i}=\\left\\{{x}_{i1},{x}_{i2},\\dots ,{x}_{iD}\\right\\}\\)\u003c/span\u003e\u003c/span\u003e and the corresponding velocities \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{i}=\\left\\{{v}_{i1},{v}_{i2},\\dots ,{v}_{iD}\\right\\}\\)\u003c/span\u003e\u003c/span\u003e and host nests \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{i}(i=\\text{1,2},\\dots ,N)\\)\u003c/span\u003e\u003c/span\u003e to its location in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(D\\)\u003c/span\u003e\u003c/span\u003e-dimensional space is a potential solution to the problem. In the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(t\\)\u003c/span\u003e\u003c/span\u003e iteration, the update speed of the first \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\\)\u003c/span\u003e\u003c/span\u003e The first nest is built by optimizing the location of the first \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\\)\u003c/span\u003e\u003c/span\u003e The first nest.\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}{pbes\\text{t}}_{i}^{\\left(t\\right)}=\\left\\{{pbest}_{i1}^{\\left(t\\right)},\\dots ,{pbest}_{i,D}^{\\left(t\\right)}\\right\\} \\left(3\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eand the optimal position for the entire population \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(gbes{t}^{\\left(t\\right)}\\)\u003c/span\u003e\u003c/span\u003e, and then update the nested positions.\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$${v}_{ij}^{\\left(t+1\\right)}=w\\times {v}_{ij}^{\\left(t\\right)}+{c}_{1}\\times {rand}\\left(\\text{0,1}\\right)\\times \\left[pbes{t}_{ij}^{\\left(t\\right)}-{x}_{ij}^{\\left(t\\right)}\\right]$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}+{c}_{2}\\times {rand}\\left(\\text{0,1}\\right)\\times \\left[gbes{t}_{j}^{\\left(t\\right)}-{x}_{ij}^{\\left(t\\right)}\\right] \\left(4\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}{x}_{ij}^{\\left(t+1\\right)}={x}_{ij}^{\\left(t\\right)}+{v}_{ij}^{\\left(t+1\\right)} \\left(5\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThese are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({v}_{i,j}^{(t+1)}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{ij}^{(t+1)}\\)\u003c/span\u003e\u003c/span\u003e are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((t+1)\\)\u003c/span\u003e\u003c/span\u003e of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(w={w}_{\\text{m}\\text{a}\\text{x}}-\\frac{{w}_{\\text{m}\\text{a}\\text{x}}-{w}_{\\text{m}\\text{i}\\text{n}}}{T}\\times t\\)\u003c/span\u003e\u003c/span\u003e are the inertia weights. Let \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{ij}^{\\left(t\\right)}=pbes{t}_{ij}^{\\left(t\\right)}\\)\u003c/span\u003e\u003c/span\u003e update the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{ij}^{(t+1)}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(L\\left(\\lambda \\right)\\sim u={t}^{-\\lambda }(1\u0026lt;\\lambda \\le 3)\\)\u003c/span\u003e\u003c/span\u003e is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{ij}^{(t+1)}={x}_{ij}^{\\left(t\\right)}+\\alpha ⊛L\\left(\\lambda \\right)\\)\u003c/span\u003e\u003c/span\u003e where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha\\)\u003c/span\u003e\u003c/span\u003e is the step size that should be proportional to the size of the optimization problem. This \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{ij}^{(t+1)}\\)\u003c/span\u003e\u003c/span\u003e will change randomly, with probability \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{a}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003ereplacements \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{ij}^{(t+1)}\\)\u003c/span\u003e\u003c/span\u003e is defined by the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{ij}^{\\left(t\\right)}\\)\u003c/span\u003e\u003c/span\u003e If the fitness value \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F\\left({x}_{ij}^{(t+1)}\\right)\u0026gt;F\\left({x}_{ij}^{\\left(t\\right)}\\right)\\)\u003c/span\u003e\u003c/span\u003e. Then, it finds the list of nests by sorting the list of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(t\\)\u003c/span\u003e\u003c/span\u003e generations of the best nests.\u003c/p\u003e \u003cp\u003eThe PSO-CS hybrid optimization algorithm combines the search capability of PSO and the global search capability of CS to improve the optimization capability of the algorithm in general. Experimentally, it is proved that the accuracy of the PSO-CS hybrid optimization algorithm is significantly better than that of the PSO algorithm, and it is more stable [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e"},{"header":"3 Forecasting framework","content":"\u003cp\u003eThis article proposes an optimal combination framework for predicting the prices of aquatic products based on the PSO-CS weighted aggregation model, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The framework consists of five steps:\u003c/p\u003e \u003cp\u003eStep 1: Data decomposition. The price data of aquatic products is decomposed into multiple sub-sequences using EWT, VMD, and SSA decomposition techniques, aiming to identify the main sequences.\u003c/p\u003e \u003cp\u003eStep 2: Individual prediction. The selected sub-sequence components are sequentially inputted into various prediction models, including LSTM, ELM, and ETS models, to obtain predictions for each component.\u003c/p\u003e \u003cp\u003eStep 3: Removal of large errors. An error analysis is performed on the predicted results of the components. Components with significant errors are removed, and the original sequence of the removed component is merged with the residual sequence.\u003c/p\u003e \u003cp\u003eStep 4: Combination. The predicted results of each group of components are summed to obtain the final prediction result for that group.\u003c/p\u003e \u003cp\u003eStep 5: Prediction aggregation. The PSO-CS weight allocation method is employed to determine the optimal weights for different individual predictions. Then, the predictions of each component are weighted accordingly to obtain the final aggregated prediction result.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4 Empirical Analysis","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Data description\u003c/h2\u003e \u003cp\u003eIn 2020, the annual aquaculture production of larimichthys crocea in China reached 254,000 tons, accounting for 14.5% of the total marine fish aquaculture production in the country [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. The larimichthys crocea aquaculture industry has become one of the distinctive pillar industries in the eastern Fujian Province.\u003c/p\u003e \u003cp\u003eThis research data comes from the WeChat official account platform of \"Ningde Larimichthys Crocea\" operated by the Fishery Association of Ningde City, Fujian Province, and selects the daily reference price for sea surface purchase of larimichthys crocea of 400-500g published by the platform as the research object. The selected time period ranges from May 13th, 2015 to May 24th, 2023, and missing values are filled using the backward filling method. A total of 2,948 daily price data points were collected, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026thinsp;\u0026minus;\u0026thinsp;1. The sample data is divided into three subsets: the training set consists of the first 80% of the price series, totaling 2,358 data points; the validation set consists of the remaining 20% of the series, totaling 590 data points.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescriptive statistics of the reference price of the sea surface purchase of Ningde's larimichthys crocea\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNorm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMaximum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMinimum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUpper quartile\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eStandard deviation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSkewness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eKurtosis\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14.7436\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e26.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11.5000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e14.5000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.1167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.3174\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e8.3753\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Evaluation indicators\u003c/h2\u003e \u003cp\u003eTo accurately evaluate the prediction ability of different models, this paper uses four indicators to evaluate the models: mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and absolute percentage error (MAPE).\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}MSE=\\frac{1}{N}\\sum _{i=1}^{N} {\\left({\\widehat{x}}_{t}-{x}_{t}\\right)}^{2} \\left(6\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}RMSE=\\sqrt{\\frac{1}{N}\\sum _{i=1}^{N} {\\left({\\widehat{x}}_{t}-{x}_{t}\\right)}^{2}} \\left(7\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}MAE=\\frac{1}{N}\\sum _{i=0}^{N-1}\\left|{\\widehat{x}}_{t}-{x}_{t}\\right| \\left(8\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}MAPE=\\frac{1}{N}\\sum _{i=1}^{N}\\left|\\frac{{\\widehat{x}}_{t}-{x}_{t}}{{x}_{t}}\\right|\\times 100\\text{%} \\left(9\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e"},{"header":"5 Results","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Decomposition result\u003c/h2\u003e \u003cp\u003eIn VMD decomposition, the parameter K represents the number of decomposed modes. A value of K that is either too large or too small can result in excessive noise or loss of information, which adversely affects the accuracy of subsequent predictions. Therefore, when selecting VMD parameters, it is necessary to balance the relationship between the value of K and prediction accuracy. Generally, the optimal value of K can be determined through methods such as cross-validation to ensure that VMD effectively extracts the important oscillatory patterns from the data and establishes accurate models for subsequent data analysis and prediction. After conducting experiments, the final decision was made to set the value of K in VMD decomposition as 5. The decomposed IMF components are shown in the following figure.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this study, the EWT (Empirical Wavelet Transform) algorithm is employed to decompose the original sequence. Subsequently, seven empirical mode components (EMCs) can be obtained, as shown in the figure. It can be observed that the EWT decomposition results exhibit a characteristic shift from low frequency to high frequency.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe original sequence was subjected to embedding, decomposition, grouping, and recombination steps through Singular Spectrum Analysis (SSA), resulting in the extraction of six distinct component sequences, as illustrated in the figure below.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Single-model prediction results\u003c/h2\u003e \u003cp\u003eAfter decomposing the original sequence, each component was subjected to combined predictions using LSTM, ELM, and ETS models. The predictive performance of individual models is evaluated and presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The corresponding MAPE accuracies for different single models are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAssessment of the results of the single-model prediction of the sea surface purchase price of greater amberjack (Lepomis macrocephalus)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSingle model\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0256\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1599\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0693\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.4846\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1569\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0658\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.4525\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVMD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0231\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0748\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.5217\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSSA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1259\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0428\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.2989\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eELM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSingle model\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0136\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1165\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0479\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.3282\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1170\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0551\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.3770\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVMD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0902\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0481\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.3307\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSSA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0113\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0775\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eETS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSingle model\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.4673\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.5708\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.1937\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.8844\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.9050\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.3802\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.1124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.5960\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVMD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.3686\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.5236\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.0953\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e17.5228\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSSA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.8503\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.3603\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.0969\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.6466\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAve\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e1.0597\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.6481\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.4928\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e3.7101\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFirstly, in most cases, the predictive accuracy of the non-decomposition model is higher than that of the models using EWT, VMD, and SSA decomposition techniques. However, the predictive accuracy of the ETS model based on VMD decomposition is lower than that of other decomposition models. In ETS prediction, errors in the VMD decomposition results are amplified.\u003c/p\u003e \u003cp\u003eSecondly, it can be observed that the predictive accuracy of the models based on LSTM and ELM is higher than that of the ETS model. The main reason for this is that LSTM and ELM are artificial intelligence algorithms that excel in handling information contained in different components after decomposition. Generally speaking, they have stronger adaptability compared to linear models. Prediction models based on artificial intelligence algorithms are more suitable when combined with decomposition techniques. On the other hand, the ETS model is a complex nonlinear prediction model that is more suited for short-term trend forecasting. These findings indicate that the performance of decomposition techniques and prediction models tends to be diverse. Therefore, the combination of models is particularly important for mitigating the risk of model selection.\u003c/p\u003e \u003cp\u003eRegarding decomposition techniques, the predictive model using the SSA decomposition technique yields better results in predicting the acquisition price of Spanish Mackerel on the sea surface compared to the predictive models using EWT, VMD decomposition, and no decomposition. The MAPE values are reduced by 37.57%, 58.54%, and 42.88% respectively, indicating that the SSA decomposition technique effectively discovers hidden factors behind price fluctuations in this dataset.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Combined model prediction results\u003c/h2\u003e \u003cp\u003eThis section presents the performance of PSO-CS weight allocation for combined prediction. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e showcases the weight allocation results for the combined prediction of the acquisition price of larimichthys crocea in the sea.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResults of the prediction weight allocation for the combination of the sea surface purchase price of greater amberjack\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWeight 1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWeight 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWeight 3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMini fitness\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.97762\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.017449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.054719\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.4956\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVMD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.45978\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.20007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.39683\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.7631\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSSA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3202\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.56079\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.16737\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.5289\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.27499\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.69521\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.081055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.5193\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eELM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.54832\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.31219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.19195\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.5163\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eETS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.13105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.90177\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.022209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.0085\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTables\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e present the evaluation of the predicted results and the reduction in prediction error for the PSO-CS weighted combination forecasting of larimichthys crocea's sea surface purchase price. In most cases, the performance of the PSO-CS weighted combination method is superior to that of the single-model forecasting methods. PSO-CS overcomes the limitations of linear methods by adaptively optimizing weights instead of directly classifying weights based on the performance of individual models, resulting in better performance. Compared to single-model forecasting methods, the PSO-CS approach reduces MSE, RMSE, MAE, and MAPE by 44.43%, 22.69%, 12.21%, and 22.88%, respectively.\u003c/p\u003e \u003cp\u003eHowever, it exhibits poor performance in the ETS-based forecasting method. This may be due to the larger errors in the ETS during the single-model forecasting process, which hinders the effective utilization of PSO-CS in the weight allocation stage, leading to inferior results. Similarly, the VMD-ETS-based forecasting already yields significant errors in the single-model forecasting stage, making it challenging for the PSO-CS weighted combination model to demonstrate its performance in the weight allocation stage.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAssessment of the results of the forecasting of the sea level purchase price combinations for greater amberjack\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on EWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.01857427\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.13628745\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.09340442\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.65263831\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on VMD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.92698336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.96279975\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.79625986\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.37405448\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on SSA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.04924591\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.22191419\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1785835\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.2566242\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on LSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00845136\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.09193128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.05254116\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.36355915\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on ELM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00692352\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.08320768\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.03967529\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.27210333\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on ETS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.16845769\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.27342422\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.91025014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e12.9420506\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAve\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e1.02977268\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.62826076\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.51178573\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e3.47683835\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eReduction rate of assessment error for the combination of forecasting results of the sea surface purchase price of greater amberjack (Lepomis macrocephalus)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on EWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.97132576\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.75282352\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.77280464\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.76762124\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on VMD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.56545996\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0443994\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0768843\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.12261747\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on SSA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.92085782\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.55914784\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5345503\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.53012071\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on LSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.62066388\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.38158246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.16872412\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.17270049\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on ELM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.22984798\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.04248147\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.02329428\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.02244412\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ebased on ETS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.6419242\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.3304881\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.3896967\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.2429374\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eAve\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.44437186\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.22685796\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.17213207\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.2287611\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e illustrates the reduction in average error of the PSO-CS method compared to single-model predictions. Considering the aforementioned, the experimental results effectively demonstrate the robustness of the proposed PSO-CS hybrid model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"6 Conclusion","content":"\u003cp\u003eThe prediction of aquatic product prices holds significant importance in the fields of agriculture and fisheries. It is crucial for decision-makers, producers, and consumers alike. Decision-makers can utilize price forecasts to formulate rational policies and strategies that promote sustainable development and maximize benefits. These aids regulatory bodies in market supervision by maintaining a fair competitive environment [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Producers can devise reasonable production plans and supply chain management based on the forecast results, thereby meeting market demand and enhancing efficiency. Consumers can better plan their purchasing behavior through price predictions, avoiding economic burdens resulting from future price increases.\u003c/p\u003e \u003cp\u003eTo address the limitations of existing models, this paper proposes a water product price prediction framework based on a Weight Allocation Intelligent Combinatorial Modelling. By utilizing daily purchase prices of larimichthys crocea in Ningde City, Fujian Province as data, the following conclusions are derived within the sample interval: Firstly, the decomposed-ensemble prediction model significantly improves the predictive performance compared to direct prediction models. Secondly, the accuracy of the SSA-ELM prediction model was 46.33% lower than the other three models on average, which is better than the other individual models. Thirdly, the combination prediction model based on PSO-CS weight allocation exhibits significantly superior performance compared to single-model predictions. In conclusion, the water product price prediction framework based on Weight Allocation Intelligent Combinatorial Modelling holds significant importance in the agricultural and fisheries sectors. Our research provides a scientific basis for decision-making and business operations in related fields, offering beneficial insights for future research and practical applications.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets generated during the current study are available from the corresponding author on reasonable request. The data of this study comes from the Fisheries Association of Ningde City, Fujian Province, China.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCRediT authorship contribution statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDaqing Wu:\u0026nbsp;\u003c/strong\u003eSupervision, Conceptualization, Methodology, Writing \u0026ndash; review \u0026amp; editing. \u003cstrong\u003eBinfeng Lu:\u003c/strong\u003e Data curation, Software, Writing \u0026ndash; original draft,\u0026nbsp;Writing \u0026ndash; review \u0026amp; editing. \u003cstrong\u003eZinuo Xu:\u003c/strong\u003e Formal analysis, Validation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was supported by the Major Social Science Projects in China (Evaluation of the Development Potential of the Deep Blue Fisheries Industry under Climate Change, No.21\u0026amp;ZD100)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of Competing Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no conflicts of interest to report regarding the present study.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eQI W, KONG L, LI J and X. YANG (2023) Research on the Relationship between Youth Consumer Lifestyle and Attitude towards Fresh Agricultural Products:Based on Netnography Theory. J Agro-Forestry Econ Manage : 1\u0026ndash;13\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHUA J, SU G and Y. JIA (2022) Research on Pork Price Forecasting and Risk Early Warning Under Impact of Swine Epidemic. Agricultural Econ Manage (06): 101\u0026ndash;113\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJia B (2014) Sales price forecast of major agricultural products in China. Stat Decis (20): 100\u0026ndash;102\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu Y and x., Wen (2016) Short-term stock price prediction based on ARIMA model. Statistics \u0026amp; Decision(23): 83\u0026ndash;86\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCao Y (2019) Quadratic Smoothing Processing and Prediction of China's Network Consumption Dynamic Price Index. 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J Chengdu Univ Technol (Natural Sci Edition) (08): 21\u0026ndash;24\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Price Forecasting, Aquatic Products, Intelligent Combinatorial Modelling, Neural Network","lastPublishedDoi":"10.21203/rs.3.rs-3966059/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3966059/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe price prediction of aquatic products is of great significance to the socio-economic development and fisheries industry. However, due to the complexity and uncertainty of the aquatic product market, traditional forecasting methods often struggle to accurately predict price fluctuations. Therefore, this study adopts a intelligence combination model to enhance the accuracy of aquatic product price prediction. Firstly, three decomposition methods, namely empirical wavelet transform, singular spectrum analysis, and variational mode decomposition, are applied to decompose the complex original price series. Secondly, a combination of bidirectional long short-term memory artificial neural network, extreme learning machine, and exponential smoothing prediction methods is used for cross-prediction on the decomposed results. Subsequently, these predicted result are input into the PSO-CS intelligence algorithm for weight allocation and generating combined prediction results. Empirical analysis is conducted using the data of daily sea purchase price of larimichthys crocea in Ningde City. The combination prediction accuracy with PSO-CS weight allocation is found to be higher than that of single model predictions, yielding superior results. Based on the weight allocation intelligent combinatorial modelling, the prediction of aquatic product prices demonstrates higher accuracy and stability, enabling better adaptation to market changes and price fluctuations.\u003c/p\u003e","manuscriptTitle":"Price Forecasting of Aquatic Products Based on Weight Allocation Intelligent Combinatorial Modelling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-20 09:54:22","doi":"10.21203/rs.3.rs-3966059/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bb572658-143c-4cec-9ca8-40100e8f2fec","owner":[],"postedDate":"February 20th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-02-23T10:02:05+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-20 09:54:22","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3966059","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3966059","identity":"rs-3966059","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}