Research on Ginger Price Prediction Model Based on Deep Learning

Abstract

In order to ensure the price stability of niche agricultural products and enhance farmers’ income, the study delves into the pattern of the ginger price fluctuation rule and its main influencing factors. By combining seasonal decomposition STL, long and short-term memory network LSTM, attention mechanism ATT and Kolmogorov-Arnold network, a combined STL-LSTM-ATT-KAN prediction model is developed, and the model parameters are finely tuned by using multi-population adaptive particle swarm optimisation algorithm (AMP-PSO). Based on an in-depth analysis of actual data on ginger prices over the past decade, the STL-LSTM-ATT-KAN model demonstrated excellent performance in terms of prediction accuracy: its mean absolute error (MAE) was 0.111, mean squared error (MSE) was 0.021, root mean squared error (RMSE) was 0.146, and the coefficient of determination (R²) was 0.998. This study provides the Ginger Industry, agricultural trade, farmers and policymakers with digitalised and intelligent aids, which are important for improving market monitoring, risk control, competitiveness and guaranteeing the stability of supply and price.

1. Introduction

As a large agricultural country, China’s agriculture is the foundation of the country’s economy. The stability of agricultural prices has a direct impact on the rural economy, market regulation and the interests of farmers and consumers. Ginger price fluctuations are influenced by a variety of factors and have a significant impact on the downstream industry chain [1]. Therefore, accurate prediction of ginger price is crucial for farmers’ production planning, consumers’ consumption arrangement and government market regulation.

For the price fluctuation of agricultural products, researchers have widely used the ARIMA model in the field of agricultural price forecasting and verified its effectiveness. And successfully predicted the price trend of agricultural products such as cabbage, corn, mango, cucumber and potato [2,3,4,5]. The model is used to forecast the price trend of agricultural products such as cabbage, corn, mango, cucumber and potato. Meanwhile, the researchers improved the accuracy of the model by applying machine learning techniques such as time series analysis, support vector machine and neural network [6,7,8,9,10,11]. Nevertheless, researchers still need to face the challenges of insufficient model generalisation capability and incomplete consideration of complex influencing factors. In recent years, significant progress has been made in research on agricultural price forecasting, covering from traditional time series analysis to advanced machine learning and deep learning techniques. Sun et al. provide a review of existing methods, pointing out that combinatorial models and intelligent forecasting methods have a promising application in the future. However, the complexity and nonlinear nature of time series makes it still challenging to accurately forecast price fluctuations [12].

Deep learning techniques are pushing traditional boundaries, and their potential in the field of prediction is becoming increasingly significant. At the same time, elements such as online public opinion and government support are being integrated into the prediction model to improve the accuracy of prediction. Jinling Teng et al. used Prophet model to predict ginger price [13]; Wang Yan improved ginger price prediction accuracy using STCN-LSTM model and improved loss function [14]; Xingchen Lv showed that online public opinion can improve the price prediction accuracy of small agricultural products [15]; Chaudhary et al. used value chain analysis to propose ginger market optimisation strategies, pointing out the importance of government and technical support [16]; Manjubala et al. used complex exponential smoothing to accurately predict weekly prices of garlic and ginger [17]; Hongfeng Li et al. investigated the price factors of ginger [18]; Fu et al. revealed the mechanism of multiple and complex factors affecting the prices of small-scale agricultural commodities [19]; Anamisa et al. used a normalised LSTM model to improve the accuracy of ginger price prediction [20]; Lin et al.’s GCRNN model improves time series classification accuracy and model interpretability [21]; CH-LSTM model developed by Linmei Hu et al. to predict future sub-events [22]; ATTAIN network proposed by Zhang et al. which improves the prediction accuracy and model interpretability through the attention mechanism [23]; Zhang Dabin et al. proposed a VMD-ELM-based integrated prediction model for agricultural futures price decomposition, which significantly improved the prediction accuracy by optimising the VMD parameters and combining with the learning capability of ELM, providing a new method for agricultural futures price prediction [24]; Wang Runzhou et al. proposed a prediction model for agricultural commodity prices based on signal decomposition and deep learning, which effectively improves the prediction accuracy and stability of agricultural commodity prices by complementary ensemble empirical modal decomposition (CEEMD) and deep learning network to extract features, combined with multidimensional data, effectively improved the prediction accuracy and stability of the price of agricultural products such as white pork, spinach, apples, eggs, etc. [25]; Xueqing Fang et al. proposed EEMD-LSTM model for short-term price prediction of agricultural products, which significantly improved the prediction performance through feature extraction and LSTM network training [26]; Gu Yeong Hyeon et al. proposed a DIA-LSTM model for cabbage and radish price forecasting in Korea, which significantly reduces the forecasting error by dynamically selecting meteorological and trading volume data from the main production areas and provides a new method to stabilise the supply and demand of agricultural products [27]; Sun Changxia et al. proposed a hybrid VMD-EEMD-LSTM forecasting model, which effectively improves the pork in China through quadratic decomposition and LSTM training, leek, mushroom and cauliflower price prediction accuracy [28].

Deep learning techniques have made remarkable achievements in the field of agricultural price prediction, but the research for multi-factor models still needs to be further deepened. Sun et al. suggested that future research directions should include the development of more effective combinatorial models in order to integrate the advantages of different models so as to improve the accuracy and stability of the prediction [12]. Price volatility is the result of a combination of factors, so it is particularly critical to analyse these factors and develop integrated forecasting models. Integrated models can effectively improve the accuracy of forecasts by combining the advantages of different models. Building an integrated model requires integrating multiple data sources and optimising the model structure. Future research needs to explore the development and optimisation of multi-factor models further to capture the factors that influence price volatility in a more comprehensive way. Sun et al. also highlighted this point and suggested that structured and unstructured data should be integrated into the model to improve the accuracy of the prediction [12]. Based on this, this paper constructs a combined STL-LSTM-ATT-KAN (Seasonal Trend Decomposition-Long and Short-Term Memory Network-Attention Mechanism-Kolmogorov-Arnold Network) model for the purpose of predicting ginger prices with the expectation that the accuracy of the prediction will be further improved by this model and its practical application value will be enhanced. In order to further improve the accuracy of ginger price prediction, an improved particle swarm optimisation algorithm, the Adaptive Multi-Population Particle Swarm Optimisation (AMP-PSO) algorithm, is introduced in this study [29]. AMP-PSO effectively improves the efficiency and accuracy of the model parameter optimisation through the multi-population structure and adaptive parameter tuning mechanism and provides a powerful model for ginger price prediction. Ginger price prediction provides powerful technical support.

2. Materials and Methods

2.1. Analysis of Factors Affecting the Price of Ginger

This study aims to investigate the fluctuation pattern of ginger prices, analyse the price history and fluctuation pattern, and identify the key influencing factors through literature review, expert interviews and fieldwork. The specific influencing factors are shown in

Table 1. Key influences on ginger prices.

Level 1 Impact Factors	Specific Influencing Factors
Agricultural price factors	The daily wholesale price of garlic
	The daily wholesale price of scallions
Agricultural production factors	Average daily temperature in the main ginger-producing areas
	Area under crops
	Production
	Production volume index
Economic indicator factors	Fresh Vegetables Consumer Price Index (CPI)
	Broad money supply M2
	Exchange rate (USD/CNY)
International market factors	Ginger export amount
	Ginger export volume
	International crude oil prices
Market Opinion Factors	Ginger public opinion

.

Ginger price fluctuations reflect regional and inter-variety trends, and market linkage effects indicate shifts in supply and demand, improving forecasting accuracy. Supply and demand indicators map supply conditions and market dynamics to predict price volatility. Agricultural valuation indicators reflect production conditions and price changes that affect the ginger market. Economic indicators show the macroeconomic impact on prices, including money supply and exchange rate movements. A comprehensive analysis of these factors allows for a more comprehensive forecast of ginger prices and improves the model’s accuracy and generalizability.

2.2. Theoretical Approach and Model Construction

This paper innovatively constructs a model consisting of a combination of STL-LSTM-ATT-KAN aimed at forecasting ginger prices. The model first decomposes the time series using STL (Seasonal Trend Decomposition), then captures the long-term dependencies through LSTM (Long Short-Term Memory Network), followed by ATT (Attention Technique) to strengthen the identification of key information, and finally optimises the integration of information through KAN network [30]. In addition, the AMP-PSO (Adaptive Multi-Particle Swarm Optimisation) algorithm was used to optimise the model parameters to improve the accuracy and performance of the prediction [29]. AMP-PSO provides an efficient and accurate solution for ginger price prediction by effectively balancing global and local search capabilities through a multi-population structure and adaptive parameter adjustment mechanism.

As shown in Figure 1, the STL-ATT-LSTM-KAN model structure contains three main steps:

(i)

The STL (Seasonal Trend Decomposition) module serves to decompose the ginger price time series into a trend component, a seasonal component and a stochastic component.

(ii)

In the LSTM-ATT-KAN process, LSTM processes time series data to capture long-term dependent information; the attention mechanism highlights key time point information, and the KAN module optimally integrates the information to improve prediction accuracy.

(iii)

The AMP-PSO optimisation step ensures optimal model prediction performance by adaptively adjusting the particle swarm search space and optimising the model parameters.

The final output module displays the model’s predictions, revealing the trend changes in the future price of ginger.

2.2.1. Seasonal-Trend Decomposition Using STL for Ginger Price Analysis

The Seasonal-Trend Decomposition using LOESS (STL) is a robust time series decomposition technique that decomposes ginger price data into three independent components:trend ($T_t$), seasonality ($S_t$), and residual ($R_t$), estimated separately using the Locally Weighted Scatterplot Smoothing (LOESS) method. The calculation formula for this method, as shown in Equation (1):

$$y_t=T_t+S_t+R_t$$

(1)

where $y_t$ represents the time series data, $T_t$ denotes the trend component, which reflects the overall upward or downward trend of prices; ${ S}_t$ denotes the seasonal component, which reveals the regularity of price fluctuations over a one-year cycle; $R_t$ denotes the residual component, which represents stochastic fluctuations in prices that cannot be explained by the model and may be caused by factors such as weather changes, natural disasters, or sudden market events.

The trend component${ T}_t$ and the seasonal component $S_t$ are calculated as shown in Equations (2) and (3).

$$T_t=\mathrm{LOESS}\left(y_t,{\lambda }_T\right)$$

(2)

$$S_t=\mathrm{LOESS}\left(y_t-T_t,{\lambda }_S\right)$$

(3)

Of these, the ${\lambda }_T$ and ${\lambda }_S$ denote the smoothing parameters for the trend and seasonal components, respectively.

In this study, STL enhances the forecasting accuracy and stability of our STL-LSTM-ATT-KAN model by isolating seasonal and trend components, enabling the subsequent LSTM layer to better capture temporal dependencies. Later experimental results demonstrate the effectiveness of STL in coping with the high volatility of ginger prices, especially during the peak harvest season.

2.2.2. LSTM-ATT-KAN Model Construction

• Step 1: LSTM in STL-LSTM-ATT-KAN Model

LSTM (Long Short-Term Memory Network) is an improved recurrent neural network (RNN) that efficiently captures long-term and short-term dependencies in time-series data by means of memory units and gating mechanisms (input gates, forgetting gates, and output gates). In this study, LSTM is combined with seasonal decomposition (STL) to process the trend and seasonal components of the decomposition and extract time-dependent features. The first layer of LSTM focuses on serial pattern modelling, while the second layer of LSTM further refines the advanced features to improve the accuracy of ginger price prediction. The basic unit structure of LSTM is shown in Figure 2.

The basic unit of the LSTM can be expressed as the following equation:

Oblivion Gate:

$$f_t=\sigma \left(W_f\cdot \left[h_{t-1},x_t\right]+b_f\right)$$

(4)

Input Gate:

$$i_t=\sigma \left(W_i\cdot \left[h_{t-1},x_t\right]+b_i\right)$$

(5)

$$\widetilde{C_t}=\tanh \left(W_C\cdot \left[h_{t-1},x_t\right]+b_C\right)$$

(6)

Memory Updates:

$$C_t=f_t\cdot C_{t-1}+i_t\cdot \widetilde{C_t}$$

(7)

Output Gate:

$$o_t=\sigma \left(W_o\cdot \left[h_{t-1},x_t\right]+b_o\right)$$

(8)

$$h_t=o_t\cdot \tanh \left(C_t\right)$$

(9)

• Step 2: Attention Mechanism in STL-LSTM-ATT-KAN Model

ATT (Attention Mechanism) is a dynamic feature selection technique that focuses on critical information in time series data while de-emphasising less relevant details, mimicking human attention allocation by calculating weights of different feature vectors to achieve high-quality feature extraction. In this study, ATT is integrated into the STL-LSTM-ATT-KAN model to enhance the focus on key time points in ginger price sequences, improving the prediction of price fluctuations. The basic principle of the attention mechanism is illustrated in Figure 3, where it dynamically prioritises influential time steps based on their relevance. Figure 3 illustrates the attention mechanism’s workflow, highlighting the dynamic weighting of time steps to prioritise relevant features in ginger price time series data.

The weight calculation is formalised in Equations (10) and (11):

$$e_t=\mathit{tanh}\left(W_e\cdot h_t+b_e\right)$$

(10)

$${\alpha }_t={\displaystyle \frac{\mathit{exp}\left(e_t\right)}{{\sum }_{i=1}^T\mathit{exp}\left(e_i\right)}}$$

(11)

where $e_t$ represents the energy score for time $t$, $W_e$ is a weight matrix, $h_t$ is the hidden state vector, $b_e$ is a bias term, $\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}$ is the hyperbolic tangent function compressing values between −1 and 1, and $exp$ with the denominator ensures ${\alpha }_t$ forms a probability distribution over all time steps $T$.

This mechanism acts as a dynamic feature selector, allowing the model to focus on key price patterns in the ginger price data. In the experiments, ATT significantly improves the performance of the STL-LSTM-ATT-KAN model by improving the capture of key temporal dependencies.

• Step 3: Kolmogorov-Arnold Network (KAN) in STL-LSTM-ATT-KAN Model

KAN (Kolmogorov-Arnold Network) is a neural network architecture based on the Kolmogorov-Arnold theorem, which decomposes complex multivariate functions into combinations of simple one-dimensional functions [30]. This enables KAN to effectively extract key features from high-dimensional data, enhancing model performance. In this study, KAN is integrated into the STL-LSTM-ATT-KAN model to process the high-dimensional features extracted by the LSTM and Attention Mechanism, further improving the expressive power for ginger price prediction.

The structure of KAN is depicted in Figure 4, comprising:

• Input Features: Represented as x1, x2, x3, these are the initial features (e.g., decomposed trends and seasonal components from ginger price data).
• One-Dimensional Functions: Each input feature is transformed by a corresponding one-dimensional function (${\varphi }_{ij}\left(x_j\right)$).
• Feature Fusion: The outputs are aggregated into a fused feature $y$, as shown in Equation (12):

  $$y=\sum _{i=1}^n{g}_i\left(\sum _{j=1}^m{\varphi }_{ij}\left(x_j\right)\right)$$

  (12)

  where $y$ is the fused feature, $g_i$ are transformation functions, ${\varphi }_{ij}$ are one-dimensional functions, and $x_j$ are input variables, with $n$ representing the number of transformation functions and $m$ the number of input features.
• Output Layer: The fused feature $y$ is mapped through a fully connected layer to generate the final prediction $\widehat{y}$, as described in Equation (13):

  $$\widehat{y}=ReLU\left(W_{fc}\cdot y+b_{fc}\right)$$

  (13)

  where $W_{fc}$ is the weight matrix mapping high-dimensional features to the target dimension, $b_{fc}$ is the bias adjusting the feature space centre, and ReLU is the rectified linear unit activation function, enabling nonlinear modelling of future ginger price trends.

This architecture enhances the STL-LSTM-ATT-KAN model’s ability to capture complex nonlinear patterns in ginger prices (e.g., market shocks and seasonal dynamics), achieving superior prediction performance for agricultural market monitoring.

2.2.3. Adaptive Multi-Population Particle Swarm Optimisation (AMP-PSO) Algorithm

The Adaptive Multi-Population Particle Swarm Optimisation (AMP-PSO) algorithm is an enhanced version of the Particle Swarm Optimisation (PSO) algorithm, incorporating a multi-population strategy and adaptive parameter adjustments to significantly improve global search capability and convergence speed. In this study, AMP-PSO is applied to optimise the parameters of the STL-LSTM-ATT-KAN model, ensuring optimal prediction performance for complex ginger price time series data.

(1)

Multi-Population Strategy

AMP-PSO divides the particle swarm into multiple sub-populations, each performing independent optimisation to balance global exploration and local exploitation. Particles are categorised into:

• • Leader Population: Conducts global searches by interacting with other sub-populations to expand the solution space.
  • Follower Population: Focuses on local refinement, leveraging local optima to enhance precision.

Through periodic particle exchanges, AMP-PSO maintains population diversity and accelerates convergence, effectively preventing traditional PSO from getting trapped in local optima.

(2)

Adaptive Parameter Adjustment

AMP-PSO dynamically adjusts the inertia weight ($\omega \left(t\right)$) and learning factors ($c_1,c_2$) to balance global and local search capabilities. The adaptive inertia weight is updated as:

$$\omega \left(t\right)={\omega }_{max}-{\displaystyle \frac{\left({\omega }_{max}-{\omega }_{min}\right)\cdot t}{T_{max}}}$$

(14)

where ${\omega }_{max}$ and ${\omega }_{min}$ are the maximum and minimum inertia weights, $t$ is the current iteration, and $T_{max}$ is the maximum iteration number. This mechanism enhances the search efficiency and convergence speed for optimising the STL-LSTM-ATT-KAN model’s parameters in ginger price prediction.

(3)

Particle Update Mechanism

Particle positions and velocities are updated for each dimension $j$ of particle $i$ using the following Equation (15):

• Velocity Update:

$$v_{i,j}\left(t+1\right)=\omega \left(t\right)\cdot v_{i,j}\left(t\right)+c_1\cdot r_1\cdot \left(p_{i,j}\left(t\right)-x_{i,j}\left(t\right)\right)+c_2\cdot r_2\cdot \left(g_{best,j}\left(t\right)-x_{i,j}\left(t\right)\right)$$

(15)

where $v_{i,j}\left(t\right)$ and $x_{i,j}\left(t\right)$ are the velocity and position of particle $i$ at dimension $j$ and iteration $t$, $p_{i,j}\left(t\right)$ is the individual best position, $g_{best,j}\left(t\right)$ is the global best position, $\omega \left(t\right)$ is the adaptive inertia weight (updated in Equation (14)), $c_1$, $c_2$ are the learning factors, and $r_1$, $r_2$~$U$(0, 1) are random numbers in [0, 1].

• Position Update:

$$x_{ij}^{t+1}=x_{ij}^t+v_{ij}^{t+1}$$

(16)

where $x_{ij}^{t+1}$ and $v_{ij}^{t+1}$ are the position and velocity of particle $i$ at dimension $j$ and iteration $t+1$, respectively, and $x_{ij}^t$ is the position at iteration $t$.

To constrain particle states within reasonable bounds, AMP-PSO applies a $sigmoid$ function to limit velocity and position elements to [0, 1]:

$$sigmoid\left(x\right)={\displaystyle \frac{1}{1+e^{-x}}}$$

(17)

During each iteration, the algorithm evaluates the objective function $F$ for each particle. If the current position yields a better fitness than the individual best, $p_{best,ij}$ is updated for each dimension $j$, as described in Equation (18). Suppose the fitness surpasses the global best, $g_{best,j}$ is updated for each dimension $j$, as described in Equation (19). Here, $F$ is the objective function, defined as minimising the prediction error of ginger prices in the STL-LSTM-ATT-KAN model, $x_{ij}(t+1)$ denotes the current position for dimension $j$ of particle $i$ at iteration $(t+1)$, and $p_{best,ij}\left(t\right)$ and $g_{best,j}\left(t\right)$ denote the individual and global best positions, respectively, for dimension $j$ at iteration $t$.

$$p_{best,ij}(t+1)=x_{ij}(t+1) if F\left(x_{ij}\right(t+1\left)\right)>F\left(p_{best,ij}\right(t\left)\right)$$

(18)

If the fitness surpasses the $g_{best,j}$ is updated for each dimension $j$:

$$g_{best,j}(t+1)=x_{ij}(t+1) if F\left(x_{ij}\right(t+1\left)\right)>F\left(g_{best,j}\right(t\left)\right)$$

(19)

where $F$ is the objective function, defined as minimising the prediction error of ginger prices in the STL-LSTM-ATT-KAN model, $p_{i,j}\left(t\right)$ denotes the current position, and $p_{best,ij}\left(t\right)$ denotes the individual best position, both for dimension $j$ of particle $i$ at iteration $t$, while $g_{best,j}\left(t\right)$ denotes the global best position for dimension $j$ at iteration $\mathrm{u}\mathrm{p}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}$ across all particles $i$ to optimise the model parameters. Note that $p_{best,ij}(t+1)$ and $g_{best,j}(t+1)$ are updated in the next iteration if the fitness improves, as described in Equations (18) and (19).

(4)

Particle Exchange Mechanism

To enhance diversity and prevent premature convergence, AMP-PSO periodically exchanges particles between the leader and follower populations after a predefined number of iterations, introducing new solution space information to accelerate convergence.

(5)

Determination of Global Optimal Solution

At each iteration, AMP-PSO updates individual and global optima based on fitness values. The algorithm terminates when reaching the maximum iteration $T_{max}$, achieving convergence of the objective function, or finding a solution meeting performance criteria (e.g., minimising prediction error). The global optimal position determines the optimal parameters for the STL-LSTM-ATT-KAN model, balancing multiple objectives to yield a Pareto-optimal solution set.

Compared to traditional PSO, AMP-PSO avoids local optima through its multi-population strategy and adaptive adjustments. The follower population’s local search capability improves parameter precision, while particle exchanges and adaptive inertia weights enhance diversity and adaptability. In our experiments, AMP-PSO significantly improved the STL-LSTM-ATT-KAN model’s prediction accuracy and stability for ginger prices, maintaining high computational efficiency for agricultural applications.

2.3. Experimental Design

2.3.1. Experimental Setup

• Experimental environment

The experiments were conducted using a Suttai ST-SN260 server with an AMD EPYC 9754 CPU (128 cores, 2.25 GHz), NVIDIA RTX 4060 GPU (8 GB), Samsung 384 GB DDR5 RAM, Samsung 2 TB SSD and 16 TB HDD. The operating system was Ubuntu 20.04 LTS version, with the installation of Python 3.8.10 and libraries PyTorch 1.9.0, NumPy 1.21.0, and Pandas 1.3.0.

• Data sources

The agricultural product price data used in the study comes from the National Key Agricultural Product Market Information Platform of the Ministry of Agriculture and Rural Affairs (PRC). The platform compiles and publishes price information from major wholesale markets for agricultural products across the country. The time span chosen for the experiment is nearly ten years, from 1 January 2014 to 29 September 2024, for the daily wholesale price data of ginger. In order to deeply explore the formation mechanism of ginger price and its fluctuation pattern, 13 dimensions of key influencing factor indicators, including daily wholesale price of garlic, daily wholesale price of green onion, temperature of main production area, planting area, production, production volume index, consumer price index (CPI) of fresh vegetables, export volume, export volume, M2 money supply, exchange rate, crude oil price, and public opinion of ginger, are selected in a comprehensive manner and in combination with the actual situation. The data for the selected indicators come from the Ministry of Agriculture and Rural Affairs (PRC), Ministry of Commerce of the People’s Republic of China (MOFCOM), National Bureau of Statistics of China (NBS), General Administration of Customs of the People’s Republic of China (GACC), The People’s Bank Of China (PBC), China Meteorological Administration (CMA), Brick Agricultural Database, Baidu Index, as well as authoritative organisations and platforms such as the Food and Agriculture Organisation of the United Nations (FAO), and the Energy Information Administration (EIA). These data sources are rich and varied and of high reference value, providing solid support for the study. Specific platform website information is detailed in the subsequent description of data sources (Abbreviations).

This study collects public data from websites through crawling techniques. Static web pages are mainly crawled using Python’s BeautifulSoup and Request libraries, while dynamically loaded content (e.g., sections requiring login authorisation) is efficiently processed using Selenium and XPath tools.

• Data processing

With regard to the data preprocessing stage, the collected ginger dataset was systematically organised and cleaned to ensure data quality. The specific steps involved are as follows:

① Initially, the data underwent a thorough cleansing process, encompassing the removal of duplicate records and the management of outliers.

② For instances where values were missing, the interpolation of similar mean values was employed to ensure the integrity and consistency of the data.

③ Conversion of the data format was conducted to facilitate the seamless progression of subsequent analyses.

The efficacy of these preprocessing steps in enhancing the reliability and applicability of the dataset is evident.

The aggregated dataset (3925 data points from 1 January 2014 to 29 September 2024) was divided into a training set (65%), a validation set (20%), and a test set (15%) according to the time series. The division is as follows: The training set contained 2551 entries (1 January 2014 to 26 December 2020), the validation set contained 785 entries (27 December 2020 to 23 February 2023), and the test set contained 589 entries (24 February 2023 to 29 September 2024). This division increases the proportion of training data to reduce the risk of overfitting while ensuring that the validation and test sets have sufficient sample sizes on unseen data to improve the generalisation ability of the model.

In order to enhance the interpretability and predictive ability of the model, the price volatility analysis was simplified by dividing the ginger price series data using the STL method. The STL decomposition separates the raw data into three components: trend, seasonal and residual. The results are displayed in Figure 5.

2.3.2. Forecast Evaluation Indicators

When forecasting ginger prices, the assessment of the model’s predictive performance is crucial. Metrics such as mean square error (MSE), mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) are usually used for the assessment.

The mean square error (MSE) is the average of the squares of the differences between the predicted and true values:

$$\mathit{MSE}={\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2$$

(20)

where $y_i$ is the true value and $\widehat{y_i}$ is the predicted value, and $n$ is the sample size.

The root mean square error (RMSE) is the difference between the observed value and the true value. The square root of the ratio of the square of the deviation of an observation from the true value to the number n of observations:

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n·{\left(y_i-\widehat{y_i}\right)}^2}$$

(21)

The Mean Absolute Error (MAE) is the average of the absolute values of the difference between the predicted and true values:

$$\mathit{MAE}={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|y_i-\widehat{y_i}\right|$$

(22)

The coefficient of determination (R²) is used to measure the proportion of total variance in the explanatory variables of the model and indicates the goodness of fit of the model:

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2}{{\sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2}}$$

(23)

where $\overline{y}$ is the mean of the true values. The value range of R² is between 0 and 1, which can intuitively reflect the goodness of fit of the model, and the closer the value of R² is to 1, the stronger the explanatory power of the model.

2.4. Model Optimisation Parameter Setting

To ensure that all parts of the model are fully functional, the parameters of the model were finely tuned in this study using the Adaptive Particle Swarm Optimisation algorithm for Multiple Populations (AMP-PSO). The main parameters of the model were set as follows: kan_units (number of KAN network units) to 10, lstm_units (number of LSTM network units) to 10, learning_rate (learning rate) to 0.005, and batch_size (batch size) to 26.908, as shown in

Table 2. AMP-PSO parameter selection.

Model Parameter	Parameter Value
kan_units	22
lstm_units	50
learning_rate	0.004
batch_size	36.451

below.

3. Results

3.1. Experimental Results

To better understand and optimise the training process of the model, in order to further validate the effect of model training, this paper plots the loss map of the STL-LSTM-ATT-KAN model during the training process, as shown in Figure 6 below.

As shown in Figure 6, the model training loss (blue line) and validation loss (orange line) vary with epoch. The initial training loss decreases rapidly, indicating that the model converges quickly and captures the training data patterns. The training loss is low and stable for most of the training cycles, indicating that the model fits well and the training process is stable.

The residual plot shows the distribution of the difference between the true value and the predicted value (i.e., the residual). By looking at the distribution of the residuals, it is possible to visually assess the model’s prediction bias and error patterns. This is shown in Figure 7.

Figure 7 shows the distribution of the residuals between the model’s predicted and true values, where the residuals are defined as the difference between the true value and the predicted value, which is used to assess prediction accuracy. In the figure, the red dashed line indicates the baseline, where the residuals are zero, and the blue dots show the residuals for each sample. Most of the blue points are distributed around the zero line (residuals range from about −0.5 to 0.5), indicating that the model predicts most of the data more accurately and close to the true value. However, when the true value is large (especially above 10), the distribution of blue points becomes more spread out and extends to a range of −1.0 to 1.5, suggesting that the model’s error in predicting high values increases. In particular, the residuals are skewed towards positive values (above the zero line) in regions where the true value is greater than 14, reflecting the fact that the model may be underestimating the true data for these high values.

In addition, the model performs better in regions with low (less than 8) or moderate (around 8–12) true values, with less fluctuation in the residuals, whereas the residuals in regions with high values fluctuate more, suggesting a limitation of the model in dealing with large or extreme values. If the distribution of residuals shows a clear pattern (e.g., trend or periodicity), this may indicate that the model is not fully capturing certain features in the time series data. In the future, the prediction accuracy and stability of the model can be improved by increasing the data set, optimising the data processing method, and improving the prediction algorithm to reduce errors in the high-value range.

Through the training and prediction process of the model, it is possible to obtain the predicted values of ginger prices. In order to visualise these predictions more, a trend comparison graph between the real and predicted values and a predicted trend graph for the next seven days were produced, respectively, as shown in Figure 8 and Figure 9.

This study demonstrates the effectiveness of AMP-PSO in optimising the parameters of the ginger price prediction model. The multi-population structure and adaptive parameters of AMP-PSO improve the searchability and convergence speed of the model, providing an efficient and accurate solution for ginger price prediction. Experiments show that the AMP-PSO optimised STL-LSTM-ATT-KAN model significantly outperforms other algorithms in terms of prediction accuracy, with specific metrics of MAE: 0.111, MSE: 0.021, RMSE: 0.146, and R²: 0.998. This demonstrates that the model has high accuracy and stability when dealing with complex time series data. Therefore, the optimised model of AMP-PSO performs well in terms of prediction accuracy, stability, and adaptability, and it provides powerful technical support for ginger price prediction. Traditional PSO is easy to fall into a local optimum, has limited accuracy, and performs poorly when dealing with complex data. Genetic algorithm GA has strong global search capability but is computationally complex and slow. Multi-population PSO (MP-PSO) improves the optimisation ability but lacks adaptive tuning and has limited effect. AMP-PSO combines multi-population and adaptive parameters and is superior in optimisation accuracy and speed. Experiments show that AMP-PSO performs well on all indicators with high computational efficiency, provides technical support for ginger price prediction, and verifies its effectiveness in complex time series prediction.

3.2. Comparative Experimental Results

In order to verify the prediction advantages of this model, it is compared with RF, SVM, ARIMA, XGBoost, CNN, RNN, LSTM, GRU, etc. RF and XGBoost are integrated models based on decision trees, which are good at dealing with nonlinear relationships. RF reduces overfitting, and XGBoost reduces errors. SVM is a linear classifier that is used by the kernel method to deal with nonlinear problems but has limited flexibility in time series prediction tasks. ARIMA is suitable for linear time series data. CNN is good at extracting local features, RNN is the basic model for time series modelling, LSTM deals with long-term dependencies, and GRU has fewer parameters and is computationally efficient. By comparing these eight models, the prediction results of different models are shown in Figure 10.

Comparative experiments and quantitative analysis were conducted to evaluate the performance of the model in ginger price prediction. The evaluation metrics and error comparisons are shown in

Table 3. Comparative experimental results.

Evaluation Metrics	AMP-PSO Optimised STL-LSTM-ATT-KAN	RF	SVM	XGBoost	CNN	RNN	LSTM	GRU
MAE	0.111	0.113	0.224	0.123	0.398	0.295	0.643	0.707
MSE	0.021	0.032	0.143	0.0409	0.268	0.1737	0.782	1.195
RMSE	0.146	0.181	0.378	0.202	0.518	0.416	0.884	1.093
R2	0.998	0.996	0.986	0.996	0.975	0.984	0.928	0.890

and Figure 11, respectively.

The MAE measures the mean absolute error between the predicted and true values. From Figure 11, the STL-LSTM-ATT-KAN model and the RF model have the smallest Mean Absolute Error (MAE) in prediction, showing that they have the least deviation from the true value. XGBoost also shows a low MAE, demonstrating the ability of these integrated learning models to capture trends and patterns in the data. In contrast, the ARIMA model has a high MAE, indicating that it performs poorly in capturing nonlinear features, leading to larger prediction errors.

The MSE not only reflects the magnitude of the prediction error but also weights the larger errors. From Figure 11, the STL-LSTM-ATT-KAN model has the lowest MSE, implying that the model not only has small errors but also exhibits better robustness and immunity to interference in the case of extreme values or outliers. This is due to its integrated model architecture of STL decomposition and attention mechanism, which can finely regulate the weights of different features to reduce large errors; the model effectively captures trends and seasonal variations in the time series and accurately identifies the key time points through the attention mechanism. The MSEs of RF and XGBoost are slightly higher, but the difference is not that big compared with STL-LSTM-ATT-KAN, which is not significant, indicating that they also have better performance in extreme error control.

RMSE, root mean square error, is the square root of MSE (mean square error), which provides a measure of error that is consistent with the scale of the original data. From Figure 11, the STL-LSTM-ATT-KAN model exhibits the lowest RMSE value in terms of processing complex time series data, which further confirms the high accuracy and consistency of the model. This suggests that the LSTM structure incorporating the attention mechanism is able to effectively capture the temporal and feature dependencies in time series data, thereby significantly reducing the overall error. Following closely behind, the RF (Random Forest) and XGBoost models also exhibit good performance, showing that their errors are relatively small and evenly distributed.

The R² metric is used to measure the model’s ability to explain changes in the data. From Figure 11, all models except the ARIMA model have high R² values, which indicates that they are able to effectively explain the variation in ginger prices. However, the STL-LSTM-ATT-KAN model not only maintains a high R² value but also significantly reduces the MAE, MSE, and RMSE, which indicates that the model demonstrates a significant advantage in terms of all-round performance when dealing with complex time series data.

3.3. Results of Ablation Experiments

The results in

Table 4. Effect of the number of ATT-KANs on STL-LSTM performance.

Evaluation Metrics	STL-LSTM-ATT-KAN	STL-LSTM(20)-ATT-KAN	STL-LSTM(75)-ATT-KAN	STL-LSTM(100)-ATT-KAN
MAE	0.111	0.129	0.181	0.139
MSE	0.021	0.026	0.044	0.030
RMSE	0.146	0.160	0.211	0.174
R2	0.998	0.997	0.995	0.997

show that the number of ATT-KAN has a significant impact on the performance of the STL-LSTM model: Too few (e.g., 20) or too many (e.g., 75, 100) ATT-KAN lead to performance degradation, while the baseline model (which may use the optimal number of ATT-KAN) performs best, suggesting that the number of ATT-KAN needs to be experimentally optimised to achieve optimal performance. The ablation analysis in

Table 5. STL-LSTM ablation analysis.

Evaluation Metrics	STL-LSTM-ATT-KAN	STL-LSTM-ATT	STL-LSTM	LSTM
MAE	0.111	0.113	0.124	0.643
MSE	0.021	0.019	0.023	0.782
RMSE	0.146	0.139	0.151	0.884
R2	0.998	0.998	0.997	0.928

also shows that STL and ATT are crucial for performance improvement, while KAN contributes little, but the complete model (STL-LSTM-ATT-KAN) has the best performance. In contrast, traditional LSTM performance deteriorates significantly when used alone, demonstrating that advanced features such as STL and ATT are essential for the task at hand. The evaluation indices show that the smaller the MAE, MSE and RMSE, the more accurate the model prediction. The closer R² is to 1, the better the model fit, and these metrics consistently validate the superior performance of the complete model on the task at hand.

Figure 12, the significant decrease in MAE, suggests that the STL-LSTM-ATT-KAN model significantly improves the prediction accuracy by incorporating the attention mechanism and the KAN network. In contrast, the STL-LSTM model that lacks the attention mechanism and KAN network leads to a significant increase in MAE, while the LSTM model that lacks the advantage of time series decomposition further exacerbates the prediction error.

The significant decrease in MSE reveals that the combination of the ATT and KAN networks not only improves forecasting accuracy but also strengthens the stability of the model, making it perform better in the face of abnormal volatility. Although the STL-LSTM model lacking ATT and KAN networks still retains the advantages of STL decomposition, it is still inferior to the full STL-LSTM model integrating ATT and KAN networks in terms of error control in complex scenarios. The LSTM model lacking STL decomposition, on the other hand, shows a higher error rate, which further proves the key role of STL in time series feature decomposition.

The significant reduction in RMSE further confirms the overall superiority of the STL-LSTM-ATT-KAN model in time series forecasting. The lower RMSE values indicate that the model is able to provide more accurate forecasts in most cases. Although the RMSE of the STL-LSTM model is lower than that of the standard LSTM model, its prediction results still suffer from a large error due to the lack of enhancement by the ATT and KAN networks. In contrast, the standard LSTM model is unable to decompose the time series efficiently, which leads to the poor stability of its prediction results.

The R² values indicate that both the STL-LSTM-ATT-KAN and STL-LSTM models can excellently elucidate the variance of ginger price fluctuations, which is mainly due to the STL decomposition technique and the LSTM network’s accurate capture of the long-term dependence of the time series. However, the R² value of the LSTM model is almost zero, which indicates that it is extremely weak in explaining the ginger price fluctuations without applying the time series decomposition, and the prediction effect is significantly reduced.

The STL-LSTM-ATT-KAN model performs optimally on the evaluation metrics with low MAE, MSE and RMSE values, showing its ability to reduce prediction errors. The achievement is attributed to the combination of STL decomposition and the attention mechanism, which improves the prediction accuracy. The increase in error after removing the attention mechanism emphasises its role in error reduction. The LSTM model, although fitting the data well, does not have as good a prediction accuracy as the STL-LSTM-ATT-KAN, confirming the enhancement of the model performance by the STL decomposition and the attention mechanism.

By applying the STL (Seasonal Trend Decomposition) technique to decompose the time series data, the model is able to handle the trend, seasonality, and residual components independently, which significantly reduces the forecast error. The Long Short-Term Memory Network (LSTM), with its superior ability to capture long-term dependencies in time-series data, enables the model to more accurately handle the long-term trend of ginger prices. Incorporating the attention mechanism in the model allows the model to focus more on key time points during the forecasting process, which improves the accuracy of the forecasts and further reduces errors. The integration of the KAN network integrates external knowledge sources, improves the generalisation ability of the model, and ensures the stability and reliability of the model when dealing with new data.

4. Discussion

The STL-LSTM-ATT-KAN ginger price prediction model proposed in this study shows significant advantages in prediction accuracy and stability. This result is due to the optimal design of the model structure and the efficient adjustment of parameters by the adaptive multi-population particle swarm optimisation (AMP-PSO) algorithm. AMP-PSO balances the global and local search ability through the multi-population strategy and the adaptive adjustment mechanism, which improves the efficiency of parameter optimisation and enhances the accuracy and stability of ginger price prediction.

However, the model has some limitations. The study covers the last ten years, and the data are more obviously affected by seasonal fluctuations, economic situations and policies. The current analysis is based on data availability and the typical cycle of ginger prices, and the performance of the model in other time horizons has not been adequately tested, and the generalisability has not been verified in a wider range of scenarios.

Future research proposes to improve the model in the following directions. The model will be applied to the price forecasting of other agricultural products, such as garlic, shallots, chillies and peppers, to assess its applicability and robustness. The dataset will be extended to more agricultural product types by introducing macroeconomic indicators (e.g., inflation rate, gross domestic product, trade-weighted exchange rate index, agricultural production costs, domestic diesel price) and climatic variables (e.g., rainfall, temperature, relative humidity, sunshine hours and frequency of extreme weather events) to capture the drivers of price fluctuations. The optimisation of data sources will improve accuracy and completeness and provide high-quality support to the model. The forecasting horizon will be extended from short-term fluctuations to long-term trends to test its adaptability over different business cycles. Improvements in algorithm design and parameter tuning methods are expected to enhance forecasting performance.

The practical value of the model will need to be validated through collaboration with agribusiness and government agencies, and it is expected to play a role in agricultural market monitoring, risk management, and policy formulation.

5. Conclusions

In the context of agricultural markets, price volatility carries significant ramifications for a range of stakeholders, including farmers, traders, consumers and policymakers. This is particularly evident in the case of agricultural products such as ginger, which are produced and consumed on a seasonal basis. Price uncertainty can result in market imbalances, fluctuations in farmers’ incomes and unpredictability in consumer spending. Consequently, the development of a model capable of accurately predicting ginger price fluctuations is imperative for enhancing market efficiency, stabilising farmers’ incomes, guiding consumer behaviour and facilitating policy formulation.

The objective of the present study is to enhance the precision and reliability of predictions by integrating seasonal decomposition, long- and short-term memory networks, attention mechanisms, and Kolmogorov-Arnold networks. The proposed STL-LSTM-ATT-KAN prediction model has been developed to address this need, with a focus on capturing seasonal fluctuations and long-term trends in ginger prices. The incorporation of an attention mechanism is a key innovation as it enables the identification of key factors affecting prices, thereby providing more reliable decision support for relevant stakeholders.

The model was constructed and validated in this study, and it was found to significantly improve the accuracy and stability of forecasting by accurately capturing the linkage effects among markets and the interactions between ginger production and macroeconomics. The introduction of the AMP-PSO algorithm further optimises the model parameters and enhances the performance of the model in complex time series forecasting. The experimental results demonstrate that the proposed model significantly outperforms alternative algorithms in terms of forecasting accuracy (MAE: 0.111, MSE: 0.021, RMSE: 0.146, R²: 0.998), thereby substantiating its efficacy in complex time series forecasting.

In addition, the model demonstrates considerable potential in the domains of agricultural market monitoring and risk early warning control, thereby providing substantial support for the stable operation of agricultural markets and the prosperous development of agricultural economies. Notwithstanding the positive outcomes achieved by this study, there is still scope for further enhancement and refinement. Future research directions include the following: the application of the model to a wider range of agricultural price forecasts to assess its generalisation ability; the addition of further influencing factors, such as climate change and policy adjustments, to capture the influences on price fluctuations more comprehensively; and the exploration of more efficient optimisation algorithms to reduce the computational complexity of the model. Expanding the model’s temporal range and incorporating macroeconomic indicators and seasonal data to assess its performance in long-term trend forecasting, and collaborating with agribusinesses and government departments to apply the model to real market monitoring and policy formulation to validate its application value in real-world scenarios.

Through these future endeavours, it is expected that the application scope of the model will be further validated and expanded, thereby providing more powerful support for agricultural market monitoring, risk early warning and control, and policy formulation.