Open AccessArticle

Research on Forecasting Sales of Pure Electric Vehicles in China Based on the Seasonal Autoregressive Integrated Moving Average–Gray Relational Analysis–Support Vector Regression Model

School of Economics and Management, Yanshan University, Qinhuangdao 066000, China

School of Vehicle and Energy, Yanshan University, Qinhuangdao 066004, China

Author to whom correspondence should be addressed.

Systems 2024, 12(11), 486; https://doi.org/10.3390/systems12110486

Submission received: 25 September 2024 / Revised: 4 November 2024 / Accepted: 11 November 2024 / Published: 13 November 2024

(This article belongs to the Topic Data-Driven Group Decision-Making)

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Figure 1
Article structure chart. "> Figure 2
SARIMA-SVR serial combined model. "> Figure 3
SARIMA-SVR parallel combined model. "> Figure 4
Principle diagram of the SVR model. "> Figure 5
Monthly sales of EVs in China. "> Figure 6
Monthly sales of EVs in China after first-order differencing. "> Figure 7
ACF plot of monthly sales of EVs in China. "> Figure 8
PACF plot of monthly sales of EVs in China. "> Figure 9
Sales forecast of EVs in China using the SARIMA model. "> Figure 10
Sales training plot of EVs in China using the GRA-SVR model. "> Figure 11
Sales forecast of EVs in China using the GRA-SVR model. "> Figure 12
Comparison of single model predictions and actual values. "> Figure 13
Sales forecast of EVs in China using the serial model. "> Figure 14
Sales forecast of EVs in China using the parallel combined model. ">

Versions Notes

Abstract

Aiming to address the complexity and challenges of predicting pure electric vehicle (EV) sales, this paper integrates a time series model, support vector machine and combined model to forecast EV sales in China. Firstly, a seasonal autoregressive integrated moving average (SARIMA) model was constructed using historical EV sales data, and the model was trained on sales statistics to obtain forecasting results. Secondly, variables that were highly correlated with sales were analyzed using gray relational analysis (GRA) and utilized as input parameters for the support vector regression (SVR) model, which was constructed to optimize sales predictions for EVs. Finally, a combined model incorporating different algorithms was verified against market sales data to explore the optimal sales prediction approach. The results indicate that the SARIMA-GRA-SVR model with the squared prediction error and inverse method achieved the best predictive performance, with MAPE, MAE and RMSE values of 12%, 1.45 and 2.08, respectively. This empirical study validates the effectiveness and superiority of the SARIMA-GRA-SVR model in forecasting EV sales.

Keywords:

pure electric vehicle; sales forecasting; combined model theory; seasonal autoregressive integrated moving average model; gray relational analysis; support vector regression model

1. Introduction

With the transformation of the global energy structure and the increasing awareness of environmental protection, EVs have experienced rapid development worldwide in recent years [1,2]. Particularly in China, driven by strong governmental support and the growing environmental consciousness among consumers, the market penetration of EVs has significantly increased. Data show that the EV sales surged from 409,000 units in 2016 to 6.657 million units in 2023, with the market share rising from 1.46% to 22.12%. China’s position in the global EV market has become increasingly prominent, with its sales accounting for over 60% of the global market in 2023, far exceeding the United States (approximately 10%) and Europe (approximately 20%). The Chinese government has implemented favorable policies, such as tax reductions and subsidies, which have substantially lowered the purchase costs for consumers and stimulated market demand [3,4]. Concurrently, technological advancements, particularly in battery, motor and charging technologies, have enhanced the driving range, charging efficiency and safety of EVs, further propelling market expansion. As zero-emission transportation options, EVs play a crucial role in reducing air pollution and mitigating greenhouse gas emissions, and their market demand is expected to continue growing [5,6]. The rapid development of China’s EV sales not only promotes the rise of the domestic EV industry but also alters the global EV market dynamics [7]. Through technological innovation, supply chain integration and policy guidance, China has continuously strengthened its influence in the global EV market, accelerated the global electrification process worldwide and provided strong support for the global goal of carbon neutrality [8]. With the international expansion of Chinese enterprises, the impact of China’s EV industry on the global market is expected to deepen further in the future [9]. However, the EV market remains in a phase of rapid development, influenced by factors such as macroeconomic conditions, policy directions and technological progress, which often exhibit complex nonlinear relationships, making sales forecasting highly challenging. Nonetheless, China’s position in the global EV market remains solid, consistently leading in terms of sales, technology, policy support and supply chain integration [10]. As the global market continues to expand, China will also face increasingly intense international competition. Therefore, accurately forecasting China’s EV sales is crucial for both companies and the government in formulating market strategies and optimizing resource allocation [11].

In the field of EV sales forecasting, despite the accumulation of predictive experiences related to traditional vehicle sales and the overall new energy vehicle market, both domestically and internationally, specialized research on the subcategory of EVs remains limited. Among the existing vehicle sales forecasting methods, the SARIMA model has demonstrated broad applicability due to its ability to comprehensively account for data trends, seasonal fluctuations and random disturbances, successfully uncovering the intrinsic patterns of sales dynamics. Researchers such as Gao [12], Ding [13], Chen [14] and Zhang [15] have proposed various forecasting models for new energy vehicle sales, including models based on structural relationship identification, SARIMA and Long Short-Term Memory (LSTM) hybrid models, ARIMA models as well as univariate and multivariate time series models. All of these approaches have shown strong performance in terms of forecasting accuracy and stability. Additionally, scholars have applied time series analysis to forecast sales in other industries, such as Li’s prediction of the CPI index [16], Li’s demand forecasting for pharmaceutical e-commerce platforms [17], Fantazzini’s forecast of automobile sales [18] and Nie’s prediction of GDP [19]. These studies have not only enriched the methodology of sales forecasting but also provided valuable support for market analysis and strategic planning by businesses.

However, given the complex and diverse factors influencing EV sales, relying solely on the SARIMA model may struggle to accurately capture the nonlinear and highly volatile characteristics of this market. To address this limitation, the SVR model has been introduced as a powerful supplementary tool. The SVR model achieves regression fitting for complex data patterns by constructing an optimal hyperplane, and its excellent nonlinear handling capability enables it to effectively address the complex variable relationships and uncertainties in EV sales forecasting, thus improving the model’s accuracy and robustness. Yao Jinhai successfully predicted stock market price fluctuations with high accuracy through the construction of a hybrid forecasting model that combines ARIMA with an information granulation-based SVR model [20]. Xu and others applied the SVR model to forecast the development potential of hydrogen fuel cell vehicles, improving prediction accuracy through parameter optimization [21]. Fan [22] and Liang [23] also utilized the SVR model to predict carbon market prices and short-term micro-tourism demand, both achieving promising results.

Sales data in the EV market may exhibit structural variations due to sudden policy shifts (such as tax adjustments or stricter environmental regulations) or technological innovations (such as breakthroughs in battery technology). Although advanced modeling techniques like LSTM and Artificial Neural Networks (ANNs) theoretically hold substantial potential, their practical application is limited by the need for large-scale datasets, showing limited advantages in environments with small or simple datasets [24]. Additionally, these models are complex, have extensive parameter distributions, require cumbersome training and involve challenging hyperparameter tuning. The interpretability and practical applicability of their predictions are also restricted, which hinders accurate forecasts for China’s EV sales. Thus, there is an urgent need to explore predictive methods that are effective with small datasets, highly interpretable and practically applicable to foster precise market forecasting and healthy development. Both the SARIMA and SVR models rely on historical data for modeling, making it challenging for a single model to quickly adapt to sudden changes, potentially distorting forecast accuracy. The SARIMA model excels at capturing linear and dynamic components in time series, while the SVR model is better suited to nonlinear relationships [25]. Since EV sales are influenced by various factors and may encompass linear, nonlinear, instantaneous and sporadic features, a single model cannot fully capture all patterns. Therefore, the SVR model and SARIMA model are combined to capture both linear and nonlinear characteristics in the data, so as to improve the prediction accuracy.

In addition, to address the challenges of data sparsity or varying quality in the forecasting process, GRA serves as a powerful tool for system analysis and decision support. It excels in revealing potential correlations and uncertainties among multiple factors under conditions of limited or low-quality data, providing a solid theoretical foundation for constructing and optimizing forecasting models. Tong and others developed a GRA method to analyze the correlation between multiple factors affecting new energy vehicle sales, offering a valuable tool for sales forecasting [26]. Yan and colleagues applied GRA to study the influencing factors of medical tourism development, identifying close relationships between medical conditions, tourism resources and tourism demand [27]. Xu utilized GRA to forecast new energy vehicle sales, achieving high prediction accuracy [28]. Therefore, incorporating GRA into the EV sales forecasting framework not only enhances the model’s adaptability to complex environments but also provides more scientific and comprehensive references for management decision-making.

In summary, the combined forecasting method incorporating SARIMA, SVR and GRA holds promise for improving prediction accuracy in the field of EV sales forecasting, thus providing strong support for industry planning, policy formulation and corporate strategy adjustments [29]. Accurate sales forecasting is particularly crucial for precise manufacturing and sales planning in the EV industry. On the one hand, accurate sales predictions enable automakers to minimize costs and time, optimize resources and enhance operational efficiency [30]. On the other hand, inaccurate forecasts may lead to negative consequences such as excess inventory, insufficient production supply, high labor costs and reputational damage [31,32]. Although previous studies have integrated different models, they have not fully combined influencing factors with the forecasting process. Therefore, this paper proposes a sales forecasting model based on SARIMA-GRA-SVR, aiming to improve the accuracy and reliability of EV sales forecasts in China.

In this study, we first conducted stationarity and seasonality tests on the time series data of EV sales. Based on the test results, a suitable SARIMA model was constructed to capture the time series characteristics and seasonal patterns of sales. The SARIMA model was trained using historical data to obtain preliminary sales forecasts. Next, GRA was employed to calculate the correlation between EV sales and various influencing factors. Based on the correlation results, the key factors affecting sales were identified, and those with a high correlation to sales were selected as input variables for the subsequent SVR model. Following this, an SVR model was constructed using the key influencing factors identified through GRA to predict EV sales, generating forecasts based on these influencing factors. Finally, the sales forecasts from the SARIMA model were combined with those from the GRA-SVR model in both serial and parallel configurations. The combined model was then evaluated using test set data, and based on the evaluation results, the model parameters were adjusted and optimized. The optimized model was applied to future real-world forecasting scenarios. A structural diagram of this paper’s contents is shown in Figure 1.

Based on the above research framework, this paper presents the following innovations:

(1): This paper innovatively utilizes GRA to select the key factors influencing EV sales as input variables for the SVR model, enhancing the model’s adaptability to complex market environments.
(2): A novel serial and parallel combination method of SARIMA and GRA-SVR models is proposed, integrating the forecasting strengths of different models and further improving the stability and accuracy of the prediction results.

2. Combined Model Theory

2.1. Data Sources

The data for this study are sourced from the China Association of Automobile Manufacturers, the China Electric Vehicle Charging Infrastructure Promotion Alliance, the National Bureau of Statistics, Qichacha, Huajing Intelligence Network, the Carbon Trading Network, the China Business Industry Research Institute and the Wind database. The sales data for EVs in China exhibit the following characteristics: consumers tend to be younger, the historical sales data span is relatively short and the volume of sales data is limited.

2.2. Combined Model Structure

In real-world time series, both linear and nonlinear information coexist. A combined forecasting dataset has a lower mean squared error than any single forecasting dataset [33]. Combined models are categorized into two types: parallel and serial.

2.2.1. Serial Combined Model Theory

A serial combined model divides the training data into linear and nonlinear components. Different models, each with distinct predictive strengths, are used to train these two parts separately. Finally, predictions from both models are combined to obtain the final forecast. Based on the principle of the serial combined model, this study assigns the linear part of the EV sales time series to the SARIMA model for forecasting, while the nonlinear part, or the residual, is predicted using the SVR model. The final forecast result is obtained by summing the two components (Figure 2).

2.2.2. Parallel Combined Model Theory

In a parallel combined model, weights are determined by calculating the prediction error of each individual model, and the weighted predictions are then aggregated to produce a final forecast that theoretically combines the strengths of multiple models for greater accuracy and robustness (Figure 3). The core of this approach is to reduce the bias and uncertainty that may arise from a single model by integrating multiple models, thereby enhancing prediction accuracy and reliability. In this study, the weights calculated from the error in the EV sales time series data are used to assign portions of the data to the SARIMA and SVR models, respectively. The final prediction of the parallel combined model is obtained by summing the results from both models. The specific calculation formula is as follows:

Y_{i} = v_{1} y_{i}^{1} + v_{2} y_{i}^{2}

(1)

In the above equation, v₁ and v₂ represent the weights of the SARIMA and SVR models, respectively, while y_i¹ and y_i² represent the prediction results of the SARIMA and SVR models, respectively.

Common methods for calculating weights include the simple weighting method, the reciprocal of the sum of squared prediction errors method, the reciprocal of the mean squared error method and the matrix advantage method [34].

(a): Simple Weighting Method: The simple weighting method improves upon the equal weighting approach. The calculation formula is as follows:

$v_{j} = \frac{j}{\sum_{j = 1}^{J} j} = \frac{2 j}{J (J + 1)}, j = 1, 2, \dots, J$

(2)

where v_j represents the weight of the j model, and J is the total number of models.

(b): Reciprocal of the Sum of Squared Prediction Errors Method: The sum of squared prediction errors quantifies the deviation between actual and predicted values and is inversely proportional to the model’s accuracy. The calculation formula is as follows:

$v_{j} = \frac{R_{j}^{- 1}}{\sum_{j = 1}^{J} R_{j}^{- 1}}, j = 1, 2, \dots, J$

(3)

where R_j⁻¹ is the reciprocal of the sum of squared prediction errors for the j model, and the formula for this is the following:

$R_{j}^{- 1} = \frac{1}{\sum_{t = 1}^{N} {(x_{t} - {\hat{x}}_{t} (j))}^{2}}, j = 1, 2, \dots, J$

(4)

(c): Reciprocal of the Mean Squared Error Method: This method is similar to the reciprocal of the sum of squared prediction errors, where the mean squared error of the model is inversely proportional to the weight. The calculation formula is as follows:

$v_{j} = \frac{R_{j}^{- \frac{1}{2}}}{\sum_{j = 1}^{J} R_{j}^{- \frac{1}{2}}}, j = 1, 2, \dots, J$

(5)

(d): Matrix Advantage Method: This method involves comparing the predicted values of the SARIMA model and the SVR model with actual values. The number of times each model’s predictions are more accurate is recorded: let n₁ denote the instances where the SARIMA model’s predictions are more accurate than those of the SVR model, and n₂ denote the instances where the SVR model outperforms the SARIMA model. The weights assigned to the two models in the combined model are then the following:

$v_{1} = \frac{n_{1}}{n_{1} + n_{2}}, v_{2} = \frac{n_{2}}{n_{1} + n_{2}}$

(6)

2.3. SARIMA Model

Due to the significant seasonal fluctuations in the EV sales in China and the suitability of the SARIMA model for forecasting time series data with distinct periodic or seasonal components, this study employed the SARIMA model to predict EV sales in China [35]. Defining the lag operator B, the specific expression for SARIMA (p, d, q) (P, D, Q, s) is as follows:

\{\begin{cases} ϕ_{(p)} (B) Φ_{(P)} (B^{s}) {(1 - B)}^{d} {(1 - B^{s})}^{D} y_{t} = c + θ_{(q)} (B) Θ_{(Q)} (B^{s}) ε_{t} \\ ϕ_{(p)} (B) = 1 - φ_{1} B - \dots - φ_{p} B^{p} \\ Φ_{(P)} (B^{S}) = 1 - φ_{1} B^{s} - \dots - φ_{p} {(B^{s})}^{p} \\ θ_{(q)} (B) = 1 - λ_{1} B - \dots - λ_{q} B^{q} \\ Θ_{(Q)} (B^{s}) = 1 - λ_{1} B^{S} - \dots - λ_{Q} {(B^{S})}^{Q} \end{cases}

(7)

where p is the non-seasonal autoregressive order; q is the non-seasonal moving average order; P is the seasonal autoregressive order; Q is the seasonal moving average order; ϕ_(P)(B) is the non-seasonal autoregressive characteristic polynomial; Φ_(P)(B^s) is the seasonal autoregressive polynomial; θ_(q)(B) is the non-seasonal moving average characteristic polynomial; Θ_(Q)(B^s) is the seasonal moving average characteristic polynomial; (1 − B)^d is the non-seasonal differencing operator; (1 − B^s)^D is the seasonal differencing operator, both of which transform the time series y_t into a stationary series; ε_t is white noise, normally distributed with a mean of 0 and constant variance; B^s is the seasonal lag operator; S is the period length; c is a constant; the subscript t denotes time; φ₁, φ₂,…, φ_p are the autoregressive coefficients; and λ₁, λ₂,…, λ_q are the moving average coefficients.

2.4. SVR Model

2.4.1. SVR Model Theory

Support vector machines (SVMs) are a type of machine learning model primarily used for data analysis in classification and regression tasks [36,37]. SVR is a specific application of SVMs designed for regression tasks. The principle of the SVR model is to identify a regression plane that minimizes the distance from all data points in the dataset to this plane (Figure 4). This study uses economic, policy and technological influencing factors, selected based on GRA, as the sample set. The SVR model is then used to forecast EV sales, resulting in sales predictions based on these influencing factors.

For a given training sample set U = {(x₁, y₁), (x₂, y₂), …, (x_m, y_m)}, it is necessary to find a regression model f(x) = w^Tx + b such that f(x) is as close as possible to y. Here, w is the normal vector of the decision plane, determining its direction, and b determines the position of the decision plane. Let the error be ε, and consider an error interval centered at f(x) with width 2ε. The optimization problem for the SVR model is then as follows:

\begin{array}{l} \min_{_{w, b}} \frac{{‖w‖}^{2}}{2} + C \sum_{i = 1}^{m} l_{ε} (f (x_{i}) - y_{i}) \\ l_{ε} (f (x_{i}) - y_{i}) = \{\begin{cases} 0, i f |f (x_{i}) - y_{i}| \leq ε \\ |f (x_{i}) - y_{i}| - ε, o t h e r w i s e \end{cases} \end{array}

(8)

where C is a constant greater than 0, serving as the penalty parameter, and

l_{ε}

is the ε’s insensitive loss function.

By solving this, the optimal solution to the primal problem is obtained, as follows:

w = \sum_{i = 1}^{m} (α_{i} - {\hat{α}}_{i}) ϕ (x_{i})

Introduce the kernel function:

K (x_{i}, x_{j}) = ϕ {(x_{i})}^{T} ϕ (x_{j})

. Among them, the Gaussian kernel function

K (x_{i}, x_{j}) = e^{- \frac{{‖x_{i} - x_{j}‖}^{2}}{2 σ^{2}}}

is the most commonly used [38]. The final SVR model is as shown here:

f (x) = \sum_{i = 1}^{m} (α_{i} - {\hat{α}}_{i}) ϕ {(x_{i})}^{T} ϕ (x_{j}) + b

(9)

2.4.2. SVR Parameter Optimization

For SVR model, this paper employs K-fold cross-validation. This method first splits the dataset into K subsets, using K − 1 subsets for training and 1 subset for validating model accuracy. During cross-validation, the validation process is performed K times, and a single estimate is produced by aggregating the results from each validation [39].

2.5. Variable Selection

2.5.1. SARIMA Model Variable Selection

The data in this section were sourced from the official website of the China Association of Automobile Manufacturers, covering the period from January 2016 to December 2023, encompassing a total 96 data points (Table 1). The 12 months after January 2023 are designated as the test sample, while the remaining data serve as the training sample.

2.5.2. SVR Model Variable Selection

Based on the key influencing factors of the EV sales in China identified through GRA [40], an SVR model was constructed to predict the sales using these factors.

(1): GRA Theory

The GRA method describes the relationships among various factors and measures the degree of association between them [41]. Its advantages include low sample size requirements, no need for regularity in the sample, a small computational load, and results that align with qualitative analysis—making it suitable for the current small data volume of EVs. The steps involved are as follows:

(a): Identify the reference sequence and the characteristic sequence. The reference sequence reflects the system’s characteristics and is denoted as x₀ = (x₀(1), x₀(2), …, x₀(n)); the characteristic sequence consists of factors affecting the system’s behavior and is represented in matrix form as follows:

{(x_{0}, x_{1}, \dots, x_{k})}^{T} = (\begin{matrix} x {}_{0}{(1)} & x {}_{1}{(1)} & \dots & x {}_{k}{(1)} \\ x {}_{0}{(2)} & x {}_{1}{(2)} & \dots & x {}_{k}{(2)} \\ ⋮ \\ x {}_{0}{(n)} & x {}_{1}{(n)} & \dots & x {}_{k}{(n)} \end{matrix})

(10)

where k is the number of influencing factors, and i is the number of data points.

(b): Data preprocessing. To eliminate the impact of dimensionality, the data must be normalized. This paper uses the mean normalization method, which is as follows:

x_{i}^{'} = {(x_{i}^{'} (1), x_{i}^{'} (2), \dots, x_{i}^{'} (n))}^{T} = {(\frac{x_{i} (1)}{{\bar{x}}_{i}}, \frac{x_{i} (2)}{{\bar{x}}_{i}}, \dots, \frac{x_{i} (n)}{{\bar{x}}_{i}})}^{T}, i = 1, 2, \dots, k

(11)

where

{\bar{x}}_{i}

is the mean value of the i-th influencing factor, expressed as follows:

{\bar{x}}_{i} = \frac{\sum_{h = 1}^{n} x_{i} (h)}{n}, i = 1, 2, \dots, k

(12)

(c): Calculate the gray relational coefficients. For a reference sequence x₀ with k comparison sequences (x₁, x₂, …, x_k)^T, the gray relational coefficient between each comparison sequence and the reference sequence at each time point can be calculated using the following formulas:

Δ_{i} (h) = |x_{0} (h) - x_{i} (h)|, i = 1, 2, \dots, k, h = 1, 2, \dots, n

(13)

m = \min_{i} \min_{j} Δ_{i} (h), i = 1, 2, \dots, k, h = 1, 2, \dots, n

(14)

M = \max_{i} \max_{h} Δ_{i} (h), i = 1, 2, \dots, k, h = 1, 2, \dots, n

(15)

ξ_{i} (h) = \frac{m + ρ M}{Δ_{i} (h) + ρ M}, i = 1, 2, \dots, k, h = 1, 2, \dots, n

(16)

where ρ is the distinguishing coefficient, which is generally set as [0,1].

(d): Calculate the gray relational degree. According to the above formula, the value of γ ranges from 1 to γ. Each factor thus has γ gray relational coefficients with the reference sequence. To assess the overall association of a factor with the reference sequence, it is difficult to measure each of these γ coefficients individually. Therefore, the arithmetic mean of these γ gray relational coefficients is calculated, which represents the gray relational degree:

γ_{i} = \frac{1}{n} \sum_{k = 1}^{n} ξ_{i (k)}, i = 1, 2, \dots, k, h = 1, 2, \dots n

(17)

(e): Gray relational degree ranking. Perform a ranking analysis on the k calculated gray relational degrees and select the desired indicator features.

(2): Specific Variable Selection

As of 22 October 2023, a total of 688 companies in the new energy vehicle sector were identified on the Royal Flush network financial station. This sector includes five main categories: complete vehicle manufacturing, components, battery power, electric motors and charging piles. To ensure the validity of the empirical results, further screening was performed using the Wind database, excluding data from companies with ST or ST* stock codes. Ultimately, data from A-share listed companies in EV manufacturing from 2016 to 2023 were selected, resulting in a sample of 20 companies (Table 2). Among these, tax refunds refer to the amount disclosed in the cash flow statement of the company’s annual report, government subsidies are the government grants included in the current period’s profit and loss, and automotive R&D expenses are the reported R&D investment data in the company’s annual report [42,43].

Through a comprehensive analysis of the factors influencing the sales of EV in China, and considering the availability of data, this paper will examine 14 variables from three perspectives: policy, economic and technological aspects, as potential determinants of annual EV sales. The descriptions of these variables are shown in Table 3.

2.6. Model Evaluation

In the forecasting of EV sales, commonly used accuracy evaluation metrics include Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE), each reflecting the model’s performance under different types of errors [44].

The determination of forecasting errors is complex and variable, influenced by the purpose of the forecast, industry standards and market uncertainties. The forecasting context, market volatility and decision-making requirements dictate varying tolerance levels for errors: short-term decisions typically require MAPE to be controlled within 5% to 10%, whereas in long-term strategic planning and under high uncertainty conditions, the tolerance range for MAPE can be relaxed to 15% to 30%. The priority of different evaluation metrics depends on the forecasting application scenario: RMSE is sensitive to large deviations and is suitable for situations where significant impacts from large deviations are critical for decision-making, such as inventory overstock or sales losses; MAE reflects the average difference between predicted and actual values, making it appropriate for tasks that demand high overall accuracy and consistency; MAPE is used to assess relative errors and can effectively reflect nonlinear market changes, generally considered reasonable within the range of 5% to 20%, although this must be judged in conjunction with the forecasting time span and market volatility.

This study selected the scenario of short-term sales forecasting for China’s EVs, aiming for the minimum MAPE while also achieving the smallest values for MAE and RMSE. The calculation formulas are as follows:

RMSE = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} {({\hat{y}}_{i} - y_{i})}^{2}}

(18)

MAE = \frac{1}{n} \sum_{i = 1}^{n} |{\hat{y}}_{i} - y_{i}|

(19)

MAPE = \frac{1}{n} \sum_{i = 1}^{n} |\frac{{\hat{y}}_{i} - y_{i}}{y_{i}}|

(20)

y_i represents the actual value, and

{\hat{y}}_{i}

represents the predicted value.

3. Results

3.1. Sales Forecast Results Based on SARIMA Model

Before modeling and forecasting sales using SARIMA, a time series plot of the sales of EVs in China from January 2016 to December 2023 was created to illustrate the development trend, as shown in Figure 5.

In this section, data from the first 7 years, totaling 84 months (from January 2016 to December 2022), were selected as training data for the SARIMA model. The monthly sales data of EVs in China exhibit an increasing trend, indicating that the series is non-stationary. Therefore, a first-order differencing was applied, as shown in Figure 6, where the differenced time series fluctuates around a mean of zero without changing over time. Figure 7 and Figure 8 display the autocorrelation plot and partial autocorrelation plot of the first-differenced data series, respectively. The autocorrelation plot shows that the lag-1 autocorrelation value does not exceed the boundary, while the partial autocorrelation plot indicates a significant non-zero value at lag-1, confirming that the series is stationary.

Based on the initial assessment of the order using the autocorrelation and partial autocorrelation plots, and after verification by comparing adjacent orders within the determined p, d, q range, the optimal model identified was SARIMA (3,1,3) (3,1,0)¹². The fitting results are presented in Table 4. The residual sequence passed the white noise test, indicating that the model fits well. The prediction results are shown in Figure 9 and Table 5, forecasting that the monthly sales of EVs will exhibit seasonal fluctuations over the next year, reaching 884,500 units by the end of the year. The accuracy evaluation shows that the RMSE is 5.92, MAE is 3.54, and MAPE is 22%, indicating that the prediction results exhibit a certain level of accuracy. However, the potential sources of bias may stem from the SARIMA model’s assumption that EV sales can be predicted through linear trends based on historical data. When factors such as changes in government subsidy policies or advancements in battery technology trigger nonlinear fluctuations in sales, SARIMA struggles to effectively capture these complex relationships, resulting in prediction errors.

3.2. GRA Results

The influencing factors for EVs in China are all continuous time series, and there is a complex interplay among these factors. Based on the data from the 14 influencing factors, the parameter setting results are shown in Table 6. This study selects the annual sales of EVs in China as the reference series x₀, with 14 representative factors (listed in Table 7) designated as comparison series x₁ − x₁₄, applying a normalization method for dimensionless processing. The gray relational degrees between each factor and sales are calculated according to Formula 16, as shown in Table 8. The goal is to identify the factors that closely align with the development trend of EVs, in order to analyze their impact on the growth trajectory of EVs.

As shown in Table 9, the correlation coefficients for the selected factors are all above 0.5, indicating a medium to high degree of correlation with the development of EVs. Among these factors, six have a gray relational degree greater than 0.6, ranked as follows: battery installation volume (x₁₁) > number of registered EV-related enterprises (x₁₄) > number of charging piles (x₃) > tax refunds (x₁) > cumulative number of registered battery recycling enterprises (x₁₂) > carbon trading prices (x₈). This indicates that these six factors significantly influence EV sales in China.

3.3. Sales Forecast Results Based on the GRA-SVR Model

The data used for the SVR model consist of the monthly data (from January 2016 to December 2022) for the six important factors identified through the gray relational degree analysis. Missing data were handled using the averaging method. The parameter ranges were set as follows: cost in the range of [2⁻⁵,2¹⁵], and ε in the range of [0,1], with a step size of 0.01. Additionally, a Gaussian radial basis function kernel was employed, with the kernel parameter set to radial. After multiple experiments using MATLAB 2022b, we determined that the penalty parameter C is 90.5097, the gamma value g is 0.0156 and the error term ε is 1.0000 × 10⁻⁴, as shown in Table 10.

The SVR model was trained using the first 84 sample data points, yielding fitting results (Table 11) with an RMSE of 2.86, MAE of 1.79 and MAPE of 13%, indicating a good fit. The training set is illustrated in Figure 10, where the fitted data closely match the actual monthly sales data, further validating the model’s fitting effectiveness. The SVR model’s fitting results consistently outperform those of the SARIMA model, indicating a superior prediction accuracy. This result also reflects that the sales data of EVs are influenced by multiple factors, which exhibit complex nonlinear relationships. From a policy-driven perspective, sudden changes in government subsidy policies or vehicle purchase taxes can lead to dramatic increases or decreases in sales, which are difficult to capture using linear models. In terms of technological advancements, breakthroughs in battery technology and charging infrastructure significantly influence consumer decisions and consequently the market. These technological advancements and the degree of market acceptance exhibit nonlinear trends, making it challenging for traditional linear models to accurately describe them. Regarding consumer behavior, with the increasing or shifting awareness of environmental issues, purchasing intentions may also experience nonlinear fluctuations. Therefore, the GRA-SVR model, by using GRA to select key factors closely related to sales and then applying the SVR model for nonlinear modeling, can better capture the complex nonlinear patterns in sales data compared to the SARIMA model. Finally, the SVR model’s sales forecast for January to December 2023 is presented in Figure 11 and Table 12, indicating that the monthly sales of EVs in China could reach a maximum of 809,200 units during this period.

3.4. Sales Forecast Results Based on the SARIMA-GRA-SVR Model

The comparison of monthly sales forecasts for EVs in China using the two single models is shown in Figure 12. The GRA-SVR model better captures the periodicity of the data compared to the SARIMA model, with its predictions being closer to the actual values. To further explore the development trend of EVs in China, both the serial and parallel combinations of the SARIMA and GRA-SVR models were employed to analyze the monthly sales data.

3.4.1. Forecast Results of the SARIMA-GRA-SVR Serial Combined Model

In this section, the linear component of the EV sales time series is predicted using the SARIMA model, while the nonlinear component, i.e., the residual part, is predicted using the SVR model. The final prediction results are obtained by summing the predictions from both models. In this simulation, the nonlinear component consists of the residual series of monthly EV sales in China predicted by the SARIMA (3,1,3) (3,1,0)¹² model, which is then trained using the SVR model. The parameter ranges were set as follows: cost in the range of [2⁻⁵,2¹⁵], and ε in the range of [0,1], with a step size of 0.01. A Gaussian radial basis function kernel was used, with the kernel parameter set to radial. After multiple simulation experiments with MATLAB 2022b, the model parameters were C = 0.0221, g = 11.3137 and ε = 1.0000 × 10⁰. The predicted residual series was then summed with the forecast results from the SARIMA model to obtain the prediction results of the serial model, as shown in Figure 13.

Based on the serial model’s predictions, the monthly sales forecast of EVs in China for January to December 2023 is shown in Figure 13 and Table 13. There is some deviation between the predicted and actual values. The results in Table 14 indicate that the fitting results of the serial model are higher than those of the GRA-SVR model, suggesting that the model’s prediction accuracy is insufficient. This also demonstrates that the serial model is not feasible for forecasting the EV sales in China.

3.4.2. Forecast Results of the SARIMA-GRA-SVR Parallel Combined Model

Here, the SARIMA-GRA-SVR parallel combined model was employed for forecasting EV sales. First, the weight values of the four parallel methods for each model were determined, as shown in Table 15. These results were then applied to the forecast outcomes of the SARIMA and SVR models, allowing for the calculation of the prediction results for each parallel model.

Figure 14 illustrates the fitting results of the parallel model for the EV sales in China from February 2017 to December 2023. The black line represents the original sales data, while the other lines represent the sales forecasts from each parallel model. According to Figure 14 and Table 16, the parallel models using the advantage matrix method and the simple weighting method exhibit significant deviation from the actual values, indicating a poor fit for these methods. In contrast, the parallel combined models using the prediction error sum of squares inverse method and the mean square inverse method fit the original data better and demonstrate improved accuracy compared to the single models.

4. Discussion

This chapter will discuss the prediction results in detail. Through a comparison of model performance (Table 16), the optimal forecasting scheme for EV sales was established. RMSE, MAE and MAPE are used as metrics, leading to the conclusion that model ⑦ performs the worst, while model ⑤ (MAPE = 12%, MAE = 1.45, RMSE = 2.08) exhibits the best fitting results. Table 17 presents the monthly sales forecast data for EVs in China for 2023.

When comparing the goodness of fit of model ⑤ with other models, the following results were obtained: MAPE improved by 45.45% compared to model ① (MAPE = 22%, MAE = 3.54, RMSE = 5.92), while MAE and RMSE decreased by 59% and 64.86%, respectively; compared to model ② (MAPE = 13%, MAE = 1.79, RMSE = 2.86), MAPE improved by 7.7%, and MAE and RMSE decreased by 18.99% and 27.27%; MAPE improved by 42.86% compared to model ③ (MAPE = 21%, MAE = 3.44, RMSE = 5.89), with MAE and RMSE decreasing by 57.85% and 64.69%, respectively; MAPE improved by 29.41% compared to model ④ (MAPE = 17%, MAE = 2.67, RMSE = 4.48), while MAE and RMSE decreased by 45.69% and 53.57%; MAPE remains the same as model ⑥ (MAPE = 12%, MAE = 1.56, RMSE = 2.37), with MAE and RMSE decreasing by 7.05% and 12.24%; MAPE improved by 78.57% compared to model ⑦ (MAPE = 56%, MAE = 6.55, RMSE = 8.41), while MAE and RMSE decreased by 77.86% and 75.27%, respectively. Actual data validation showed that the prediction error squared reciprocal method SARIMA-GRA-SVR parallel combined model (model ⑤) demonstrates high accuracy in forecasting monthly sales of EVs, accurately depicting seasonal fluctuations and development trends in sales, providing industry participants with a more solid data support and decision-making basis.

In summary, the prediction error squared reciprocal method parallel combined model has the highest accuracy in short-term forecasting. However, due to the complexity of factors influencing EV sales, along with the high nonlinearity and unpredictability, the model struggles to accurately capture market dynamics. Factors that may affect forecasting accuracy include the following: (1) Policy changes: Government subsidy policies are crucial in driving EV sales. Changes in policies can cause fluctuations in market sales, leading to forecasting deviations. Therefore, it is necessary to adjust the model promptly, incorporate external variables, and closely monitor policy changes. (2) Macroeconomic factors: A gradually recovering economy will bolster consumer purchasing power and confidence, promoting demand for EVs. Although macroeconomic changes and sudden events may not yield certainty, companies are thus more proactive in risk management and market research on hoe to adapt to new environments. (3) Technological advancements: Breakthroughs in battery technology, cost reductions or improved charging speeds can greatly enhance consumer purchasing willingness, potentially leading to sales exceeding expectations. The rapid development of charging infrastructure can also alleviate consumer concerns about charging convenience, driving sales growth. (4) Global supply chain risks: EVs rely on global supply chains, and any disruptions in the supply of critical raw materials or chips can affect production and sales. Fluctuations in the global supply chain may lead to insufficient market supply, resulting in sales falling short of predictions, and models often struggle to fully account for the impact of such unforeseen events. (5) International market uncertainties: Changes in international oil prices, geopolitical factors and trade policies significantly affect EV sales. In summary, the forecasting of the EV market faces multiple complex external risks, and the model should be flexibly adjusted to respond to these nonlinear and unpredictable factors.

5. Conclusions

5.1. Main Conclusions

This study explored the development trajectory of monthly EV sales in China by comprehensively applying market data, enhancing time series analysis and utilizing support vector machines. It systematically assessed the advantages and limitations of each theoretical framework and constructed a hybrid forecasting model using both serial and parallel combinations. This model analyzed the dynamic changes in monthly EV sales in China from January 2016 to December 2022 to forecast monthly sales for January to December 2023.

Firstly, the SARIMA model was developed to analyze the temporal dependencies and seasonality within the sales data, yielding initial forecasts based on historical training data. Secondly, GRA was introduced to analyze multidimensional factors affecting EV sales, identifying key influencing factors for input into the SVR model to enhance prediction accuracy. Subsequently, a serial and parallel strategy effectively integrated the time series forecasting strengths of the SARIMA model with the nonlinear forecasting capabilities of the SVR model, creating a complementary forecasting system. Finally, the prediction model’s accuracy was verified through actual data, demonstrating its feasibility and providing industry participants with a robust data foundation for decision-making.

5.2. Recommendations

(1): The forecast results indicate that the EV market is expected to continue robust growth in the near future, although the growth rate may stabilize as market maturity increases. This insight is crucial for guiding corporate strategic planning, optimizing production layouts, and formulating government policies.
(2): Infrastructural Investment: The government should continue to increase investment in infrastructure, particularly charging facilities for EVs, to meet the growing market demand. As the growth rate of EV sales stabilizes, the government may consider adjusting incentive policies, such as purchase subsidies and tax benefits, to maintain market vitality.

Corporate Strategy: Companies should invest in research and development in the field of EV technology, enhancing product quality and performance to meet consumer demands for high-quality products. Based on the forecast results, companies should strategically position themselves in the market and develop targeted marketing strategies to adapt to market changes.

6. Future Outlook

6.1. Limitations

The SARIMA-GRA-SVR model performs well in short-term forecasting; however, its predictive accuracy may decline for long-term forecasts. This is because the model for predicting EV sales in China heavily relies on past time series and historical data. Additionally, external factors (such as policies, economic fluctuations and technological advancements) exhibit high nonlinearity and unpredictability, making it difficult for the prediction model to accurately capture real market changes, which leads to poor long-term forecasting performance. Therefore, to reduce forecasting gaps, the model must be continuously adjusted and more external variables introduced, while maintaining close monitoring of policies, technologies and market trends. Separating long-term and short-term forecasts is advisable; the SARIMA-GRA-SVR combined model can continue to be used for short-term predictions, while long-term forecasting could utilize scenario simulation or expert system models to address the complexity of the external environment.

6.2. Future Studies

In order to further enhance the predictive performance of the model and address its inertia, complexity regarding external factors and deficiencies in long-term forecasting capabilities, future research will focus on the following three aspects:

(1): Model Optimization: By introducing dynamic external parameters, regularization techniques, model simplification and hybrid architectures, we can improve the predictive accuracy and robustness of the model.
(2): Integration of Multisource Data: Combining data from internet big data and industry planning with the forecasting model can enhance the accuracy and timeliness of EV sales predictions.
(3): Long-term Forecasting: Building on short-term and medium-term forecasts and exploring methods and technologies for long-term trend prediction will provide strong support for the sustainable development of the EV industry.

In summary, the SARIMA-GRA-SVR parallel combined model has demonstrated significant advantages and potential in predicting EV sales, providing valuable support for government decision-making and corporate strategic planning. With continued optimization of the model and advancements in multisource data integration technology, this model is expected to play an increasingly important role in the EV industry.

Author Contributions

Conceptualization, R.Y. and X.W.; methodology, X.X.; software, R.Y.; validation, X.W.; investigation, R.Y. and X.X.; resources, X.X. and X.W.; writing—original draft preparation, R.Y.; writing—review and editing, R.Y. and Z.Z.; supervision, X.X.; project administration, X.X.; funding acquisition, R.Y. and X.W. All authors have read and agreed to the published version of the manuscript.

Funding

This study was supported by the Hebei Provincial Higher Education Science and Technology Research Fund Project “Research on Industrial Carbon Emission Pathways in the Beijing Tianjin Hebei Region under the Background of Digital Economy” (Grant No. QN2023213).

Data Availability Statement

The original contributions presented in this study are included in the article.

Acknowledgments

The authors would like to thank the editor and anonymous reviewers for their patient and valuable comments on this paper.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Article structure chart.

Figure 2. SARIMA-SVR serial combined model.

Figure 3. SARIMA-SVR parallel combined model.

Figure 4. Principle diagram of the SVR model.

Figure 5. Monthly sales of EVs in China.

Figure 6. Monthly sales of EVs in China after first-order differencing.

Figure 7. ACF plot of monthly sales of EVs in China.

Figure 8. PACF plot of monthly sales of EVs in China.

Figure 9. Sales forecast of EVs in China using the SARIMA model.

Figure 10. Sales training plot of EVs in China using the GRA-SVR model.

Figure 11. Sales forecast of EVs in China using the GRA-SVR model.

Figure 12. Comparison of single model predictions and actual values.

Figure 13. Sales forecast of EVs in China using the serial model.

Figure 14. Sales forecast of EVs in China using the parallel combined model.

Table 1. Monthly sales of EVs from 2016 to 2023 in China (10 t.h.s unit).

Time	2016	2017	2018	2019	2020	2021	2022	2023
January	0.78	0.50	2.68	7.49	3.30	15.00	34.10	28.70
February	1.72	1.39	2.35	3.97	1.07	9.20	25.80	37.60
March	1.8	2.54	5.22	9.60	4.00	19.00	39.50	49.00
April	2.4	2.86	6.48	7.10	5.10	17.10	23.10	47.10
May	2.6	3.85	8.20	8.32	6.40	17.90	34.70	52.20
June	3.4	4.80	6.30	12.91	8.20	21.20	47.60	57.30
July	2.6	4.40	6.00	6.10	7.80	22.00	45.70	54.10
August	2.8	5.60	7.32	6.90	8.80	26.50	52.20	59.70
September	3.5	6.40	9.42	6.30	11.20	29.70	53.90	62.70
October	3.9	7.70	11.12	5.90	13.30	31.60	54.10	64.60
November	5.8	10.59	13.81	8.10	16.70	36.10	61.50	70.20
December	9.3	14.40	19.30	14.03	21.10	44.80	62.40	82.50
Total	40.9	65.03	98.20	96.72	106.97	290.10	534.60	665.70

Table 2. Data on A-share listed companies manufacturing EVs.

Stock Abbreviation	Stock Code	Listing Date	Stock Abbreviation	Stock Code	Listing Date
Ankai Bus	000868	25 July 1997	FAW Jiefang	000800	18 June 1997
BAIC BluePark	600733	16 August 1996	Yutong Bus	600066	08 May 1997
BYD	002594	03 June 2011	Hanma Technology	600375	10 April 2003
Dongfeng Motor	600006	27 July 1997	JAC Motors	600418	24 August 2001
GAC Group	601238	09 March 2012	JMC	000550	01 December 1993
Haima Automobile	000572	08 August 1994	King Long Bus	600686	08 November 1993
Lifan Technology	601777	25 November 2010	Changan Automobile	000625	10 June 1997
Seres	601127	15 June 2016	Great Wall Motor	601633	28 September 2011
SAIC Motor	600104	25 November 1997	Zhongtong Bus	000957	13 January 2000
Yaxing Bus	600213	31 August 1999	Foton Motor	600166	02 June 1998

Table 3. Factors influencing the sales of EVs.

Primary Indicators	Secondary Indicators	Tertiary Indicators
Factors Influencing the Sales of EV	Policy Factors	x₁	Tax Refunds/100 million RMB
		x₂	Government Subsidies/100 million RMB
		x₃	Number of Charging Piles/10,000 Units
	Economic Factors	x₄	Per Capita GDP/10,000 RMB
		x₅	Consumer Price Index (1978 = 100)
		x₆	Per Capita Disposable Income of Urban Residents/10,000 RMB
		x₇	Per Capita Disposable Income of Rural Residents/10,000 RMB
		x₈	Carbon Trading Price/RMB
		x₉	Crude Oil Production/10,000 Tons
	Technological Factors	x₁₀	Automobile R&D Expenditure/100 million RMB
		x₁₁	Installed Capacity of Power Batteries/GWh
		x₁₂	Cumulative Registered Battery Recycling Companies/10,000 Companies
		x₁₃	Traditional Automobile Sales/10,000 Units
		x₁₄	Registered EV-Related Companies/10,000 Companies

Table 4. Fitting results of the SARIMA model parameters.

Prediction Accuracy	RMSE	MAE	MAPE	Normalized BIC
Value	5.92	3.54	22%	2.9

Table 5. SARIMA model forecast results for January–December 2023 (10 t.h.s unit).

Month	Month	January	February	March	April	May	June	July	August	September	October	November
Value	54.91	49.51	58.07	48.45	58.13	67.17	70.78	74.48	77.29	81.11	85.53	88.45

Table 6. Parameter settings.

Parameters	m	M	$ρ$
Value	0.0044	1.7341	0.5

Table 7. Influencing factors of EV sales.

	2016	2017	2018	2019	2020	2021	2022	2023
Factor	2016	2017	2018	2019	2020	2021	2022	2023
x₁	52.69	59.26	97.92	106.39	140.22	142.71	383.23	465.06
x₂	75.68	89.30	137.22	155.43	118.09	152.37	149.70	149.60
x₃	20.40	44.60	77.70	121.90	168.10	261.70	521.00	859.60
x₄	5.38	5.96	6.55	7.01	7.18	8.14	8.57	8.94
x₅	1783.20	1901.70	2041.90	2166.00	2111.90	2352.80	2374.10	2586.50
x₆	3.36	3.64	3.93	4.24	4.38	4.74	4.93	5.18
x₇	1.24	1.34	1.46	1.60	1.71	1.89	2.01	2.17
x₈	16.33	17.52	19.42	22.61	29.19	42.80	55.30	68.13
x₉	19,969.00	19,150.61	18,932.42	19,162.83	19,476.86	19,888.10	20,472.20	20,900.00
x₁₀	354.46	398.50	481.03	517.61	532.67	666.87	828.73	1107.48
x₁₁	28.20	36.24	56.90	62.20	64.00	154.50	294.60	387.70
x₁₂	743.00	1096.00	1331.00	3737.00	5925.00	26,839.00	43,097.00	45,949.00
x₁₃	2437.69	2471.83	2370.98	2144.40	2017.80	2148.20	2356.30	3009.40
x₁₄	2.31	2.99	4.36	4.70	8.18	17.75	24.69	30.93

Table 8. Correlation coefficients of influencing factors for EV sales.

	2016	2017	2018	2019	2020	2021	2022	2023
Factor	2016	2017	2018	2019	2020	2021	2022	2023
x₁	0.8793	0.9416	0.8716	0.8286	0.7394	0.6673	0.8679	0.7967
x₂	0.6760	0.6738	0.5706	0.5206	0.6586	0.9595	0.4454	0.3487
x₃	0.9036	0.8956	0.8850	0.9334	0.8285	0.8026	0.7827	0.6256
x₄	0.6030	0.6121	0.6376	0.6073	0.6228	0.9012	0.4505	0.3593
x₅	0.5720	0.5903	0.6216	0.5952	0.6318	0.8647	0.4303	0.3529
x₆	0.5882	0.6033	0.6354	0.6015	0.6123	0.8785	0.4411	0.3544
x₇	0.6068	0.6234	0.6556	0.6146	0.6120	0.9010	0.4532	0.3674
x₈	0.7377	0.7819	0.8449	0.7709	0.6892	0.9574	0.5843	0.5265
x₉	0.5093	0.5558	0.6148	0.6076	0.6269	0.8014	0.4179	0.3345
x₁₀	0.6808	0.6970	0.6994	0.6648	0.6832	0.8687	0.4936	0.4707
x₁₁	0.9598	0.9930	0.9920	0.9446	0.9949	0.9126	0.9187	0.9279
x₁₂	0.8742	0.8093	0.7253	0.8324	0.8975	0.6621	0.6707	0.9324
x₁₃	0.5041	0.5310	0.5972	0.6367	0.6943	0.7335	0.4096	0.3640
x₁₄	0.9764	0.9731	0.9466	0.9823	0.8024	0.7721	0.8201	0.8038

Table 9. Gray relational degree of influencing factors for EV sales.

Influencing Factor	Relational Degree	Influencing Factor	Relational Degree
Tax Refunds (x₁)	0.7245	Carbon Trading Price (x₈)	0.6708
Government Subsidies (x₂)	0.5631	Crude Oil Production (x₉)	0.5167
Number of Charging Piles (x₃)	0.7539	Automobile R&D Expenditure (x₁₀)	0.5984
Per Capita GDP (x₄)	0.5543	Installed Capacity of Power Batteries (x₁₁)	0.8395
Consumer Price Index (1978 = 100) (x₅)	0.5382	Cumulative Registered Battery Recycling Companies (x₁₂)	0.6839
Per Capita Disposable Income of Urban Residents (x₆)	0.5450	Traditional Automobile Sales (x₁₃)	0.5133
Per Capita Disposable Income of Rural Residents (x₇)	0.5583	Registered EV-Related Companies (x₁₄)	0.7841

Table 10. GRA-SVR model parameters.

Parameters	C	g	ε
Value	90.5097	0.0156	1.0000 × 10⁻⁴

Table 11. Fitting results of the GRA-SVR model parameters.

Prediction Accuracy	RMSE	MAE	MAPE
Value	2.86	1.79	13%

Table 12. GRA-SVR model forecast results for January–December 2023 (10 t.h.s unit).

Month	January	February	March	April	May	June	July	August	September	October	November	December
Value	34.85	44.25	52.96	49.16	53.74	60.86	60.17	63.81	65.64	65.82	77.18	80.92

Table 13. SARIMA-GRA-SVR serial combined model forecast results for January–December 2023 (10 t.h.s unit).

Month	January	February	March	April	May	June	July	August	September	October	November	December
Value	54.99	49.56	58.09	48.45	58.12	67.15	70.76	74.45	77.26	81.09	85.51	88.44

Table 14. Fitting results of the SARIMA-GRA-SVR serial combined parameters.

Prediction Accuracy	RMSE	MAE	MAPE
Value	5.89	3.44	21%

Table 15. Weights of the SARIMA-GRA-SVR parallel combined model.

Parallel Methods	SARIMA Model	SVR Model
Simple Weighting Method	66.67%	33.33%
Reciprocal of the Sum of Squared Prediction Error Method	10.97%	89.03%
Reciprocal of the Mean Squared Error Method	25.98%	74.00%
Matrix Advantage Method	30.12%	69.88%

Table 16. Model evaluation metrics.

Prediction Accuracy	RMSE	MAE	MAPE
① SARIMA Model	5.92	3.54	22%
② GRA-SVR Model	2.86	1.79	13%
③ SARIMA-GRA-SVR Serial Combined Model	5.89	3.44	21%
④ Simple Weighting Method	4.48	2.67	17%
⑤ Reciprocal of the Sum of Squared Prediction Errors Method	2.08	1.45	12%
⑥ Reciprocal of the Mean Squared Error Method	2.37	1.56	12%
⑦ Matrix Advantage Method	8.41	6.55	56%

Table 17. SARIMA-GRA-SVR parallel model forecast results for January–December 2023 (10 t.h.s unit).

Month	January	February	March	April	May	June	July	August	September	October	November	December
④	47.36	46.92	55.45	47.75	55.73	64.06	66.18	69.84	72.45	74.89	81.37	84.43
⑤	33.73	42.24	50.73	46.48	51.41	58.45	57.87	61.46	63.70	63.67	73.86	77.18
⑥	36.99	43.36	51.86	46.78	52.44	59.79	59.86	63.46	65.79	66.35	75.66	78.91
⑦	38.53	43.89	52.39	46.92	52.93	60.42	60.79	64.41	66.77	67.62	76.50	79.73
Actual values	28.70	37.60	49.00	47.10	52.20	57.30	54.10	59.70	62.70	64.60	70.20	82.50

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Yu, R.; Wang, X.; Xu, X.; Zhang, Z. Research on Forecasting Sales of Pure Electric Vehicles in China Based on the Seasonal Autoregressive Integrated Moving Average–Gray Relational Analysis–Support Vector Regression Model. Systems 2024, 12, 486. https://doi.org/10.3390/systems12110486

AMA Style

Yu R, Wang X, Xu X, Zhang Z. Research on Forecasting Sales of Pure Electric Vehicles in China Based on the Seasonal Autoregressive Integrated Moving Average–Gray Relational Analysis–Support Vector Regression Model. Systems. 2024; 12(11):486. https://doi.org/10.3390/systems12110486

Chicago/Turabian Style

Yu, Ru, Xiaoli Wang, Xiaojun Xu, and Zhiwen Zhang. 2024. "Research on Forecasting Sales of Pure Electric Vehicles in China Based on the Seasonal Autoregressive Integrated Moving Average–Gray Relational Analysis–Support Vector Regression Model" Systems 12, no. 11: 486. https://doi.org/10.3390/systems12110486

APA Style

Yu, R., Wang, X., Xu, X., & Zhang, Z. (2024). Research on Forecasting Sales of Pure Electric Vehicles in China Based on the Seasonal Autoregressive Integrated Moving Average–Gray Relational Analysis–Support Vector Regression Model. Systems, 12(11), 486. https://doi.org/10.3390/systems12110486

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