Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 12, No. 3, 2023 

 

51 

A	Stock	Index	Prediction	Model	Based	on	LSTM:	Taking	
New	Energy	Vehicles	as	an	Example	
Xinyi He1, a 

1School of Management Science and Engineering, Tianjin University of Finance and Economics, Tianjin, 300222, China 
alctangy@163.com 

 

Abstract: Stock indices can partially reflect the overall price level and variations of various stocks in the market. Therefore, 
analyzing the stock index of new energy vehicles aids in predicting future market trends. However, stock prices, as time series 
data, display traits of nonlinearity and high noise. This study proposes employing the denoising method of Singular Spectrum 
Analysis (SSA) on the CNI New Energy Vehicles Index (399417) and constructing an SSA-LSTM model. Comparative results 
with a single LSTM model demonstrate that the evaluation indicators R2 of the SSA-LSTM model increase by 0.06, RMSE 
decreases by 54.37, and MAE decreases by 49.49. These findings suggest that SSA can enhance the predictive accuracy of the 
model. 

Keywords: Singular Spectrum Analysis; Long Short-Term Memory; Stock Index Prediction. 
 

1. Introduction 
Driven by the green development strategy and the 

promotion of low-carbon economy, new energy vehicles have 
represented the general trend in industrial development and a 
pivotal aspect of automotive industry transformation. 
Simultaneously, the stock market, as an integral part of the 
market economy, has long been a primary focus for scholars 
around the world in terms of predicting stock index prices. 
This not only aids investors in comprehending the 
performance of stock prices in relevant sectors but also offers 
insights into national policies. Despite the growing 
significance of the new energy vehicle industry, research has 
focused primarily on vehicle performance and policy 
initiatives, with limited attention paid to the prediction of 
stock indices. 

Long Short-Term Memory (LSTM) represents a distinct 
form of recurrent neural networks (RNN) which efficiently 
address the challenges of gradient vanishing and exploding. 
Moreover, LSTM resolves the prevalent problem of long-
term dependency in conventional neural networks, making it 
well-suited for managing non-linear and highly noisy time 
series data. 

Singular Spectrum Analysis (SSA) is a methodology 
employed for examining non-linear time series data. It 
involves decomposing and reconstructing the trajectory 
matrix of the time series to extract various component 
sequences, such as noise, long-term trends, and seasonal 
trends. Nevertheless, SSA is currently underutilized in 
financial research. 

This paper aims to employ Singular Spectrum Analysis to 
denoise the original time data and integrate it with an LSTM 
model for data prediction. Ultimately, an evaluation of the 
prediction outcomes will be conducted. 

2. Literature Review 
In recent years, there has been a significant attention 

towards energy-related issues and the concept of a low-carbon 
economy. The transportation sector, ranking as the world's 
second-largest emitter of carbon, has contributed to 

substantial depletion of resources and environmental 
contamination challenges. The automotive industry faces a 
dilemma as it heavily relies on petroleum and simultaneously 
expands. To effectively tackle escalating global climate issues 
and expedite the shift towards a green and low-carbon society, 
countries worldwide are endorsing new energy vehicles as a 
national strategy for cultivating low-carbon transportation. 

New energy vehicles play a crucial role in the global energy 
governance by reducing energy costs and mitigating 
greenhouse gas emissions. Thus offering countries a 
significant pathway to achieve development of clean energy 
and renewable energy [1,2]. These vehicles are now the 
primary focus of the automotive industry's transformation 
worldwide, acting as a key driver for sustained global 
economic growth. The development of new energy vehicles 
represents a strategic response to climate change and the 
promotion of sustainable green practices. In recent years, 
extensive research has been conducted domestically and 
internationally in this field, with a predominant focus on 
power batteries [3,4], government subsidies [5], strategic 
studies [6,7], and optimization of charging infrastructure [8]. 
Notably, there remains a research gap in the prediction of 
stock prices for new energy vehicle companies. Despite the 
significance of stocks in facilitating financing, risk 
management, and policy development for such enterprises, 
investors consider stock price prediction as a crucial factor for 
generating profits and avoiding risks. Hence, conducting 
research on the stock price predictions in the context of new 
energy vehicle industry holds immense importance. 

The stock market, as a crucial component of the market 
economy, consistently garners considerable attention due to 
its trends. As artificial intelligence and big data technologies 
continue to advance rapidly, the field of stock market 
prediction has gained widespread recognition and interest. 

Traditional stock forecasting models rely significantly on 
mathematical statistics for researching and forecasting. In 
their study, Yuxia Wu and Xin Wen analyzed and forecasted 
price fluctuations of Huatai Securities, a listed stock on the 
ChiNext board, by using the ARIMA model. Remarkably, 
they achieved favorable outcomes in short-term price 
prediction [9]. Similarly, in the analysis of the stock price of 



 

52 

Shanghai Dazhong Public Utilities (600635), Qi Yang and 
Xianbing Cao found that ARMA-GARCH model has a high 
accuracy in its prediction [10]. Despite the fact that 
conventional stock prediction models exhibit relatively 
dependable forecasting capabilities for short-term 
fluctuations in stock prices, it is important to acknowledge 
that they face significant limitations. The stock price data has 
the characteristics of nonlinearity, high noise, complexity, and 
vulnerability to the impact of national policies. 

With the emergence of the big data era, machine learning 
methods have been employed in forecasting stock prices. 
Specifically, the Backpropagation [11], support vector 
machine [12,13], and random forest [14] have been utilized in 
this field. For error reduction and improvement of accuracy, 
Guisheng Zhang and Xindong Zhang introduced the SVM-
GARCH model for forecasting the Nikkei 225 stock index 
and proved that the superiority of this model over the 
conventional ARMA-GARCH model [15]. Moreover, Jihong 
Xiao, Xuehong Zhu, Chuangxia Huang et al. developed a new 
method that integrates SSA with SVM for stock prediction 
[16]. Additionally, Fangzhong Qi, Shaoqian Lin and Tingting 
Yu devised the PCA-IFOA-BP stock price prediction model, 
which exhibits superior accuracy compared to the 
Backpropagation, PCA-BP, and PCA-FOA-BP [17]. 

The progress of computer capabilities has resulted in a 
widespread application of deep learning algorithms 
possessing highly improved predictive abilities in predicting 
financial sequence data. Convolutional Neural Networks 
(CNN) and Long Short-Term Memory (LSTM) are some of 
the algorithms used in various studies. Currently, an 
increasing number of researchers aspire to achieve 
breakthroughs in the area of stock prediction through the 
utilization of deep learning techniques. Yan Peng, Yuhong Liu 
and Rongfen Zhang conducted experiments involving LSTM 
models with varying layers and hidden neurons. They 
determined that the optimal configuration was comprised of 2 
layers and 10 neurons [18]. Xiaojian Yu, Guopeng Liu, Jianlin 
Liu et al. conducted an analysis of text data from individual 
stock comments, extracted market sentiment features, and 
incorporated them with LSTM to predict stock prices [19]. 
Furthermore, there has been a recent application of mixed 
deep learning models in the domain of stock forecasting. 
Several scholars integrated LSTM and CNN models for the 
purpose of predicting stock prices by employing time series 
data and stock images [20,21]. Bowen Cai conducted a 
comparative analysis of economic predictions in the new 
energy vehicle industry by utilizing financial information 
derived from annual reports. The findings revealed that the 
fusion model of CNN and GRU demonstrated the most 
superior combination property [22]. Zexin Hu, Yiqi Zhao and 
Matloob Khushi conducted a comprehensive research 
analysis on the utilization of diverse deep learning methods 
on the part of financial prediction. The findings revealed that 
models combining LSTM with other methods exhibited 
superior performance [23]. Zaheer Shahzad, Nadeem Anjum, 
Saddam Hussain et al. conducted a comparative analysis of 
prediction results from multiple hybrid deep learning models 
on stock parameters, specifically close price and high price 
[24]. 

Simultaneously, Singular Spectrum Analysis (SSA), which 
is a robust technique used for time series analysis, has been 
widely employed to address a multitude of practical problems. 
Hossein Hassani utilized SSA on a renowned dataset 
containing monthly accidental deaths rates in the United 

States, and observed a significantly higher level of accuracy 
in forecasting compared to other methods [25]. Cong Wang, 
Hongli Zhang and Ping Ma combine Singular Spectrum 
Analysis with a hybrid Laguerre neural network to forecast 
future wind power values [26]. Kutubuddin Ansari, Sampad 
Kumar Panda and Punyawi Jamjareegulgarn found that the 
SSA method can be a predictive tool for Total Electron 
Content (TEC) sequences in the region of Nepal [27]. 

3. Methodology 

3.1. Singular Spectrum Analysis (SSA) 
Singular Spectrum Analysis (SSA) is a robust method 

utilized for time series analysis, initially proposed by 
Colebrook in 1978. The aim of this method is the 
decomposition of the original sequence into components that 
contain information which is independent of each other. The 
key steps of SSA include the following four: 

3.1.1. Embedding 
Consider a one-dimensional time series 𝑌 , represented by 

𝑦 , 𝑦 , ⋯ , 𝑦 , with a length of 𝑁. To obtain the trajectory 
matrix 𝑋, the one-dimensional time series is transformed into 
a multi-dimensional sequence by selecting a suitable window 
length 𝐿. The resulting trajectory matrix is as follows: 

 

𝑋

⎣
⎢
⎢
⎢
⎡
𝑦 𝑦 𝑦 ⋯ 𝑦
𝑦 𝑦 𝑦 ⋯ 𝑦
𝑦 𝑦 𝑦 ⋯ 𝑦
⋮ ⋮ ⋮ ⋱ ⋮

𝑦 𝑦 𝑦 ⋯ 𝑦 ⎦
⎥
⎥
⎥
⎤

1  

 
Among these parameters, it is standard to select a window 

length 𝐿 that typically falls in the range of 2  𝐿  𝑁/2, 
where 𝐾  𝑁  𝐿  1. 
3.1.2. Singular Value Decomposition (SVD) 

The next step is use SVD to process the trajectory matrix, 
decomposing it into the following format: 

 
𝑋 𝑈Σ𝑉 2  

 
In the above equation, U represents the left singular matrix 

of 𝐿 𝐿 , and its orthogonal vectors are known as the left 
singular vectors. Σ is the singular value diagonal matrix of 
𝐿 𝐾, where all non-diagonal elements are 0. The singular 
values, denoted as Σ 𝜆 , 𝜆 , ⋯ , 𝜆  , are the elements on 
the diagonal that satisfy 𝜆 𝜆 ⋯ 𝜆 0 . 𝑉 
represents the 𝐾 𝐾  right singular matrix, and its 
orthogonal vectors are called the right singular vectors. 
Subsequently, the singular entropy theory is employed for 
noise extraction. 

Entropy is a fundamental concept in information theory, 
essential for quantifying the amount of information in a 
message. In order to separate the noise information from stock 
price time series, the concept of singular entropy has been 
introduced to determine the order of the reconstructed 
sequence obtained through singular value decomposition 
(SVD). The calculation formula for singular entropy and its 
increment is presented below. 

 
𝐸 Σ Δ𝐸 , 𝑘 𝑚 3  

 

Δ𝐸
𝜆

Σ 𝜆
𝑙𝑜𝑔

𝜆

Σ 𝜆
4  



 

53 

According to the theory of singular entropy, if the 
decrement of the singular value increment Δ𝐸   tends to 
stabilize when the singular values reach the 𝑘 th order, it 
suggests that the meaningful information is widely enclosed 
within the singular values from order one to 𝑘. 
3.1.3. Grouping 

Group the singular values in Σ based on their magnitude. 
Larger singular values correspond to signal components, 
while smaller ones are associated with noise. If the singular 
values' extraction is predetermined with 𝑘 , the resulting 
grouping is denoted as, where 𝑋 𝑋 𝑋 ⋯ 𝑋  , 
where 𝑋 𝜆 𝑈 𝑉 . 

3.1.4. Reconstruction 
The previous matrix is converted into a one-dimensional 

sequence with a length of 𝑁 through diagonal averaging. Let 
𝑇 ∈ 𝑅   represents the matrix, where 𝑇 ,   indicates the 
element at position 𝑖, 𝑗  in the matrix, corresponding to the 
element located in the 𝑖th row and 𝑗th column. The indices 
are subject to the conditions 1 𝑖 𝐿 and 1 𝑗 𝐾. The 
matrix 𝑇 undergoes a transformation into a one-dimensional 
time series of length 𝑁  through diagonal averaging by 
defining 𝐾 ∗ max 𝐿, 𝐾  and 𝐿∗ min 𝐿, 𝐾 , denotes as 
𝑡 , 𝑡 , ⋯ , 𝑡  . The reconstructed sequence can be calculated 
using the following formula:  

 

𝑡

⎩
⎪⎪
⎨

⎪⎪
⎧

1
𝑘

𝑇 , , 1 𝑘 𝐿
∗

1
𝐿∗

𝑇 ,

∗

, 𝐿∗ 𝑘 𝐾 ∗

1
𝑁 𝑘 1

𝑇 ,

∗

∗
, 𝐾 ∗ 𝑘 𝑁

5  

 

3.2. Long Short-Term Memory(LSTM) 
LSTM (Long Short-Term Memory) is a type of recurrent 

neural network specifically designed for processing 
sequential data and capturing past information. A basic LSTM 
unit consists of a cell and three gates: an input, output and 
forget gate. The flow of information through LSTM is 
regulated by the three gates, or gate mechanisms, which 
enables LSTM to handle lengthy sequential data efficiently. 
Figure 1 provides a detailed depiction of the structure. 

 

 
Figure 1. LSTM network structure 

 
The forget gate in LSTM regulates the selective forgetting 

of information within the cell state. At time 𝑡, by using the 
Sigmoid function to assess the input signal 𝑥  and the output 
signal ℎ   from time 𝑡 1 , the evaluation leads to the 

attainment of a value ranging from 0 to 1. In this context, 0 
signifies complete forgetting, while 1 indicates complete 
retention. The below formula provides the specific calculation. 

 
𝑓 𝜎 𝑊 ℎ , 𝑥 𝑏 6  

 
The input gate of the LSTM is of paramount importance in 

determining what proportion of input information to store in 
the current state. By taking 𝑥   and ℎ   as inputs, the 
Sigmoid function generates 𝑖  as an output. In addition, the 
tanh function integrates the inputs 𝑥   and ℎ   to form a 
candidate cell state 𝐶 . The cell state 𝐶  is updated based on 
𝑖  and 𝐶 . The following specific formulas show the update 
of 𝐶  at time step 𝑡: 

 
𝑖 𝜎 𝑊 ℎ , 𝑥 𝑏 7  

 
𝐶 𝑡𝑎𝑛ℎ 𝑊 ℎ , 𝑥 𝑏 8  

 
𝐶 𝑓 ∗ 𝐶 𝑖 ∗ 𝐶 9  

 
The output gate determines the output value ℎ  by taking 

into account 𝐶 . The output gate combines the current input 
signal 𝑥   with the cell state 𝐶   and the previous output 
signal ℎ   from time step 𝑡 1  to generate the present 
output signal. The input signal 𝑥  and previous output ℎ  
are passed through the sigmoid function, resulting in a value 
𝑜 , which falls within the range of 0 to 1. To obtain an output 
signal ℎ , the cell state 𝐶  is processed by the tanh function, 
yielding a value within the interval of 1,1  , and then 
multiplied by 𝑜 . Furthermore, ℎ  is propagated as the input 
signal for the subsequent time step, initiating further 
processing. The calculation formulas for ℎ  are as follows. 

 
𝑜 𝜎 𝑊 ℎ , 𝑥 𝑏 10  

 
ℎ 𝑜 ∗ tanh 𝐶 11  

4. Empirical Analysis 

4.1. Experimental data 
4.1.1. Data sources 

This paper employed information on CNI New Energy 
Vehicles Index (399417) spanning from 1 July 2013 to 30 
June 2023. The dataset comprises information on opening, 
closing, lowest and highest prices, as well as trading volumes 
and price variations, totaling 2425 data points. 

4.1.2. Data preprocessing 
The raw data obtained may contain issues such as missing 

values, disorder, and inconsistent formatting. Consequently, 
preprocessing the raw data becomes imperative, entailing 
tasks such as handling missing values, sorting, and adjusting 
data formats. These operations are undertaken to acquire a 
standardized dataset. 

4.2. Data denoising and normalization 
Raw time series data of stocks frequently includes data 

noise, which may impact the convergence speed of data, 
model accuracy, and prediction effectiveness. In order to 
tackle this matter, this study utilizes the Singular Spectrum 
Analysis (SSA) for data denoising. 

4.2.1. Selection of window length 𝑳 
The selection of an appropriate window length is important 



 

54 

in SSA as it directly impacts the effectiveness of the analysis 
and the resulting decomposition. In a time series of length 𝑁, 
the window length need not surpass 𝑁/2 . Moreover, a 
lengthier window length 𝐿  leads to a more detailed 
decomposition of the sequence. Conversely, if 𝐿 is too small, 
it impedes the extraction of components [28]. To determine 
the appropriate window length, this study empirically selects 
a value of 1200. Additionally, the incremental values of each 
singular value are computed using singular entropy. The 
change in the increment of the singular entropy is shown in 
Figure 2. 

 

 
Figure 2. The variation of the singular entropy increment 
 

4.2.2. Order selection for singular value reconstruction 
sequences 

From the data presented in Figure 2, it is evident that the 
increment of the singular values stabilizes when the order 
reaches 300. Therefore, this paper proposes selecting the 
singular value reconstruction sequence up to the 300th order. 

4.2.3. Normalization 
To remove the influence of dimensionality among 

indicators, normalization of the feature sequence is required, 
which involves mapping it onto the interval 0,1 . 

4.3. Experimental results and analysis 
This article compares experimental results for assessing 

model accuracy and prediction precision by using the 
evaluation metrics of coefficient of determination (R2), root 
mean square error (RMSE) and mean absolute error (MAE). 
A smaller RMSE and MAE value signifies a smaller error and 
improved prediction performance. The calculation formulas 
are as given below. 

 

𝑅𝑀𝑆𝐸
1
𝑛

𝑦 𝑦

/

12  

 

𝑀𝐴𝐸
1
𝑛

| 𝑦 𝑦 | 13  

 
The values of R2 vary between 0 and 1. The model’s fit and 

prediction performance improve as the R2 value approaches 1. 
The calculation formula is presented below. 

𝑅 1
∑ 𝑦 𝑦
∑ 𝑦 𝑦

14  

 
This experiment employs the LSTM, comprising two 

LSTM layers and one Dense layer, with a configuration of 10 

hidden neurons. The model is set with specific parameters: 
batch_size of 32, 50 epochs, and a division of the data into 
training and testing sets at an 8:2 ratio. The predictions are 
performed separately on the data subjected to SSA and the 
original non-processed data. Figure 3 and Figure 4 
respectively show the experimental outcomes of the SSA-
LSTM model and the LSTM model. 

 

 
 

Figure 3. Results of SSA-LSTM model predictions 
 

 
Figure 4. Results of LSTM model predictions 

 
The evaluation metrics for the two models were calculated 

individually, and Table 1 presents the corresponding results 
below. 

 
Table 1. Comparison of evaluation metrics for SSA-

LSTM model and LSTM model 
 R2 RMSE MAE 

LSTM 0.82 281.62 241.75 
SSA-LSTM 0.88 227.25 192.26 
 
Table 1 displays the findings which indicate that the SSA-

LSTM model reduces the RMSE and MAE by 54.37 and 
49.49, respectively, in comparison to the LSTM model. 
Additionally, the R2 increases by 0.06. These results 
demonstrate the superior capability of the LSTM model for 
forecasting financial time series data, particularly in 
predicting stock prices. Moreover, the results suggest that 
SSA enhances the extraction of more relevant data, leading to 
an improved accuracy of the predictions. 

5. Conclusion 
Given the intricacy and unpredictability of the stock market, 

this study suggests a blended approach that combines SSA 
with LSTM to enhance the analysis and prediction of stock 
prices. The chosen dataset for this research comprises the CNI 



 

55 

New Energy Vehicles Index (399417), which reasonably 
reflects the general level and fluctuations of stock market 
prices in the broader new energy vehicle stock market. 
Following preprocessing steps involving SSA denoising and 
normalization techniques, the SSA-LSTM model is 
developed for the analysis and prediction of the price of the 
CNI New Energy Vehicles Index (399417), subsequently 
comparing it against the LSTM model. The findings 
demonstrate that incorporating SSA effectively enhances the 
prediction accuracy of the LSTM model. 

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