# Forecasting Method of Stock Market Volatility Based on Multidimensional Data Fusion

Authors: Xiaoyong Zhang; Li Zhang
Journal: Wireless Communications and Mobile Computing
 (2022)

---

## Abstract

The volatility of the stock market is related to the vital interests of stockholders and is essential for maintaining a stable financial environment. Through the analysis of data changes, excellent professional traders can extract information about the direction of stock changes, whether it is worth investing, and long-term or short-term trading. This article aims to study the forecasting methods of stock market volatility, by integrating multiparty data, in-depth analysis of the direction of data changes, predicting the price changes of the stock market, and better guiding stockholders’ investment. This paper proposes a multisource data fusion method to analyze the stock market price changes and find the best risk prediction method. The experimental results in this paper show that multisource data fusion can better help the stock market predict stock changes and reduce financial investment risks by 20%. Comparing the obtained prediction results with the real data, the MSE predicted by the ARIMA model is calculated to be 2.35. It provides a new idea for effectively analyzing nonstationary time series data with complex trend fusion characteristics by rationally screening feature signals and trend signals and modeling probability distribution.


---

## Body

## 1. Introduction

The theory of data prediction and classification is the crystallization of the integration of different disciplines such as management science, economics, mathematics, and computer. Multidimensional data fusion is widely used in energy price market analysis, financial market price prediction and risk control, biological information identification, business intelligence customer behavior analysis, and many other fields. The financial market is an important force for the stable development of the domestic economic system, and it plays an important role in supporting the stability of the country and the prosperity of the nation. As the role of the financial market has become more prominent, more and more experts and scholars have begun to pay attention to the financial field. As an important part of the financial field, stocks are increasingly sought after by experts and scholars. The prediction of stocks has also become a hot research topic, but the stock market is fickle and elusive. There are many factors that affect it (the economy, the politics, the company itself, the market, etc.). Some factors can even lead to earth-shaking changes in the financial market. At the same time, it is difficult to predict the emergence of uncertain factors and emergencies. The application of data prediction and fusion theory in electric power, biology, finance, business intelligence, and other fields has been relatively mature, among which the data prediction theory has been widely used in power load prediction, financial time series prediction, energy price prediction, commodity sales forecast, and other fields. The stock market has been in an unstable state, and there will be rapid growth or rapid decline from time to time. These unpredictable stock rises and falls reflect the movements of the economic market and will also have an important impact on the market economy status. These uncertainties and instabilities make the prediction of the stock market more difficult and less accurate. Many experts and scholars have conducted a large number of empirical tests in the literature, and the research shows that the stock market can be predicted. This paper presents a new framework for complex data forecasting from the perspective of mode discrimination, which provides new ideas for the study of high-dimensional data fluctuation law analysis and nonstationary high-frequency fluctuation data forecasting.For stock forecasts, domestic and foreign experts and scholars have achieved some results. Li’s research examines the impact of the economic policy uncertainty (EPU) index of China and G7 countries on the volatility of the Chinese stock market and uses principal component analysis (PCA) to further construct a new diffusion index based on these indexes to enhance forecasting capabilities. The Economic Policy Uncertainty Index is an index used to reflect the economic and policy uncertainty of the world’s major economies. The EPU index has a significant inverse relationship with actual macroeconomic variables, such as economic growth and employment, and even explains large swings in equity markets. The results in the sample show that the EPU index of China and some G7 countries has a significant negative impact on future volatility. In addition, the out-of-sample results show that the prediction accuracy of the diffusion index is significantly higher than the EPU itself and the combined prediction [1]. Jeric has collected data on the expectations of Croatian stock market participants about the future level of the Croatian stock index CROBEX. The results showed that the groups studied were not rational in predicting index values. Forecasters tend to be biased and generally tend to overestimate the actual index value during the sampling period. Some forecasters failed the efficiency test with correlations between forecast errors and past CROBEX values or Croatian industrial production known to the forecaster at the time the forecast was made. Furthermore, there is considerable individual heterogeneity [2]. Davide introduced the GARCH model used to analyze and predict the S&P500 stock market index. The purpose is to directly deal with possible structural interruptions in the observed time series through empirical evaluation and comparison of alternative forecast combinations of different estimation windows. The results prove that there are structural fractures and unstable parameters in the S&P500 series. In addition, for all considered GARCH type specifications and all implemented innovation conditions distribution, the average performance of the volatility predictions generated by the various prediction models estimated using different window sizes is good, and it seems to provide a useful method to predict the S&P500 stock market index [3]. Feng fills this gap by studying the ability of oil volatility risk to predict stock market volatility. Using oil VRP as a predictor, he found that oil VRP does show statistically and economically significant in-sample and out-of-sample forecasting capabilities for G7 countries and even controls some popular macroeconomic variables. When alternative agents are used to measure the volatility of stocks and oil, these findings are reliable [4]. Carlston uses information from liquidity and volatility indicators to predict real gross domestic product (GDP) growth and business cycles. He estimated more than 5,000 NYSE liquidity and volatility indicators and extracted a common factor to determine uncertainty in the ability of real GDP, industrial production, the consumer price index, real consumption, and real investment to change. The results of the survey found that the positive impact on the uncertainty factor occurred in the quarters before and at the beginning of the recession. In the few quarters that the recession is about to end, uncertainties will be negatively impacted [5]. Kim constructed a model to predict stock price fluctuations, which is a fusion of mixed long-term short-term memory and various generalized autoregressive conditional heteroscedasticity. He analyzed and compared various fusion ratios and found that the model formed by fusion of long-term short-term memory and various generalized autoregressive conditional heteroscedasticity at a ratio of 1 : 3 has the lowest prediction error [6]. Gamba-Santamaria uses the DCC-GARCH framework to model the diversified relationships between market volatility. Extending the framework of Diebold and Yilmaz, taking into account the time-varying structure of the covariance matrix, the spillover index is directly calculated from the return series. The results are as follows: first, the total spillover shows a huge time series change, which is higher at times of market turbulence. Second, the net heads of each country did not change during the sample period; however, their intensity showed important temporal changes. Finally, as expected, the transmission of stock market volatility originated in the most developed markets. It is particularly important that although the Chinese stock market has achieved important growth over time, it is still a net receiver of volatility [7]. Werner Kristjanpoller analyzed the volatility forecasts associated with the prices of gold, silver, and copper. First, a set of GARCH models are used to predict volatility, including explanatory variables such as the dollar-euro and dollar-yen exchange rates, oil prices, and stock market indexes in China, India, the United Kingdom, and the United States. Subsequently, these model predictions are used as input to the neural network to analyze the increase in hybrid prediction capabilities. The results obtained show that for these three metals, the use of a hybrid neural network model improves the predictive ability of out-of-sample volatility [8]. Facing the growing mass of data information, although it contains extremely rich business knowledge and valuable decision-making information, how to more fully and effectively collect and sort out complex data and extract valuable and usable information from it is still a problem is a very challenging question.Based on the forecast of stock volatility, this article analyzes the reasons of stock volatility, finds the factors that affect stock volatility, determines the relevant variables of volatility, builds a stock volatility price prediction model, and uses the model to achieve stock price prediction. Compared with other stock forecasting methods, the short-term forecasting results of the model constructed by this method are more accurate, and the forecasting efficiency is higher, which can well meet the needs of users. This provides a direction for stock volatility forecasts and also points the way for stocks to reduce related risks.


## 2. Introduction to the Principle of Multidimensional Data Fusion and Stock Forecasting Methods

### 2.1. Data Fusion

Data fusion is a formal framework whose main content is to integrate information from different sources with mathematical methods or technical means to obtain high-quality or valuable information [9, 10]. According to the definition of data fusion, the construction of available models (or frameworks) is an important content, which mainly includes functional models, structural models, and mathematical models. The difference between the three models lies in the different fusion angles, and the functional model focuses on the fusion process, as shown in Figure 1. It mainly involves the integration of the main functions, roles and interactions of various systems. The structural model focuses on information flow, and the fusion work form is the focus of fusion, emphasizing the information interaction process between the system and the outside world; the mathematical model mainly refers to the algorithm of data processing.Figure 1
Recommended revised data fusion model.


#### 2.1.1. Functional Model

Level 0 signal/feature estimation: estimate the state of a signal or feature. Signals and features are patterns obtained by processing in different waysLevel 1 entity estimation: estimate the state or attributes of an entity. Entities generally refer to individualsThe second level of situation assessment: an estimate of the partial structure of the actual environment. It mainly completes the estimation of the connection between entities and the implicit connection with the state of related entitiesThe third level of impact estimation: the estimation of the availability and cost of each parameter state of the first three levels, including the estimation of the availability and cost of a certain action plan of the systemThe fourth-level process estimation: compare the system effect with the expected performance, and realize the self-assessment structure model of the fusion system


#### 2.1.2. Structural Model

There are two classification methods for structural models. As shown in Figure2, a classification according to the degree of data processing before fusion can be divided into three typical structure types: centralized, distributed, and hybrid. The other can be divided into three structure types: pixel level, feature level, and decision level according to the resolution in the data fusion process [11].Figure 2
Structural model classification method.Multisource data fusion is a comprehensive discipline involving science, engineering, computing, and other fields. The related technologies are control theory, signal processing, software engineering, computational intelligence, information theory, probability and statistics, biological sciences, and cognitive psychology [12]. For the entire data fusion system, the processed data can come from one level or multiple conceptual levels. The processing method is mainly to integrate the data of one level first and then combine the results with the data of the next level. Therefore, the fusion process is actually a layer-by-layer abstraction, layer by layer to achieve the integration of multisource data from different levels.JDL, the Joint Conference of Laboratory Directors, was the first to give the most widely accepted definition of data fusion. The technologies are classified level by level according to the four-level fusion model of JDL except level 0 as follows:Level 1: target estimation level fusion can be divided into data association, state estimation, classification, and recognitionLevels 2 and 3: the task of situation assessment is to build connections between entities to obtain higher-level evaluation results, such as actions or events. The tasks that affect the estimation include estimating the hazard level, evaluating the opponent’s combat effectiveness, etc. The main algorithms are as follows: clustering algorithms, learning, reasoning, and retrieval strategiesLevel 4: the task of process optimization is to carry out monitoring and evaluation and implement guidance on the effect of fusion to reach the optimal conclusion. The main functions include the following: performance evaluation, fusion control, information source processing, and task management.


### 2.2. Related Theories of Stock Volatility

#### 2.2.1. Basic Principles of Stock Forecasting

The efficient market hypothesis (EMH) theory subdivides the efficiency patterns of the financial market into three situations and points out the corresponding prediction methods for each efficiency pattern. The hypothesis believes that if participants in the financial securities market can understand all information without barriers, then when a valuable new interest is generated, investors will quickly grab and react to it. Under the action of this “perfect competition” mechanism, every new information will be fully reflected by the market price of securities. In other words, the information advantage cannot be used to obtain additional income in the market, and the price of the securities at this time is consistent with the true value of the securities. As shown in Figure3, the efficient market hypothesis points out that the three forms of market efficiency are the following [13]:
(1)
Weak-form efficiency. In this market, investors can allocate shares based on fundamental analysis. That is, starting from several factors such as the economic environment, industrial prosperity, and business operation conditions, choose a reasonable investment strategy. However, technical analysis is invalid; that is, it is impossible to predict the possible trend of stock prices through mathematical models or logical deliberation methods based on the historical performance of the securities market. This is because in a weakly efficient market, the price of a stock has fully reflected historical information that affects stock price changes, such as transaction price and transaction volume(2)
Semi-strong efficiency. In this market, investors can only obtain abnormal profits by using inside information, that is, by grasping some undisclosed information that has a greater impact on the stock price, using information advantages to obtain excess returns. The semi-strong efficient market assumes that some public information such as national economic policies, industrial economic conditions, and company financial conditions have been fully reflected in the fluctuations in stock prices(3)
Strong efficiency. In a strong efficiency market, investors are never likely to get excess profits. Powerful efficiency Information processing is fast, and all kinds of information are continuously collected, processed, analyzed, and used to exert powerful functionsFigure 3
Introduction to efficient market theory.In the three types of markets, technical analysis and fundamental analysis are difficult to effectively perform their functions. Therefore, the efficiency of the market must be verified before predicting stock prices. The test needs to follow a certain order, because the efficiency of the three markets is strengthened in sequence, so the test can be carried out sequentially starting from the weakly efficient market. The efficiency of weak form can be verified by serial autocorrelation function and stationarity ADF test. As a common tool for time series analysis, the autocorrelation function can clarify the relationship between the current stock price and the stock price of several lagging periods and can also explain the degree of influence of historical data on the stock price trend. The ADF test has a relatively common application in the market efficiency verification problem. It can reflect whether the market satisfies the conditions of random walk. The semi-strong efficiency is mainly verified by tracking the development of events. If the new financial data released by the company and the new financial policy proposed by the government can quickly affect the equilibrium of the stock price, then the current market can be regarded as a semi-strong effective market. As for strong efficiency, it is theoretically necessary to verify the relationship between inside information and stock returns, but it can often be concluded based on experience that inside information will greatly increase investment wealth. Today, national laws and industry codes of conduct clearly stipulate the illegal and illegal nature of insider trading.The exploration of market price prediction in the field of financial research has always been full of unique charm. Over the years, scholars from various countries have proposed various prediction models to reveal the inherent laws of stock price changes. Although these models have improved our ability to predict future price trends to a certain extent, the prediction results have not been completely satisfactory. The reason is that there are still many problems waiting to be overcome in the stock price forecasting, such as the uncertainty of the forecast, the high noise of the sample data, and the mixed information.


#### 2.2.2. Stock Market Volatility

From a narrow perspective, stock market volatility refers to the volatility of stock prices, which are affected by various factors and fluctuate over time. Out of the emphasis on risk, investors are paying more and more attention to the volatility of the entire stock market. Investors buy and sell stocks to get high profits, but the benefits and risks are at the same time, and volatility can well reflect the degree of risk in obtaining benefits.According to the different attitudes of investors to risk, we can divide investors into three categories: they are risk appetite, risk aversion, and risk neutral. Different types of investors have different choices of risk and return [2] as shown in Table 1.Table 1
Different types of investors’ preference for risk and return.
Investor typeInvestment preferenceRisk appetiteHigh risk and high returnRisk neutralBetween two risksRisk aversionLow risk and low returnThe volatility of the stock market is directly proportional to the degree of investor risk aversion. Studying the volatility of the stock market can better guide investors to participate in investment decisions.In the past, the volatility of company stock returns was the focus of research. The company’s stock return volatility is expressed by the variance of the company’s stock’s monthly return in the current year, which measures the company’s operating risk. In fact, stock volatility is caused by investors’ frequent stock trading operations, so stock turnover rate is the best measure. The higher the stock turnover rate, the greater the stock volatility. In addition, there is a large amount of information noise in the stock market, which indicates volatility. Specifically, it is expressed as the synchronization of the price of multiple stocks with the performance of the market, that is, “the same rise and fall.” In comprehensive considerations, this article believes that the three indicators of stock turnover rate, stock return volatility, and stock price synchronicity should be considered at the same time on the market volatility.The first problem to be solved in the study of the volatility of the stock market is how to quantify the volatility of the stock market. The current methods to quantify the volatility of the stock market mainly include the following:(1) Range Method. This method measures the volatility of the stock market according to the difference between the extreme values in stock price fluctuations, and its quantitative formula is
(1)Bt=maxJt−minJt.Among them,Jt represents the extreme value in the stock volatility. The index selection of this method is rough, the accuracy of the volatility measurement is not high enough and it is not comparative. On the premise that stock market volatility obeys Brownian motion, it is mathematically deduced that the volatility in Brownian motion is just the standard deviation of the log price. Starting from the stock itself, the standard deviation of the logarithmic price of the stock is the standard deviation of the daily rate of return of the stock. Taken together, from the nature of Brownian motion, we can deduce that the volatility of the stock price is the volatility of the Brownian motion, and it is equal to the stock price. Daily volatility can be used to quantify stock market volatility. The calculation formula is as follows:
(2)γ⌢park,t=InGt−InDt24In2.(2) Spread Rate Method. Through the analysis and comparison of the range method, it is improved, and the relative amplitude is proposed to measure the volatility of the stock market. The specific calculation formula is as follows:
(3)ABt=maxJt−minJtmaxJt+minJt2×100%.(3) Standard Deviation Method. The spread rate method can only measure the local characteristics of volatility, and is not applicable to the overall level of volatility. Markowitz proposed in 1982 to use the standard deviation method to quantify the size of the stock market volatility [14]; the specific calculation formula is as follows:
(4)∂⌢2=1T∑x=1Tst−s,where ∂⌢2 represents the estimation of the method, st is the rate of return of the stock price at time t, and s is the mean value of st in the statistical time period.


### 2.3. Introduction to Commonly Used Stock Market Indicators

#### 2.3.1. Homeopathic Index (CCI)

The trend indicator is an overbought and oversold indicator. Overbought and oversold indicators in the market are mainly technical indicator graphics formed by calculating the running trend of stock prices. When the stock is overbought and hyped by the market, it is an overbought signal and a reference signal for risk selling. Conversely, when the stock is oversold and sold by the market, it is an oversold signal and a reference signal for an opportunity to buy a point. It judges whether the stock price has changed significantly by comparing the difference between the stock price on the day and the average value. CCI calculation formula:(5)CCIi=M−Kir×Ni,(6)M=max+min+close3,(7)Ki=∑x=1icloseii,(8)Ni=∑x=1iKi−closeii.Among them,M is the average value of the stock’s highest price, lowest price, and closing price; Ki represents the average closing price within the day; and r=0.015 is the calculation coefficient.


#### 2.3.2. Rate of Change Indicator (ROC)

The rate of change indicator is to measure the relationship between current stock fluctuations and market supply and demand by comparing the closing price of the day with the previous period, so as to judge whether the market can reverse the price with stock fluctuations. ROC calculation formula:(9)ROCx=Ni−NNi×100.Among them,N represents the closing price of the stock on the day, and Ni represents the closing price of the stock before i. The calculation time period of the ROC indicator is generally 6 days, 12 days, or 24 days.


#### 2.3.3. Relative Strength Index (RSI)

The relative strength indicator compares the average closing price within a certain period of time and analyzes the strength of the long and short sides to predict stock market changes. Because the RSI indicator can more sensitively reflect the changes in stock prices in the short term, it is widely used for short-term operations. RSI calculation formula:(10)RSIi=ZiZi+Di.Among them,Zi represents the average value of the total increase in stock prices in day i, and Di represents the average value of the total decrease in stock prices in day i.


#### 2.3.4. Ultimate Volatility Index (UOS)

Extreme volatility index is to solve the sensitivity problem of oscillating index. Oscillator sensitivity refers to that for a certain technical indicator, under certain parameter setting conditions, after traversing and analyzing long-term historical data, when the indicator conditions are met, the price fluctuation of the investment product is consistent with the direction and range indicated by the indicator. Under the premise, when the indicator gives clear indication information, the corresponding price movement volume accounts for the percentage of the entire price movement volume. Oscillator sensitivity is a parameter that measures how quickly a technical indicator responds to price fluctuations. The parameters of the oscillator are different, and the results are also different. In order to maximize returns, investors should choose the best combination of parameters when using oscillating indicators. In fact, it is difficult for investors to choose appropriate cycle parameters. The ultimate volatility indicator is calculated by multiplying the three oscillation indicators with different periods by the corresponding constant factor to obtain the ultimate volatility indicator that comprehensively considers various oscillation indicators. After a series of parameter calculations, this indicator is more adaptable to different stock market conditions than a single-parameter oscillating indicator [15]. UOS calculation formula:
(11)AC1=∑x=1N1Cx−JDx∑x=1N1JDx−JXx,(12)AC2=∑x=1N2Cx−JDx∑x=1N2JDx−JXx,(13)AC3=∑x=1N3Cx−JDx∑x=1N3JDx−JXx,(14)UOS=AC1×N2×N3+AC2×N1×N3+AC3×N1×N2N1×N2+N1×N3+N2×N3.Among them,JDx is the larger value of the highest stock price on the xth day and the closing price of the stock on the x−1th day, JXx is the smaller value of the highest stock price on day x and the closing price of stock on day x−1, Cx represents the closing price of the stock on the first day, and N1, N2, and N3 are three time period parameters, set to 7, 14, and 28, respectively.


#### 2.3.5. Simple Volatility Index (EMV)

The simple volatility indicator is a technical indicator that studies the relationship between changes in trading volume and stock prices. It can guide investors to buy the stock when the stock is highly concerned and the trading volume is active. And when other enthusiastic investors did not find that the stock’s trading volume was gradually decreasing and the stock price trend was about to reverse, they were guided to sell the stock in time to obtain additional income. EMV calculation formula:(15)Px=Gx+Dx2,(16)Qx=Gx−1+Dx−12,(17)Wx=Gx−Dx,(18)EMx=Px−Qx×WxVx,(19)EMVx=∑x=1NEMx.Among them,Gx is the highest stock price on the xth day, Dx is the lowest stock price on the xth day, Vx represents the stock trading volume on the xth day, and N represents the time period.


### 2.4. Stock Analysis Method

#### 2.4.1. Traditional Analysis Methods

The traditional analysis method is based on the observation and analysis of various characteristics of the stock itself [16]. The three analysis methods of fundamental analysis, technical analysis, and evolution analysis help investors have a certain degree of grasp of the trend of the stock market to a certain extent and can obtain a higher degree of accuracy in judging the future rise or fall of stocks. But its limitation is that it can only predict the trend, but cannot achieve a relatively accurate output of the magnitude of the fluctuation.(1) Fundamental Analysis. The main idea of fundamental analysis is to analyze stocks by analyzing the changes and developments of various basic factors that affect the trend of the stock market. Through the analysis of fundamentals, correctly grasp the factors that lead to stock price fluctuations and then analyze and decide the stocks to invest in. The fundamentals mainly include economic situation, economic policy, political system, and internal company factors [17]. Fundamental analysis is qualitative analysis. When using fundamental analysis to analyze various factors that affect stock prices, we can only determine the next trend of stock price changes, that is, rise or fall, and cannot accurately give the magnitude of the rise or fall. Fundamental analysis is more applicable to the analysis of the long-term investment.(2) Technical Analysis (K-Line). Technical analysis mainly uses historical data to predict the trend of the stock market through mathematical methods and discover its inherent laws. Its prerequisites are as follows: (1) market behavior contains all information and does not require specific analysis of specific factors; (2) stock price fluctuations are regular; (3) the market changes periodically, and analysts can get the law of changes in stock prices through induction and summary. Technical analysis puts aside external factors and simply analyzes the stock itself. The main research objects include graphics, forms, and technical indicators. Specifically, it includes stock trend, trading volume, new highs of stock prices, new lows of stock prices, K-line theory, wave theory, and other technical indicators and technical graphic analysis.(3) Evolution Analysis. Evolutionary analysis integrates the development and changes of the stock market with the idea of biological evolution. Analyze the stress, profitability, variability, adaptability, metabolism, plasticity, and cyclicality of the stock market; make rational judgments on market trends and future development; and provide evaluation conclusions for investment.


#### 2.4.2. Modern Technical Analysis Methods

Modern technical analysis methods conduct scientific mathematical modeling of related variables by observing the changing characteristics of the related properties of stocks. It reduces the reliance on economics-related theories and analyzes it from a mathematical point of view. Nonlinear forecasting combines the characteristics of many disciplines, based on statistics, and according to the actual needs of actual problems, and brings data into related models for regression forecasting. It is more scientific, and the results obtained are generally more optimized [18].(1) Neural Network Prediction Method. The neural network prediction method is to train the existing past n sample data, establish the most suitable model, and use this model to predict the value of m time in the future. Taking past data as a sample does not mean that the requirements for the sample are high. The neural network has a strong ability of induction. For uncertain information, it can give appropriate substitute values through reasoning. This is also convenient for solving problems that cannot be solved simply by establishing a mathematical model. This is also convenient for solving problems that cannot be solved simply by establishing a mathematical model. Stock prices are generally nonlinearly distributed, with a certain degree of randomness and irregularities. Neural networks can also get better results for this.(2) Fuzzy Time Series Forecasting. The main research objects of fuzzy mathematics are uncertain things. Fuzzy mathematics is based on basic mathematics and introduces fuzzy concepts to obscure the definition of “yes” and “no.” Set a confidence interval between the two to expand the value range of a variable with a single value. The difference between fuzzy time series and traditional time series is that the value of fuzzy time series at a certain moment is a fuzzy number, which can also be described as a set. The value of a traditional time series at a certain moment is an accurate value. The general model of fuzzy time series forecasting can be expressed as the following formula:
(20)SVt=ao+a1t+a2t2+⋯+altl+ω,where SVt∈B,l∈N,ax∈B,x=1,2,3⋯,l. B is the set of fuzzy numbers, and ω is the random error expected to be zero.The fuzzy time series forecasting model is based on the coefficient and the fuzzy number of the time series, and the forecast result is also a fuzzy set. The evaluation standard of the traditional time series forecastSVt model is usually defined as the accuracy of the forecast result, while the fuzzy time series forecast model only needs to judge whether the actual change is included in the forecast result. Therefore, the practical range of fuzzy time series forecasting SVt is more extensive.


### 2.5. Time Series Analysis Theory

The research object of time series analysis is a collection of data arranged in time. In real life, currency exchange rates between countries, daily closing prices of stocks, daily business turnover, daily maximum temperatures, and human electrocardiograms are all recorded in a time-series manner. To mine the deep information hidden in the sequence, time series analysis theory will be a very powerful “weapon.” With this tool, we can achieve two goals: first, recognize the operating mechanism that produced the sequence; second, make advance predictions of possible future situations or interfere with and control the current situation.


#### 2.5.1. Stationarity Test

When making statistical inferences about a phenomenon based on historical data, it is usually necessary for the sequence to first satisfy theoretical assumptions with a certain degree of rationality, of which the stationarity assumption is the most important. The significance of stationarity is to ensure that the statistical properties will not change over time. According to the mathematical definition, stability can be divided into strict stability and wide stability [19]: strictly stable means that any statistical characteristics of time series will not differ from time to time, that is, the joint distribution of time series is only related to the time lag a and has nothing to do with the time node t. If the time series Xt satisfies the following conditions, the series is said to be strictly stationary. It can be expressed as:
(21)Ft1,t2,⋯,tmx1,x2,⋯,xm=Ft1+a,t2+a,⋯,tm+ax1,x2,⋯,xm∀tx,tx+a∈T,x=1,2,3,⋯,m.Broad stationary has relatively weak conditional requirements. It means that the mean function of the time series takes a fixed constant at any point in time and the covariance function is only related to the time interval terma. That is, if the time series always meets the following conditions for any t, s, and k, the series is said to be broadly stationary. It can be expressed as
(22)EXt2∞,EXt=κ,EXt−κtXs−κs=EXa−κaXa+s−t−κa+s−t.As shown in Figure4, according to the time series change, we can infer that there is no stationarity in the sequence of time series a. According to the sequence of time series b, although its long-term trend is uncertain, in the short term, fluctuations around a fixed value are obvious. Generally speaking, in terms of stationarity, the stationarity of b is obviously better than that of a.Figure 4
Comparison of stationarity of different series.Trend graphs and autocorrelation function graphs can show the stationarity of the time series, but the more commonly used test method is the unit root test [20]. The principle of the unit root test is to detect whether there is a root of 1 in the characteristic equation of the regression model, and the sequence with unit root can be smoothed by means such as difference. In statistical methods, ADF statistics can test the existence of unit roots. Here we mainly introduce the principles of ADF: the ADF test must be carried out in three cases, no intercept item and no trend item, including intercept item, and including intercept item and trend item, respectively, corresponding to the following formulas:
(23)Δyt=λyt−1+∑x=1mδtΔyt−x+ut,t=1,2,⋯,T,(24)Δyt=λyt−1+a+∑x=1mδtΔyt−x+ut,t=1,2,⋯,T,(25)Δyt=λyt−1+a+ηt+∑x=1mδtΔyt−x+ut,t=1,2,⋯,T.The null hypothesis and alternative hypothesis set by the ADF test are all about the value ofy, where Q0 is the null hypothesis.
(26)Q0:λ=0,Q1:λ0.Q0 means that a unit root is tested, and the sequence is not stationary; Q1 shows that the time series has no unit root and passed the stationarity test.


#### 2.5.2. ARIMA Model

ARMA is the first model to consider in the process of modeling stationary time series, but the data series we need to deal with often show nonstationarity. Therefore, on the basis of ARMA, scholars have explored a theoretical model that can specifically analyze uneven data, that is, the ARIMA model. It is very similar to ARMA but adds a single integration process. The so-called single integration refers to the time series that needs to be differentiated to achieve stability. Corresponding to the “I” in the abbreviation of the name, it usually takes 1 to 2 in use to achieve the smoothing of the sequence.The establishment of the ARIMA(a,b,c) model needs to determine the values of three of the parameters [21], which are the nth order difference model, the moving average model MA, and the autoregressive model AR. Figure 5 shows the process of ARIMA building a stock time series forecasting model:Figure 5
Schematic diagram of the process of constructing a financial time series forecasting model based on ARIMA.Before using the ARIMA model, it is first necessary to verify whether the financial series constructed based on financial data is locally stable. If not, it needs to be smoothed. On the basis of the financial data set, an index of time is established, and the financial time series are constructed together with data such as the highest price (high), closing price (close), and opening price (open) as attributes as shown in Figure6.Figure 6
Financial time series chart.Subsequently, the stationarity of the financial time series was verified. Taking 601728 (China Telecom) as an example, the ADF test was performed on the original time series. It can be seen that the ADF statistics and they value are both greater than the Mackinnon critical value, the Mackinnon critical value is the one-sided test probability value proposed by McKinnon, which is used for the ADF significance level test. The smaller the Mackinnon critical value, the more rejected the unit root test null hypothesis. So it can be concluded that there is no stationarity in this time series. Correlation processing is needed for this series. The commonly used method is first-order difference processing. Figure 7 shows the sequence diagram after processing:Figure 7
Schematic diagram of the original time series and the first-order difference processing sequence.ADF examines the processed sequence and concludes that 601728 time series has been processed with stationarity. Construct the ARIMA model according to the sequence, and construct the partial autocorrelation function PACF graph and the autocorrelation function ACF graph to determine the values ofa and b. Figure 8 shows the autocorrelation and partial correlation function graphs of the differential sequence.Figure 8
601728 smoothed first-order difference sequence ACF diagram and PACF diagram.Censoring refers to the phenomenon that the autocorrelation coefficient “oscillates to 0.” The order of ACF and PACF is related to the position of the truncation. As shown in Figure8, the AR component has a fixed order p of 8, and the MA component has a fixed order q of 1. Then the constructed ARIMA model is [22]:ARIMA8,1,1=AR8+Difference1+MA1.


## 2.1. Data Fusion

Data fusion is a formal framework whose main content is to integrate information from different sources with mathematical methods or technical means to obtain high-quality or valuable information [9, 10]. According to the definition of data fusion, the construction of available models (or frameworks) is an important content, which mainly includes functional models, structural models, and mathematical models. The difference between the three models lies in the different fusion angles, and the functional model focuses on the fusion process, as shown in Figure 1. It mainly involves the integration of the main functions, roles and interactions of various systems. The structural model focuses on information flow, and the fusion work form is the focus of fusion, emphasizing the information interaction process between the system and the outside world; the mathematical model mainly refers to the algorithm of data processing.Figure 1
Recommended revised data fusion model.


### 2.1.1. Functional Model

Level 0 signal/feature estimation: estimate the state of a signal or feature. Signals and features are patterns obtained by processing in different waysLevel 1 entity estimation: estimate the state or attributes of an entity. Entities generally refer to individualsThe second level of situation assessment: an estimate of the partial structure of the actual environment. It mainly completes the estimation of the connection between entities and the implicit connection with the state of related entitiesThe third level of impact estimation: the estimation of the availability and cost of each parameter state of the first three levels, including the estimation of the availability and cost of a certain action plan of the systemThe fourth-level process estimation: compare the system effect with the expected performance, and realize the self-assessment structure model of the fusion system


### 2.1.2. Structural Model

There are two classification methods for structural models. As shown in Figure2, a classification according to the degree of data processing before fusion can be divided into three typical structure types: centralized, distributed, and hybrid. The other can be divided into three structure types: pixel level, feature level, and decision level according to the resolution in the data fusion process [11].Figure 2
Structural model classification method.Multisource data fusion is a comprehensive discipline involving science, engineering, computing, and other fields. The related technologies are control theory, signal processing, software engineering, computational intelligence, information theory, probability and statistics, biological sciences, and cognitive psychology [12]. For the entire data fusion system, the processed data can come from one level or multiple conceptual levels. The processing method is mainly to integrate the data of one level first and then combine the results with the data of the next level. Therefore, the fusion process is actually a layer-by-layer abstraction, layer by layer to achieve the integration of multisource data from different levels.JDL, the Joint Conference of Laboratory Directors, was the first to give the most widely accepted definition of data fusion. The technologies are classified level by level according to the four-level fusion model of JDL except level 0 as follows:Level 1: target estimation level fusion can be divided into data association, state estimation, classification, and recognitionLevels 2 and 3: the task of situation assessment is to build connections between entities to obtain higher-level evaluation results, such as actions or events. The tasks that affect the estimation include estimating the hazard level, evaluating the opponent’s combat effectiveness, etc. The main algorithms are as follows: clustering algorithms, learning, reasoning, and retrieval strategiesLevel 4: the task of process optimization is to carry out monitoring and evaluation and implement guidance on the effect of fusion to reach the optimal conclusion. The main functions include the following: performance evaluation, fusion control, information source processing, and task management.


## 2.1.1. Functional Model

Level 0 signal/feature estimation: estimate the state of a signal or feature. Signals and features are patterns obtained by processing in different waysLevel 1 entity estimation: estimate the state or attributes of an entity. Entities generally refer to individualsThe second level of situation assessment: an estimate of the partial structure of the actual environment. It mainly completes the estimation of the connection between entities and the implicit connection with the state of related entitiesThe third level of impact estimation: the estimation of the availability and cost of each parameter state of the first three levels, including the estimation of the availability and cost of a certain action plan of the systemThe fourth-level process estimation: compare the system effect with the expected performance, and realize the self-assessment structure model of the fusion system


## 2.1.2. Structural Model

There are two classification methods for structural models. As shown in Figure2, a classification according to the degree of data processing before fusion can be divided into three typical structure types: centralized, distributed, and hybrid. The other can be divided into three structure types: pixel level, feature level, and decision level according to the resolution in the data fusion process [11].Figure 2
Structural model classification method.Multisource data fusion is a comprehensive discipline involving science, engineering, computing, and other fields. The related technologies are control theory, signal processing, software engineering, computational intelligence, information theory, probability and statistics, biological sciences, and cognitive psychology [12]. For the entire data fusion system, the processed data can come from one level or multiple conceptual levels. The processing method is mainly to integrate the data of one level first and then combine the results with the data of the next level. Therefore, the fusion process is actually a layer-by-layer abstraction, layer by layer to achieve the integration of multisource data from different levels.JDL, the Joint Conference of Laboratory Directors, was the first to give the most widely accepted definition of data fusion. The technologies are classified level by level according to the four-level fusion model of JDL except level 0 as follows:Level 1: target estimation level fusion can be divided into data association, state estimation, classification, and recognitionLevels 2 and 3: the task of situation assessment is to build connections between entities to obtain higher-level evaluation results, such as actions or events. The tasks that affect the estimation include estimating the hazard level, evaluating the opponent’s combat effectiveness, etc. The main algorithms are as follows: clustering algorithms, learning, reasoning, and retrieval strategiesLevel 4: the task of process optimization is to carry out monitoring and evaluation and implement guidance on the effect of fusion to reach the optimal conclusion. The main functions include the following: performance evaluation, fusion control, information source processing, and task management.


## 2.2. Related Theories of Stock Volatility

### 2.2.1. Basic Principles of Stock Forecasting

The efficient market hypothesis (EMH) theory subdivides the efficiency patterns of the financial market into three situations and points out the corresponding prediction methods for each efficiency pattern. The hypothesis believes that if participants in the financial securities market can understand all information without barriers, then when a valuable new interest is generated, investors will quickly grab and react to it. Under the action of this “perfect competition” mechanism, every new information will be fully reflected by the market price of securities. In other words, the information advantage cannot be used to obtain additional income in the market, and the price of the securities at this time is consistent with the true value of the securities. As shown in Figure3, the efficient market hypothesis points out that the three forms of market efficiency are the following [13]:
(1)
Weak-form efficiency. In this market, investors can allocate shares based on fundamental analysis. That is, starting from several factors such as the economic environment, industrial prosperity, and business operation conditions, choose a reasonable investment strategy. However, technical analysis is invalid; that is, it is impossible to predict the possible trend of stock prices through mathematical models or logical deliberation methods based on the historical performance of the securities market. This is because in a weakly efficient market, the price of a stock has fully reflected historical information that affects stock price changes, such as transaction price and transaction volume(2)
Semi-strong efficiency. In this market, investors can only obtain abnormal profits by using inside information, that is, by grasping some undisclosed information that has a greater impact on the stock price, using information advantages to obtain excess returns. The semi-strong efficient market assumes that some public information such as national economic policies, industrial economic conditions, and company financial conditions have been fully reflected in the fluctuations in stock prices(3)
Strong efficiency. In a strong efficiency market, investors are never likely to get excess profits. Powerful efficiency Information processing is fast, and all kinds of information are continuously collected, processed, analyzed, and used to exert powerful functionsFigure 3
Introduction to efficient market theory.In the three types of markets, technical analysis and fundamental analysis are difficult to effectively perform their functions. Therefore, the efficiency of the market must be verified before predicting stock prices. The test needs to follow a certain order, because the efficiency of the three markets is strengthened in sequence, so the test can be carried out sequentially starting from the weakly efficient market. The efficiency of weak form can be verified by serial autocorrelation function and stationarity ADF test. As a common tool for time series analysis, the autocorrelation function can clarify the relationship between the current stock price and the stock price of several lagging periods and can also explain the degree of influence of historical data on the stock price trend. The ADF test has a relatively common application in the market efficiency verification problem. It can reflect whether the market satisfies the conditions of random walk. The semi-strong efficiency is mainly verified by tracking the development of events. If the new financial data released by the company and the new financial policy proposed by the government can quickly affect the equilibrium of the stock price, then the current market can be regarded as a semi-strong effective market. As for strong efficiency, it is theoretically necessary to verify the relationship between inside information and stock returns, but it can often be concluded based on experience that inside information will greatly increase investment wealth. Today, national laws and industry codes of conduct clearly stipulate the illegal and illegal nature of insider trading.The exploration of market price prediction in the field of financial research has always been full of unique charm. Over the years, scholars from various countries have proposed various prediction models to reveal the inherent laws of stock price changes. Although these models have improved our ability to predict future price trends to a certain extent, the prediction results have not been completely satisfactory. The reason is that there are still many problems waiting to be overcome in the stock price forecasting, such as the uncertainty of the forecast, the high noise of the sample data, and the mixed information.


### 2.2.2. Stock Market Volatility

From a narrow perspective, stock market volatility refers to the volatility of stock prices, which are affected by various factors and fluctuate over time. Out of the emphasis on risk, investors are paying more and more attention to the volatility of the entire stock market. Investors buy and sell stocks to get high profits, but the benefits and risks are at the same time, and volatility can well reflect the degree of risk in obtaining benefits.According to the different attitudes of investors to risk, we can divide investors into three categories: they are risk appetite, risk aversion, and risk neutral. Different types of investors have different choices of risk and return [2] as shown in Table 1.Table 1
Different types of investors’ preference for risk and return.
Investor typeInvestment preferenceRisk appetiteHigh risk and high returnRisk neutralBetween two risksRisk aversionLow risk and low returnThe volatility of the stock market is directly proportional to the degree of investor risk aversion. Studying the volatility of the stock market can better guide investors to participate in investment decisions.In the past, the volatility of company stock returns was the focus of research. The company’s stock return volatility is expressed by the variance of the company’s stock’s monthly return in the current year, which measures the company’s operating risk. In fact, stock volatility is caused by investors’ frequent stock trading operations, so stock turnover rate is the best measure. The higher the stock turnover rate, the greater the stock volatility. In addition, there is a large amount of information noise in the stock market, which indicates volatility. Specifically, it is expressed as the synchronization of the price of multiple stocks with the performance of the market, that is, “the same rise and fall.” In comprehensive considerations, this article believes that the three indicators of stock turnover rate, stock return volatility, and stock price synchronicity should be considered at the same time on the market volatility.The first problem to be solved in the study of the volatility of the stock market is how to quantify the volatility of the stock market. The current methods to quantify the volatility of the stock market mainly include the following:(1) Range Method. This method measures the volatility of the stock market according to the difference between the extreme values in stock price fluctuations, and its quantitative formula is
(1)Bt=maxJt−minJt.Among them,Jt represents the extreme value in the stock volatility. The index selection of this method is rough, the accuracy of the volatility measurement is not high enough and it is not comparative. On the premise that stock market volatility obeys Brownian motion, it is mathematically deduced that the volatility in Brownian motion is just the standard deviation of the log price. Starting from the stock itself, the standard deviation of the logarithmic price of the stock is the standard deviation of the daily rate of return of the stock. Taken together, from the nature of Brownian motion, we can deduce that the volatility of the stock price is the volatility of the Brownian motion, and it is equal to the stock price. Daily volatility can be used to quantify stock market volatility. The calculation formula is as follows:
(2)γ⌢park,t=InGt−InDt24In2.(2) Spread Rate Method. Through the analysis and comparison of the range method, it is improved, and the relative amplitude is proposed to measure the volatility of the stock market. The specific calculation formula is as follows:
(3)ABt=maxJt−minJtmaxJt+minJt2×100%.(3) Standard Deviation Method. The spread rate method can only measure the local characteristics of volatility, and is not applicable to the overall level of volatility. Markowitz proposed in 1982 to use the standard deviation method to quantify the size of the stock market volatility [14]; the specific calculation formula is as follows:
(4)∂⌢2=1T∑x=1Tst−s,where ∂⌢2 represents the estimation of the method, st is the rate of return of the stock price at time t, and s is the mean value of st in the statistical time period.


## 2.2.1. Basic Principles of Stock Forecasting

The efficient market hypothesis (EMH) theory subdivides the efficiency patterns of the financial market into three situations and points out the corresponding prediction methods for each efficiency pattern. The hypothesis believes that if participants in the financial securities market can understand all information without barriers, then when a valuable new interest is generated, investors will quickly grab and react to it. Under the action of this “perfect competition” mechanism, every new information will be fully reflected by the market price of securities. In other words, the information advantage cannot be used to obtain additional income in the market, and the price of the securities at this time is consistent with the true value of the securities. As shown in Figure3, the efficient market hypothesis points out that the three forms of market efficiency are the following [13]:
(1)
Weak-form efficiency. In this market, investors can allocate shares based on fundamental analysis. That is, starting from several factors such as the economic environment, industrial prosperity, and business operation conditions, choose a reasonable investment strategy. However, technical analysis is invalid; that is, it is impossible to predict the possible trend of stock prices through mathematical models or logical deliberation methods based on the historical performance of the securities market. This is because in a weakly efficient market, the price of a stock has fully reflected historical information that affects stock price changes, such as transaction price and transaction volume(2)
Semi-strong efficiency. In this market, investors can only obtain abnormal profits by using inside information, that is, by grasping some undisclosed information that has a greater impact on the stock price, using information advantages to obtain excess returns. The semi-strong efficient market assumes that some public information such as national economic policies, industrial economic conditions, and company financial conditions have been fully reflected in the fluctuations in stock prices(3)
Strong efficiency. In a strong efficiency market, investors are never likely to get excess profits. Powerful efficiency Information processing is fast, and all kinds of information are continuously collected, processed, analyzed, and used to exert powerful functionsFigure 3
Introduction to efficient market theory.In the three types of markets, technical analysis and fundamental analysis are difficult to effectively perform their functions. Therefore, the efficiency of the market must be verified before predicting stock prices. The test needs to follow a certain order, because the efficiency of the three markets is strengthened in sequence, so the test can be carried out sequentially starting from the weakly efficient market. The efficiency of weak form can be verified by serial autocorrelation function and stationarity ADF test. As a common tool for time series analysis, the autocorrelation function can clarify the relationship between the current stock price and the stock price of several lagging periods and can also explain the degree of influence of historical data on the stock price trend. The ADF test has a relatively common application in the market efficiency verification problem. It can reflect whether the market satisfies the conditions of random walk. The semi-strong efficiency is mainly verified by tracking the development of events. If the new financial data released by the company and the new financial policy proposed by the government can quickly affect the equilibrium of the stock price, then the current market can be regarded as a semi-strong effective market. As for strong efficiency, it is theoretically necessary to verify the relationship between inside information and stock returns, but it can often be concluded based on experience that inside information will greatly increase investment wealth. Today, national laws and industry codes of conduct clearly stipulate the illegal and illegal nature of insider trading.The exploration of market price prediction in the field of financial research has always been full of unique charm. Over the years, scholars from various countries have proposed various prediction models to reveal the inherent laws of stock price changes. Although these models have improved our ability to predict future price trends to a certain extent, the prediction results have not been completely satisfactory. The reason is that there are still many problems waiting to be overcome in the stock price forecasting, such as the uncertainty of the forecast, the high noise of the sample data, and the mixed information.


## 2.2.2. Stock Market Volatility

From a narrow perspective, stock market volatility refers to the volatility of stock prices, which are affected by various factors and fluctuate over time. Out of the emphasis on risk, investors are paying more and more attention to the volatility of the entire stock market. Investors buy and sell stocks to get high profits, but the benefits and risks are at the same time, and volatility can well reflect the degree of risk in obtaining benefits.According to the different attitudes of investors to risk, we can divide investors into three categories: they are risk appetite, risk aversion, and risk neutral. Different types of investors have different choices of risk and return [2] as shown in Table 1.Table 1
Different types of investors’ preference for risk and return.
Investor typeInvestment preferenceRisk appetiteHigh risk and high returnRisk neutralBetween two risksRisk aversionLow risk and low returnThe volatility of the stock market is directly proportional to the degree of investor risk aversion. Studying the volatility of the stock market can better guide investors to participate in investment decisions.In the past, the volatility of company stock returns was the focus of research. The company’s stock return volatility is expressed by the variance of the company’s stock’s monthly return in the current year, which measures the company’s operating risk. In fact, stock volatility is caused by investors’ frequent stock trading operations, so stock turnover rate is the best measure. The higher the stock turnover rate, the greater the stock volatility. In addition, there is a large amount of information noise in the stock market, which indicates volatility. Specifically, it is expressed as the synchronization of the price of multiple stocks with the performance of the market, that is, “the same rise and fall.” In comprehensive considerations, this article believes that the three indicators of stock turnover rate, stock return volatility, and stock price synchronicity should be considered at the same time on the market volatility.The first problem to be solved in the study of the volatility of the stock market is how to quantify the volatility of the stock market. The current methods to quantify the volatility of the stock market mainly include the following:(1) Range Method. This method measures the volatility of the stock market according to the difference between the extreme values in stock price fluctuations, and its quantitative formula is
(1)Bt=maxJt−minJt.Among them,Jt represents the extreme value in the stock volatility. The index selection of this method is rough, the accuracy of the volatility measurement is not high enough and it is not comparative. On the premise that stock market volatility obeys Brownian motion, it is mathematically deduced that the volatility in Brownian motion is just the standard deviation of the log price. Starting from the stock itself, the standard deviation of the logarithmic price of the stock is the standard deviation of the daily rate of return of the stock. Taken together, from the nature of Brownian motion, we can deduce that the volatility of the stock price is the volatility of the Brownian motion, and it is equal to the stock price. Daily volatility can be used to quantify stock market volatility. The calculation formula is as follows:
(2)γ⌢park,t=InGt−InDt24In2.(2) Spread Rate Method. Through the analysis and comparison of the range method, it is improved, and the relative amplitude is proposed to measure the volatility of the stock market. The specific calculation formula is as follows:
(3)ABt=maxJt−minJtmaxJt+minJt2×100%.(3) Standard Deviation Method. The spread rate method can only measure the local characteristics of volatility, and is not applicable to the overall level of volatility. Markowitz proposed in 1982 to use the standard deviation method to quantify the size of the stock market volatility [14]; the specific calculation formula is as follows:
(4)∂⌢2=1T∑x=1Tst−s,where ∂⌢2 represents the estimation of the method, st is the rate of return of the stock price at time t, and s is the mean value of st in the statistical time period.


## 2.3. Introduction to Commonly Used Stock Market Indicators

### 2.3.1. Homeopathic Index (CCI)

The trend indicator is an overbought and oversold indicator. Overbought and oversold indicators in the market are mainly technical indicator graphics formed by calculating the running trend of stock prices. When the stock is overbought and hyped by the market, it is an overbought signal and a reference signal for risk selling. Conversely, when the stock is oversold and sold by the market, it is an oversold signal and a reference signal for an opportunity to buy a point. It judges whether the stock price has changed significantly by comparing the difference between the stock price on the day and the average value. CCI calculation formula:(5)CCIi=M−Kir×Ni,(6)M=max+min+close3,(7)Ki=∑x=1icloseii,(8)Ni=∑x=1iKi−closeii.Among them,M is the average value of the stock’s highest price, lowest price, and closing price; Ki represents the average closing price within the day; and r=0.015 is the calculation coefficient.


### 2.3.2. Rate of Change Indicator (ROC)

The rate of change indicator is to measure the relationship between current stock fluctuations and market supply and demand by comparing the closing price of the day with the previous period, so as to judge whether the market can reverse the price with stock fluctuations. ROC calculation formula:(9)ROCx=Ni−NNi×100.Among them,N represents the closing price of the stock on the day, and Ni represents the closing price of the stock before i. The calculation time period of the ROC indicator is generally 6 days, 12 days, or 24 days.


### 2.3.3. Relative Strength Index (RSI)

The relative strength indicator compares the average closing price within a certain period of time and analyzes the strength of the long and short sides to predict stock market changes. Because the RSI indicator can more sensitively reflect the changes in stock prices in the short term, it is widely used for short-term operations. RSI calculation formula:(10)RSIi=ZiZi+Di.Among them,Zi represents the average value of the total increase in stock prices in day i, and Di represents the average value of the total decrease in stock prices in day i.


### 2.3.4. Ultimate Volatility Index (UOS)

Extreme volatility index is to solve the sensitivity problem of oscillating index. Oscillator sensitivity refers to that for a certain technical indicator, under certain parameter setting conditions, after traversing and analyzing long-term historical data, when the indicator conditions are met, the price fluctuation of the investment product is consistent with the direction and range indicated by the indicator. Under the premise, when the indicator gives clear indication information, the corresponding price movement volume accounts for the percentage of the entire price movement volume. Oscillator sensitivity is a parameter that measures how quickly a technical indicator responds to price fluctuations. The parameters of the oscillator are different, and the results are also different. In order to maximize returns, investors should choose the best combination of parameters when using oscillating indicators. In fact, it is difficult for investors to choose appropriate cycle parameters. The ultimate volatility indicator is calculated by multiplying the three oscillation indicators with different periods by the corresponding constant factor to obtain the ultimate volatility indicator that comprehensively considers various oscillation indicators. After a series of parameter calculations, this indicator is more adaptable to different stock market conditions than a single-parameter oscillating indicator [15]. UOS calculation formula:
(11)AC1=∑x=1N1Cx−JDx∑x=1N1JDx−JXx,(12)AC2=∑x=1N2Cx−JDx∑x=1N2JDx−JXx,(13)AC3=∑x=1N3Cx−JDx∑x=1N3JDx−JXx,(14)UOS=AC1×N2×N3+AC2×N1×N3+AC3×N1×N2N1×N2+N1×N3+N2×N3.Among them,JDx is the larger value of the highest stock price on the xth day and the closing price of the stock on the x−1th day, JXx is the smaller value of the highest stock price on day x and the closing price of stock on day x−1, Cx represents the closing price of the stock on the first day, and N1, N2, and N3 are three time period parameters, set to 7, 14, and 28, respectively.


### 2.3.5. Simple Volatility Index (EMV)

The simple volatility indicator is a technical indicator that studies the relationship between changes in trading volume and stock prices. It can guide investors to buy the stock when the stock is highly concerned and the trading volume is active. And when other enthusiastic investors did not find that the stock’s trading volume was gradually decreasing and the stock price trend was about to reverse, they were guided to sell the stock in time to obtain additional income. EMV calculation formula:(15)Px=Gx+Dx2,(16)Qx=Gx−1+Dx−12,(17)Wx=Gx−Dx,(18)EMx=Px−Qx×WxVx,(19)EMVx=∑x=1NEMx.Among them,Gx is the highest stock price on the xth day, Dx is the lowest stock price on the xth day, Vx represents the stock trading volume on the xth day, and N represents the time period.


## 2.3.1. Homeopathic Index (CCI)

The trend indicator is an overbought and oversold indicator. Overbought and oversold indicators in the market are mainly technical indicator graphics formed by calculating the running trend of stock prices. When the stock is overbought and hyped by the market, it is an overbought signal and a reference signal for risk selling. Conversely, when the stock is oversold and sold by the market, it is an oversold signal and a reference signal for an opportunity to buy a point. It judges whether the stock price has changed significantly by comparing the difference between the stock price on the day and the average value. CCI calculation formula:(5)CCIi=M−Kir×Ni,(6)M=max+min+close3,(7)Ki=∑x=1icloseii,(8)Ni=∑x=1iKi−closeii.Among them,M is the average value of the stock’s highest price, lowest price, and closing price; Ki represents the average closing price within the day; and r=0.015 is the calculation coefficient.


## 2.3.2. Rate of Change Indicator (ROC)

The rate of change indicator is to measure the relationship between current stock fluctuations and market supply and demand by comparing the closing price of the day with the previous period, so as to judge whether the market can reverse the price with stock fluctuations. ROC calculation formula:(9)ROCx=Ni−NNi×100.Among them,N represents the closing price of the stock on the day, and Ni represents the closing price of the stock before i. The calculation time period of the ROC indicator is generally 6 days, 12 days, or 24 days.


## 2.3.3. Relative Strength Index (RSI)

The relative strength indicator compares the average closing price within a certain period of time and analyzes the strength of the long and short sides to predict stock market changes. Because the RSI indicator can more sensitively reflect the changes in stock prices in the short term, it is widely used for short-term operations. RSI calculation formula:(10)RSIi=ZiZi+Di.Among them,Zi represents the average value of the total increase in stock prices in day i, and Di represents the average value of the total decrease in stock prices in day i.


## 2.3.4. Ultimate Volatility Index (UOS)

Extreme volatility index is to solve the sensitivity problem of oscillating index. Oscillator sensitivity refers to that for a certain technical indicator, under certain parameter setting conditions, after traversing and analyzing long-term historical data, when the indicator conditions are met, the price fluctuation of the investment product is consistent with the direction and range indicated by the indicator. Under the premise, when the indicator gives clear indication information, the corresponding price movement volume accounts for the percentage of the entire price movement volume. Oscillator sensitivity is a parameter that measures how quickly a technical indicator responds to price fluctuations. The parameters of the oscillator are different, and the results are also different. In order to maximize returns, investors should choose the best combination of parameters when using oscillating indicators. In fact, it is difficult for investors to choose appropriate cycle parameters. The ultimate volatility indicator is calculated by multiplying the three oscillation indicators with different periods by the corresponding constant factor to obtain the ultimate volatility indicator that comprehensively considers various oscillation indicators. After a series of parameter calculations, this indicator is more adaptable to different stock market conditions than a single-parameter oscillating indicator [15]. UOS calculation formula:
(11)AC1=∑x=1N1Cx−JDx∑x=1N1JDx−JXx,(12)AC2=∑x=1N2Cx−JDx∑x=1N2JDx−JXx,(13)AC3=∑x=1N3Cx−JDx∑x=1N3JDx−JXx,(14)UOS=AC1×N2×N3+AC2×N1×N3+AC3×N1×N2N1×N2+N1×N3+N2×N3.Among them,JDx is the larger value of the highest stock price on the xth day and the closing price of the stock on the x−1th day, JXx is the smaller value of the highest stock price on day x and the closing price of stock on day x−1, Cx represents the closing price of the stock on the first day, and N1, N2, and N3 are three time period parameters, set to 7, 14, and 28, respectively.


## 2.3.5. Simple Volatility Index (EMV)

The simple volatility indicator is a technical indicator that studies the relationship between changes in trading volume and stock prices. It can guide investors to buy the stock when the stock is highly concerned and the trading volume is active. And when other enthusiastic investors did not find that the stock’s trading volume was gradually decreasing and the stock price trend was about to reverse, they were guided to sell the stock in time to obtain additional income. EMV calculation formula:(15)Px=Gx+Dx2,(16)Qx=Gx−1+Dx−12,(17)Wx=Gx−Dx,(18)EMx=Px−Qx×WxVx,(19)EMVx=∑x=1NEMx.Among them,Gx is the highest stock price on the xth day, Dx is the lowest stock price on the xth day, Vx represents the stock trading volume on the xth day, and N represents the time period.


## 2.4. Stock Analysis Method

### 2.4.1. Traditional Analysis Methods

The traditional analysis method is based on the observation and analysis of various characteristics of the stock itself [16]. The three analysis methods of fundamental analysis, technical analysis, and evolution analysis help investors have a certain degree of grasp of the trend of the stock market to a certain extent and can obtain a higher degree of accuracy in judging the future rise or fall of stocks. But its limitation is that it can only predict the trend, but cannot achieve a relatively accurate output of the magnitude of the fluctuation.(1) Fundamental Analysis. The main idea of fundamental analysis is to analyze stocks by analyzing the changes and developments of various basic factors that affect the trend of the stock market. Through the analysis of fundamentals, correctly grasp the factors that lead to stock price fluctuations and then analyze and decide the stocks to invest in. The fundamentals mainly include economic situation, economic policy, political system, and internal company factors [17]. Fundamental analysis is qualitative analysis. When using fundamental analysis to analyze various factors that affect stock prices, we can only determine the next trend of stock price changes, that is, rise or fall, and cannot accurately give the magnitude of the rise or fall. Fundamental analysis is more applicable to the analysis of the long-term investment.(2) Technical Analysis (K-Line). Technical analysis mainly uses historical data to predict the trend of the stock market through mathematical methods and discover its inherent laws. Its prerequisites are as follows: (1) market behavior contains all information and does not require specific analysis of specific factors; (2) stock price fluctuations are regular; (3) the market changes periodically, and analysts can get the law of changes in stock prices through induction and summary. Technical analysis puts aside external factors and simply analyzes the stock itself. The main research objects include graphics, forms, and technical indicators. Specifically, it includes stock trend, trading volume, new highs of stock prices, new lows of stock prices, K-line theory, wave theory, and other technical indicators and technical graphic analysis.(3) Evolution Analysis. Evolutionary analysis integrates the development and changes of the stock market with the idea of biological evolution. Analyze the stress, profitability, variability, adaptability, metabolism, plasticity, and cyclicality of the stock market; make rational judgments on market trends and future development; and provide evaluation conclusions for investment.


### 2.4.2. Modern Technical Analysis Methods

Modern technical analysis methods conduct scientific mathematical modeling of related variables by observing the changing characteristics of the related properties of stocks. It reduces the reliance on economics-related theories and analyzes it from a mathematical point of view. Nonlinear forecasting combines the characteristics of many disciplines, based on statistics, and according to the actual needs of actual problems, and brings data into related models for regression forecasting. It is more scientific, and the results obtained are generally more optimized [18].(1) Neural Network Prediction Method. The neural network prediction method is to train the existing past n sample data, establish the most suitable model, and use this model to predict the value of m time in the future. Taking past data as a sample does not mean that the requirements for the sample are high. The neural network has a strong ability of induction. For uncertain information, it can give appropriate substitute values through reasoning. This is also convenient for solving problems that cannot be solved simply by establishing a mathematical model. This is also convenient for solving problems that cannot be solved simply by establishing a mathematical model. Stock prices are generally nonlinearly distributed, with a certain degree of randomness and irregularities. Neural networks can also get better results for this.(2) Fuzzy Time Series Forecasting. The main research objects of fuzzy mathematics are uncertain things. Fuzzy mathematics is based on basic mathematics and introduces fuzzy concepts to obscure the definition of “yes” and “no.” Set a confidence interval between the two to expand the value range of a variable with a single value. The difference between fuzzy time series and traditional time series is that the value of fuzzy time series at a certain moment is a fuzzy number, which can also be described as a set. The value of a traditional time series at a certain moment is an accurate value. The general model of fuzzy time series forecasting can be expressed as the following formula:
(20)SVt=ao+a1t+a2t2+⋯+altl+ω,where SVt∈B,l∈N,ax∈B,x=1,2,3⋯,l. B is the set of fuzzy numbers, and ω is the random error expected to be zero.The fuzzy time series forecasting model is based on the coefficient and the fuzzy number of the time series, and the forecast result is also a fuzzy set. The evaluation standard of the traditional time series forecastSVt model is usually defined as the accuracy of the forecast result, while the fuzzy time series forecast model only needs to judge whether the actual change is included in the forecast result. Therefore, the practical range of fuzzy time series forecasting SVt is more extensive.


## 2.4.1. Traditional Analysis Methods

The traditional analysis method is based on the observation and analysis of various characteristics of the stock itself [16]. The three analysis methods of fundamental analysis, technical analysis, and evolution analysis help investors have a certain degree of grasp of the trend of the stock market to a certain extent and can obtain a higher degree of accuracy in judging the future rise or fall of stocks. But its limitation is that it can only predict the trend, but cannot achieve a relatively accurate output of the magnitude of the fluctuation.(1) Fundamental Analysis. The main idea of fundamental analysis is to analyze stocks by analyzing the changes and developments of various basic factors that affect the trend of the stock market. Through the analysis of fundamentals, correctly grasp the factors that lead to stock price fluctuations and then analyze and decide the stocks to invest in. The fundamentals mainly include economic situation, economic policy, political system, and internal company factors [17]. Fundamental analysis is qualitative analysis. When using fundamental analysis to analyze various factors that affect stock prices, we can only determine the next trend of stock price changes, that is, rise or fall, and cannot accurately give the magnitude of the rise or fall. Fundamental analysis is more applicable to the analysis of the long-term investment.(2) Technical Analysis (K-Line). Technical analysis mainly uses historical data to predict the trend of the stock market through mathematical methods and discover its inherent laws. Its prerequisites are as follows: (1) market behavior contains all information and does not require specific analysis of specific factors; (2) stock price fluctuations are regular; (3) the market changes periodically, and analysts can get the law of changes in stock prices through induction and summary. Technical analysis puts aside external factors and simply analyzes the stock itself. The main research objects include graphics, forms, and technical indicators. Specifically, it includes stock trend, trading volume, new highs of stock prices, new lows of stock prices, K-line theory, wave theory, and other technical indicators and technical graphic analysis.(3) Evolution Analysis. Evolutionary analysis integrates the development and changes of the stock market with the idea of biological evolution. Analyze the stress, profitability, variability, adaptability, metabolism, plasticity, and cyclicality of the stock market; make rational judgments on market trends and future development; and provide evaluation conclusions for investment.


## 2.4.2. Modern Technical Analysis Methods

Modern technical analysis methods conduct scientific mathematical modeling of related variables by observing the changing characteristics of the related properties of stocks. It reduces the reliance on economics-related theories and analyzes it from a mathematical point of view. Nonlinear forecasting combines the characteristics of many disciplines, based on statistics, and according to the actual needs of actual problems, and brings data into related models for regression forecasting. It is more scientific, and the results obtained are generally more optimized [18].(1) Neural Network Prediction Method. The neural network prediction method is to train the existing past n sample data, establish the most suitable model, and use this model to predict the value of m time in the future. Taking past data as a sample does not mean that the requirements for the sample are high. The neural network has a strong ability of induction. For uncertain information, it can give appropriate substitute values through reasoning. This is also convenient for solving problems that cannot be solved simply by establishing a mathematical model. This is also convenient for solving problems that cannot be solved simply by establishing a mathematical model. Stock prices are generally nonlinearly distributed, with a certain degree of randomness and irregularities. Neural networks can also get better results for this.(2) Fuzzy Time Series Forecasting. The main research objects of fuzzy mathematics are uncertain things. Fuzzy mathematics is based on basic mathematics and introduces fuzzy concepts to obscure the definition of “yes” and “no.” Set a confidence interval between the two to expand the value range of a variable with a single value. The difference between fuzzy time series and traditional time series is that the value of fuzzy time series at a certain moment is a fuzzy number, which can also be described as a set. The value of a traditional time series at a certain moment is an accurate value. The general model of fuzzy time series forecasting can be expressed as the following formula:
(20)SVt=ao+a1t+a2t2+⋯+altl+ω,where SVt∈B,l∈N,ax∈B,x=1,2,3⋯,l. B is the set of fuzzy numbers, and ω is the random error expected to be zero.The fuzzy time series forecasting model is based on the coefficient and the fuzzy number of the time series, and the forecast result is also a fuzzy set. The evaluation standard of the traditional time series forecastSVt model is usually defined as the accuracy of the forecast result, while the fuzzy time series forecast model only needs to judge whether the actual change is included in the forecast result. Therefore, the practical range of fuzzy time series forecasting SVt is more extensive.


## 2.5. Time Series Analysis Theory

The research object of time series analysis is a collection of data arranged in time. In real life, currency exchange rates between countries, daily closing prices of stocks, daily business turnover, daily maximum temperatures, and human electrocardiograms are all recorded in a time-series manner. To mine the deep information hidden in the sequence, time series analysis theory will be a very powerful “weapon.” With this tool, we can achieve two goals: first, recognize the operating mechanism that produced the sequence; second, make advance predictions of possible future situations or interfere with and control the current situation.


### 2.5.1. Stationarity Test

When making statistical inferences about a phenomenon based on historical data, it is usually necessary for the sequence to first satisfy theoretical assumptions with a certain degree of rationality, of which the stationarity assumption is the most important. The significance of stationarity is to ensure that the statistical properties will not change over time. According to the mathematical definition, stability can be divided into strict stability and wide stability [19]: strictly stable means that any statistical characteristics of time series will not differ from time to time, that is, the joint distribution of time series is only related to the time lag a and has nothing to do with the time node t. If the time series Xt satisfies the following conditions, the series is said to be strictly stationary. It can be expressed as:
(21)Ft1,t2,⋯,tmx1,x2,⋯,xm=Ft1+a,t2+a,⋯,tm+ax1,x2,⋯,xm∀tx,tx+a∈T,x=1,2,3,⋯,m.Broad stationary has relatively weak conditional requirements. It means that the mean function of the time series takes a fixed constant at any point in time and the covariance function is only related to the time interval terma. That is, if the time series always meets the following conditions for any t, s, and k, the series is said to be broadly stationary. It can be expressed as
(22)EXt2∞,EXt=κ,EXt−κtXs−κs=EXa−κaXa+s−t−κa+s−t.As shown in Figure4, according to the time series change, we can infer that there is no stationarity in the sequence of time series a. According to the sequence of time series b, although its long-term trend is uncertain, in the short term, fluctuations around a fixed value are obvious. Generally speaking, in terms of stationarity, the stationarity of b is obviously better than that of a.Figure 4
Comparison of stationarity of different series.Trend graphs and autocorrelation function graphs can show the stationarity of the time series, but the more commonly used test method is the unit root test [20]. The principle of the unit root test is to detect whether there is a root of 1 in the characteristic equation of the regression model, and the sequence with unit root can be smoothed by means such as difference. In statistical methods, ADF statistics can test the existence of unit roots. Here we mainly introduce the principles of ADF: the ADF test must be carried out in three cases, no intercept item and no trend item, including intercept item, and including intercept item and trend item, respectively, corresponding to the following formulas:
(23)Δyt=λyt−1+∑x=1mδtΔyt−x+ut,t=1,2,⋯,T,(24)Δyt=λyt−1+a+∑x=1mδtΔyt−x+ut,t=1,2,⋯,T,(25)Δyt=λyt−1+a+ηt+∑x=1mδtΔyt−x+ut,t=1,2,⋯,T.The null hypothesis and alternative hypothesis set by the ADF test are all about the value ofy, where Q0 is the null hypothesis.
(26)Q0:λ=0,Q1:λ0.Q0 means that a unit root is tested, and the sequence is not stationary; Q1 shows that the time series has no unit root and passed the stationarity test.


### 2.5.2. ARIMA Model

ARMA is the first model to consider in the process of modeling stationary time series, but the data series we need to deal with often show nonstationarity. Therefore, on the basis of ARMA, scholars have explored a theoretical model that can specifically analyze uneven data, that is, the ARIMA model. It is very similar to ARMA but adds a single integration process. The so-called single integration refers to the time series that needs to be differentiated to achieve stability. Corresponding to the “I” in the abbreviation of the name, it usually takes 1 to 2 in use to achieve the smoothing of the sequence.The establishment of the ARIMA(a,b,c) model needs to determine the values of three of the parameters [21], which are the nth order difference model, the moving average model MA, and the autoregressive model AR. Figure 5 shows the process of ARIMA building a stock time series forecasting model:Figure 5
Schematic diagram of the process of constructing a financial time series forecasting model based on ARIMA.Before using the ARIMA model, it is first necessary to verify whether the financial series constructed based on financial data is locally stable. If not, it needs to be smoothed. On the basis of the financial data set, an index of time is established, and the financial time series are constructed together with data such as the highest price (high), closing price (close), and opening price (open) as attributes as shown in Figure6.Figure 6
Financial time series chart.Subsequently, the stationarity of the financial time series was verified. Taking 601728 (China Telecom) as an example, the ADF test was performed on the original time series. It can be seen that the ADF statistics and they value are both greater than the Mackinnon critical value, the Mackinnon critical value is the one-sided test probability value proposed by McKinnon, which is used for the ADF significance level test. The smaller the Mackinnon critical value, the more rejected the unit root test null hypothesis. So it can be concluded that there is no stationarity in this time series. Correlation processing is needed for this series. The commonly used method is first-order difference processing. Figure 7 shows the sequence diagram after processing:Figure 7
Schematic diagram of the original time series and the first-order difference processing sequence.ADF examines the processed sequence and concludes that 601728 time series has been processed with stationarity. Construct the ARIMA model according to the sequence, and construct the partial autocorrelation function PACF graph and the autocorrelation function ACF graph to determine the values ofa and b. Figure 8 shows the autocorrelation and partial correlation function graphs of the differential sequence.Figure 8
601728 smoothed first-order difference sequence ACF diagram and PACF diagram.Censoring refers to the phenomenon that the autocorrelation coefficient “oscillates to 0.” The order of ACF and PACF is related to the position of the truncation. As shown in Figure8, the AR component has a fixed order p of 8, and the MA component has a fixed order q of 1. Then the constructed ARIMA model is [22]:ARIMA8,1,1=AR8+Difference1+MA1.


## 2.5.1. Stationarity Test

When making statistical inferences about a phenomenon based on historical data, it is usually necessary for the sequence to first satisfy theoretical assumptions with a certain degree of rationality, of which the stationarity assumption is the most important. The significance of stationarity is to ensure that the statistical properties will not change over time. According to the mathematical definition, stability can be divided into strict stability and wide stability [19]: strictly stable means that any statistical characteristics of time series will not differ from time to time, that is, the joint distribution of time series is only related to the time lag a and has nothing to do with the time node t. If the time series Xt satisfies the following conditions, the series is said to be strictly stationary. It can be expressed as:
(21)Ft1,t2,⋯,tmx1,x2,⋯,xm=Ft1+a,t2+a,⋯,tm+ax1,x2,⋯,xm∀tx,tx+a∈T,x=1,2,3,⋯,m.Broad stationary has relatively weak conditional requirements. It means that the mean function of the time series takes a fixed constant at any point in time and the covariance function is only related to the time interval terma. That is, if the time series always meets the following conditions for any t, s, and k, the series is said to be broadly stationary. It can be expressed as
(22)EXt2∞,EXt=κ,EXt−κtXs−κs=EXa−κaXa+s−t−κa+s−t.As shown in Figure4, according to the time series change, we can infer that there is no stationarity in the sequence of time series a. According to the sequence of time series b, although its long-term trend is uncertain, in the short term, fluctuations around a fixed value are obvious. Generally speaking, in terms of stationarity, the stationarity of b is obviously better than that of a.Figure 4
Comparison of stationarity of different series.Trend graphs and autocorrelation function graphs can show the stationarity of the time series, but the more commonly used test method is the unit root test [20]. The principle of the unit root test is to detect whether there is a root of 1 in the characteristic equation of the regression model, and the sequence with unit root can be smoothed by means such as difference. In statistical methods, ADF statistics can test the existence of unit roots. Here we mainly introduce the principles of ADF: the ADF test must be carried out in three cases, no intercept item and no trend item, including intercept item, and including intercept item and trend item, respectively, corresponding to the following formulas:
(23)Δyt=λyt−1+∑x=1mδtΔyt−x+ut,t=1,2,⋯,T,(24)Δyt=λyt−1+a+∑x=1mδtΔyt−x+ut,t=1,2,⋯,T,(25)Δyt=λyt−1+a+ηt+∑x=1mδtΔyt−x+ut,t=1,2,⋯,T.The null hypothesis and alternative hypothesis set by the ADF test are all about the value ofy, where Q0 is the null hypothesis.
(26)Q0:λ=0,Q1:λ0.Q0 means that a unit root is tested, and the sequence is not stationary; Q1 shows that the time series has no unit root and passed the stationarity test.


## 2.5.2. ARIMA Model

ARMA is the first model to consider in the process of modeling stationary time series, but the data series we need to deal with often show nonstationarity. Therefore, on the basis of ARMA, scholars have explored a theoretical model that can specifically analyze uneven data, that is, the ARIMA model. It is very similar to ARMA but adds a single integration process. The so-called single integration refers to the time series that needs to be differentiated to achieve stability. Corresponding to the “I” in the abbreviation of the name, it usually takes 1 to 2 in use to achieve the smoothing of the sequence.The establishment of the ARIMA(a,b,c) model needs to determine the values of three of the parameters [21], which are the nth order difference model, the moving average model MA, and the autoregressive model AR. Figure 5 shows the process of ARIMA building a stock time series forecasting model:Figure 5
Schematic diagram of the process of constructing a financial time series forecasting model based on ARIMA.Before using the ARIMA model, it is first necessary to verify whether the financial series constructed based on financial data is locally stable. If not, it needs to be smoothed. On the basis of the financial data set, an index of time is established, and the financial time series are constructed together with data such as the highest price (high), closing price (close), and opening price (open) as attributes as shown in Figure6.Figure 6
Financial time series chart.Subsequently, the stationarity of the financial time series was verified. Taking 601728 (China Telecom) as an example, the ADF test was performed on the original time series. It can be seen that the ADF statistics and they value are both greater than the Mackinnon critical value, the Mackinnon critical value is the one-sided test probability value proposed by McKinnon, which is used for the ADF significance level test. The smaller the Mackinnon critical value, the more rejected the unit root test null hypothesis. So it can be concluded that there is no stationarity in this time series. Correlation processing is needed for this series. The commonly used method is first-order difference processing. Figure 7 shows the sequence diagram after processing:Figure 7
Schematic diagram of the original time series and the first-order difference processing sequence.ADF examines the processed sequence and concludes that 601728 time series has been processed with stationarity. Construct the ARIMA model according to the sequence, and construct the partial autocorrelation function PACF graph and the autocorrelation function ACF graph to determine the values ofa and b. Figure 8 shows the autocorrelation and partial correlation function graphs of the differential sequence.Figure 8
601728 smoothed first-order difference sequence ACF diagram and PACF diagram.Censoring refers to the phenomenon that the autocorrelation coefficient “oscillates to 0.” The order of ACF and PACF is related to the position of the truncation. As shown in Figure8, the AR component has a fixed order p of 8, and the MA component has a fixed order q of 1. Then the constructed ARIMA model is [22]:ARIMA8,1,1=AR8+Difference1+MA1.


## 3. Stock Prediction Verification Experiment

### 3.1. Data Selection and Descriptive Analysis

Take the China Telecom stock in the A-shares of the above securities as an example, select the daily data of the stock from November 20, 2000, to November 19, 2021, and reserve the last twenty-one years as test data. The data includes five variables: China Telecom’s daily opening price, highest price, lowest price, closing price, and trading volume. The unit of stock price is yuan, and the unit of trading volume is lot. The data comes from Big Wisdom Software. In order to have a preliminary understanding of the data as a whole, we make a descriptive statistics of these five variables, as shown in Table2:Table 2
Descriptive analysis of each variable.
StatisticsOpening priceHighest priceLowest priceClosing priceVolumeMean2.5302.5502.5102.534134560000Max6.0106.1905.8705.94276540000Minimum-0.309-0.205-0.412-0.385678000Variance1.5261.6761.4321.5038.059e+11Standard deviation1.4031.4851.3911.40110310000Skewness0.9640.9430.9160.9572.185463Kurtosis0.5870.4760.5640.6155.435781It can be seen from the descriptive analysis that the skewness of the five variables are all greater than 0, showing a right-skewed distribution, indicating that the distribution of sequence values greater than the mean is more discrete. The kurtosis of the opening price, the highest price, the lowest price, and the closing price are all less than 3, and the frequency distribution curve is a flat peak curve. This shows that the central tendency of the sequence values of these four variables is not obvious, and the degree of variation of the sequence values is large. We also did a Jarque-Bera normality test on the opening prices of the main variables to be studied. The test result shows that theP value is less than 0.01, so the null hypothesis that the opening price is normally distributed is rejected.The test result shows that theP value is less than 0.01, so the null hypothesis that the opening price is normally distributed is rejected. Before modeling, the data should be tested for stationarity. Since the data is skewed to the right, we draw the sequence diagram after taking the logarithm. From Figure 9 of the opening price sequence, it can be seen that the sequence has a certain upward trend, which is obviously not stable, let alone white noise. So we try to make a first-order difference on the opening price data and use the unit root to test the stationarity of the series after the difference. Since the P value of the difference test result is less than 0.01, the null hypothesis is rejected.Figure 9
Logarithmic sequence diagram of opening price.It is considered that the stock sequence after the first-order difference is stable, and the corresponding ARMA model can be established for it. Observe the autocorrelation (ACF) and partial autocorrelation (PACF) of the differential sequence as shown in Figure10 to determine the order of the ARMA model. It can be seen from the correlation graph that the autocorrelation graph of the sequence after the difference shows a tailing situation, while the partial autocorrelation graph shows a fourth-order truncation. Therefore, we can try to establish an ARIMA(4,1,0) model for the opening price series and use the maximum likelihood method to estimate the parameters.Figure 10
The autocorrelation and partial autocorrelation of the sequence after the difference.Using Ljung-Box to perform white noise test on the residuals, the results are shown in Table3:Table 3
Ljung-Box test results.
X-squaredDfP-value0.027513120.85420.026894120.84390.027485120.85140.027132120.8497It can be seen that theP value of the Ljung-Box test of the residual sequence is greater than 0.01. Therefore, it can be regarded as a white noise sequence, and ARIMA(4,1,0) extracts most of the information in the sequence and can be used for prediction. The forecast of the opening price in the next five days is shown in Table 4:Table 4
Comparison of AR model prediction results and actual results.
TimePredictive value (¥)Actual value (¥)T12.537832.524T22.529652.495T32.528172.493T42.534212.506T52.530182.513In this experiment, the ARIMA prediction model is used to predict the stock price, and the obtained prediction result shows a small oscillation and tends to be stable, with a large confidence interval. It shows that the prediction result can be floated in a large range, and the prediction effect is very likely to be unsatisfactory. Comparing the obtained prediction results with the real data, the MSE predicted by the ARIMA model is calculated to be 2.35. For stock prices, which require high accuracy data, the mean square error of 2.35 is not ideal for predicting stock prices. Part of the code used in the article’s stock trading is shown in Figure11.Figure 11
Part of the code used in the article’s stock trading (some content comes from Baidu).


## 3.1. Data Selection and Descriptive Analysis

Take the China Telecom stock in the A-shares of the above securities as an example, select the daily data of the stock from November 20, 2000, to November 19, 2021, and reserve the last twenty-one years as test data. The data includes five variables: China Telecom’s daily opening price, highest price, lowest price, closing price, and trading volume. The unit of stock price is yuan, and the unit of trading volume is lot. The data comes from Big Wisdom Software. In order to have a preliminary understanding of the data as a whole, we make a descriptive statistics of these five variables, as shown in Table2:Table 2
Descriptive analysis of each variable.
StatisticsOpening priceHighest priceLowest priceClosing priceVolumeMean2.5302.5502.5102.534134560000Max6.0106.1905.8705.94276540000Minimum-0.309-0.205-0.412-0.385678000Variance1.5261.6761.4321.5038.059e+11Standard deviation1.4031.4851.3911.40110310000Skewness0.9640.9430.9160.9572.185463Kurtosis0.5870.4760.5640.6155.435781It can be seen from the descriptive analysis that the skewness of the five variables are all greater than 0, showing a right-skewed distribution, indicating that the distribution of sequence values greater than the mean is more discrete. The kurtosis of the opening price, the highest price, the lowest price, and the closing price are all less than 3, and the frequency distribution curve is a flat peak curve. This shows that the central tendency of the sequence values of these four variables is not obvious, and the degree of variation of the sequence values is large. We also did a Jarque-Bera normality test on the opening prices of the main variables to be studied. The test result shows that theP value is less than 0.01, so the null hypothesis that the opening price is normally distributed is rejected.The test result shows that theP value is less than 0.01, so the null hypothesis that the opening price is normally distributed is rejected. Before modeling, the data should be tested for stationarity. Since the data is skewed to the right, we draw the sequence diagram after taking the logarithm. From Figure 9 of the opening price sequence, it can be seen that the sequence has a certain upward trend, which is obviously not stable, let alone white noise. So we try to make a first-order difference on the opening price data and use the unit root to test the stationarity of the series after the difference. Since the P value of the difference test result is less than 0.01, the null hypothesis is rejected.Figure 9
Logarithmic sequence diagram of opening price.It is considered that the stock sequence after the first-order difference is stable, and the corresponding ARMA model can be established for it. Observe the autocorrelation (ACF) and partial autocorrelation (PACF) of the differential sequence as shown in Figure10 to determine the order of the ARMA model. It can be seen from the correlation graph that the autocorrelation graph of the sequence after the difference shows a tailing situation, while the partial autocorrelation graph shows a fourth-order truncation. Therefore, we can try to establish an ARIMA(4,1,0) model for the opening price series and use the maximum likelihood method to estimate the parameters.Figure 10
The autocorrelation and partial autocorrelation of the sequence after the difference.Using Ljung-Box to perform white noise test on the residuals, the results are shown in Table3:Table 3
Ljung-Box test results.
X-squaredDfP-value0.027513120.85420.026894120.84390.027485120.85140.027132120.8497It can be seen that theP value of the Ljung-Box test of the residual sequence is greater than 0.01. Therefore, it can be regarded as a white noise sequence, and ARIMA(4,1,0) extracts most of the information in the sequence and can be used for prediction. The forecast of the opening price in the next five days is shown in Table 4:Table 4
Comparison of AR model prediction results and actual results.
TimePredictive value (¥)Actual value (¥)T12.537832.524T22.529652.495T32.528172.493T42.534212.506T52.530182.513In this experiment, the ARIMA prediction model is used to predict the stock price, and the obtained prediction result shows a small oscillation and tends to be stable, with a large confidence interval. It shows that the prediction result can be floated in a large range, and the prediction effect is very likely to be unsatisfactory. Comparing the obtained prediction results with the real data, the MSE predicted by the ARIMA model is calculated to be 2.35. For stock prices, which require high accuracy data, the mean square error of 2.35 is not ideal for predicting stock prices. Part of the code used in the article’s stock trading is shown in Figure11.Figure 11
Part of the code used in the article’s stock trading (some content comes from Baidu).


## 4. Discussion

The article uses the ARIMA forecasting model to predict the volatility of stocks, and after analyzing the stationarity of the stocks, the unsteady data is processed with a first-order difference square sequence to obtain stable data. After that, the autocorrelation (ACF) and partial autocorrelation (PACF) diagrams of each data are analyzed by data modeling, the pricing of the model is determined, the ARIMA model is established, and the stock price is predicted based on the model. In actual application, due to various factors such as the market, enterprises, and policies, there is a large error between the results of experimental predictions and the actual results. Therefore, when predicting stock price fluctuations in the future, various factors should be considered, and comprehensive comparisons should be made to determine the stock forecast standard.


## 5. Conclusions

Combined with typical cases, compared with other research results, the article builds a new data model and analysis framework based on the characteristics of complex data objects, which has strong theoretical innovation significance and practical application value. With the rapid economic development today, stocks have become an important part of people’s lives. The huge benefits make more and more people join the ranks of stocks. However, wanting to get something for nothing is unrealistic, and speculation is not the right way to get returns in the stock market. This article uses ARIMA to predict and analyze stock prices, filter out effective signals through data, and process the information to determine the appropriate time series. Then model according to the time series, and predict the price fluctuation of the series according to the model. The experimental results of this article have certain guiding significance, but this article is only limited to the prediction of the closing price, ignoring the influence of external factors on the stock price and the mutual influence between stocks; in terms of data selection, this article only selects one stock data for analysis and modeling, and the data is still relatively single. As an interdisciplinary subject, the research on complex data prediction and classification methods will never end. With the rise of cloud computing, the Internet of Things, big data, and other emerging technologies and the continuous development of mathematical analysis methods, there are still many problems to be studied and discussed in the future. At the same time, sequence prediction has the problem of large amount of calculation and high modeling cost. In the future, we will optimize the shortcomings of the appeal and select more stable indicators for experimental prediction, so as to better guide users’ investment decisions. In practical applications, how to determine the corresponding analysis method according to the distribution and characteristics of massive data, and combine it with distributed parallel computing frameworks such as Map-Reduce, will be the next research direction of big data prediction and classification.



---

*Source: 6344064-2022-04-25.xml*