After more than two decades of development, the Chinese capital market has become increasingly mature, and stock investment has become an important part of people's daily lives. As the stock price is affected by many factors, its changing law has complex nonlinearity and randomness [1]. Therefore, establishing an effective stock price prediction method has extremely important theoretical significance and application value.

Domestic and foreign scholars have studied and discussed stock price forecasting from different perspectives and put forward various forecasting methods. At the earliest, scholars used autoregressive models, moving average autoregressive models, differential autoregressive moving average models, regression analysis methods, gray forecasting methods, and Markov chains to solve stock price prediction problems. However, due to violent price fluctuations and high noise, it exhibits complex nonlinearity and uncertainty. These linear prediction methods are difficult to reveal their inherent laws. Later, scholars proposed autoregressive conditional heteroscedasticity model (ARCH), generalized autoregressive conditional heteroscedasticity model (GARCH), artificial neural network (ANN), fuzzy neural network (FNN), BP neural network, RBF neural network, and support vector reversion Machine (SVR), and so on [2]. Currently, most of the single methods are used for stock price forecasting. Still, a single forecasting method cannot cover comprehensive and effective information about stock prices with complex and nonlinear stock price data. Therefore, the accuracy of the forecast results is relatively low. Aiming at the difficulty of a single model to fully utilize practical information, some scholars have proposed a stock price prediction method (CAR-SVM) that combines support vector machines (SVM) and autoregressive (CAR) and verified the effectiveness of the method through a case. However, the accuracy of combined prediction often depends heavily on the prediction accuracy of a single model, and the higher correlation between the prediction results of a single model will significantly reduce the combined prediction accuracy. In addition, issues such as the selection of a single model and the determination of combined weights will also affect the prediction accuracy to a large extent.

This article attempts to introduce error correction methods into the stock price forecasting research. This article proposes a new idea of improving the accuracy of stock price prediction by error prediction correction [3]. Firstly, the generalized autoregressive conditional heteroscedasticity forecasting model (GARCH) is used to make a preliminary forecast of stock prices. Then, a regression model is introduced to analyze and fit the unexplained part of the GARCH residual sequence and predict the future residuals. Finally, the error forecast value is used to correct the preliminary forecast value of the stock price to obtain the corrected forecast value [4]. Among them, correlation analysis is used to screen relevant influencing factors when selecting regression model variables. We introduce principal component analysis to extract the main information to reduce the dimensionality of independent variables. The analysis of the Shanghai Composite Index sample data shows that the corrected prediction accuracy has been significantly improved, which verifies the model's effectiveness.

The GARCH model is also the generalized autoregressive conditional heteroscedasticity model. It was obtained by Bollerslev, who extended some of the constraints of the ARCH model. Since the GARCH model was produced, it has been widely used in the financial field [5]. If the random variable _{t}_{t}_{0} > 0, _{1} ⋯ _{q}_{1} ⋯ _{p}

First, use the GARCH model to predict the future stock price. Due to the limitations of the GARCH model, the predicted residual sequence must contain unexplained components. Next, establish a regression model to simulate the residual sequence and apply the regression model to future residual sequence prediction [6]. Finally, the preliminary prediction results of GARCH are corrected with this predicted value. We eliminate redundant information between variables and apply correlation between variables and principal component analysis to screen the independent variables of the regression model.

Modeling in this paper includes three processes: (1) Using historical data GARCH modeling to fit and predict stock price sequence _{t}

The specific modeling and prediction process of the method proposed in this paper is shown in Figure 1.

This article selects the closing price of each trading day of the Shanghai Composite Index from October 09, 2016, to October 20, 2020, as a sample to analyze the latest development and changes of the Shanghai Composite Index. _{t}_{t}, t_{t}_{t}_{t}

_{t} sequence descriptive statistics.

N | 984 |
---|---|

Mean | −0.00091 |

Std Deviation | 0.019474 |

Maximum | 0.1255 |

Minimum | −0.0842 |

Skewness | 0.188468 |

Kurtosis | 6.830535 |

Jarque-Bera | 607.4183 |

Probability | 0 |

It can be seen from Table 1 that the kurtosis value of the time series of log returns _{t}

It can be seen from Table 2 that the AD test statistic of _{t}_{t}_{t}^{2} = 54.32103,

Stationarity test performance table.

variable | ADF statistics | Significance level (critical value) |
---|---|---|

Lnɛi | −28.79395 | (1%)–3.436782 |

(5%)–2.864269 | ||

(10%)–2.568275 |

The result of parameter estimation of the GARCH model is given. And we write the estimated results of the parameters into the GARCH regression equation [9]. Mean value equation:

Variance equation:

The coefficients ARCH(1) (i.e. _{1}) and GARCC(1) (i.e. _{1}) in the equation are all positive. It satisfies the constraints of the parameters and _{1} + _{1} = 0.99371 <1 [10]. Estimate the residuals of the 1st order lag, 10th order lag, and 20th order lag in the equation. Neither the F statistic nor the _{t}

We take the opening price, highest price, lowest price, transaction volume, and transaction value of the Shanghai Stock Exchange Index at the corresponding time and process the data as in (4). Denoted by _{1}, _{2}, _{3}, _{4}, _{5} respectively. Then analyze its correlation with the proper error sequence. It turns out that only _{1}, _{2}, and _{3}, have a certain correlation with the fitting error [11]. Then use principal component analysis to extract the information in influencing factors and reduce the dimensionality of independent variables. The variance contribution of independent variables and principal components is shown in Figure 3. The results show that the first two principal components account for 97% of the variability, while the first principal component occupies nearly 80%. Here, the first and second principal components are selected as the final independent variables of the regression model and denoted by _{1}, and _{2} respectively.

Table 4 reflects the principal component loading. The first component is positively correlated with the respective variables [12]. The second principal component is negatively correlated with the independent variable _{1} and independent variable _{3}, and positively correlated with the independent variable _{2}. Model the GARCH residuals accordingly. It can be seen from Table 3 that the available residual information (that is, the dependent variable

GARCH forecast results.

Date | Actual value | GARCH forecast (_{t} |
Error/% |
---|---|---|---|

2020/10/21 | 2317.275 | 2328.8085 | 0.50% |

2020/10/24 | 2370.333 | 2317.3251 | −2.24% |

2020/10/25 | 2409.672 | 2368.1104 | −1.72% |

2020/10/26 | 2427.48 | 2409.1882 | −0.75% |

2020/10/27 | 2435.614 | 2425.5667 | −0.41% |

2020/10/28 | 2473.41 | 2434.8203 | −1.56% |

2020/10/31 | 2468.25 | 2,471.70 | 0.14% |

2020/11/1 | 2470.019 | 2467.2555 | −0.11% |

2020/11/2 | 2,504.11 | 2468.4613 | −1.42% |

2020/11/3 | 2508.09 | 2502.9791 | −0.20% |

2020/11/4 | 2528.294 | 2506.6032 | −0.86% |

2020/11/7 | 2509.799 | 2,527.08 | 0.69% |

2020/11/8 | 2503.836 | 2508.3703 | 0.18% |

2020/11/9 | 2524.919 | 2502.5857 | −0.88% |

2020/11/10 | 2,479.54 | 2523.5189 | 1.77% |

2020/11/11 | 2,481.08 | 2478.2691 | −0.11% |

2020/11/14 | 2528.714 | 2479.7309 | −1.94% |

Principal component loading matrix.

Independent variable | 1st principal component | 2nd principal component | 3rd principal component |
---|---|---|---|

X1 | 0.617 | −0.3035 | −0.7261 |

X2 | 0.5031 | 0.8616 | 0.0674 |

X3 | 0.6052 | −0.4069 | 0.6842 |

We use the principal component loading matrix to construct the first component and the second principal component, and then use EVIEWS 7.0 to establish the regression equation based on these 12 sets of data as:

The ^{2} = 0.7197,

We put the results of the independent variables of the principal component analysis (the first principal component and the second principal component) into the above equation to predict the possible value of the GARCIV residual from November 8, 2020, to November 14, 2020.

Correct the GARCH prediction according to the predicted residual value to get the final predicted value. It can be seen from Table 5 that the corrected error is significantly reduced [14]. We can judge that the regression model has a certain contribution to improving the accuracy of stock price prediction modeling.

Regression equation residual prediction results.

Date | Actual value | GARCH residuals/% | Regression prediction residual/% | After correction/% |
---|---|---|---|---|

2020/11/8 | 2503.836 | 0.18 | 0.34 | −0.16 |

2020/11/9 | 2524.919 | −0.88 | −0.23 | −0.65 |

2020/11/10 | 2479.536 | 1.77 | 0.63 | 114 |

2020/11/11 | 2481.084 | −0.32 | −0.11 | −0.21 |

2020/11/14 | 2528.714 | −1.94 | −1.01 | −0.93 |

MAPE/% | 0.64 | 0.35 | ||

MSPE/% | 0.38 | 0.2 |

From the calculation results in the above table, it can be seen that the corrected average absolute percentage error (MAPE) and mean square percentage error (MSPE) are 0.35% and 0.20%. They are respectively lower than 0.64% and 0.38% predicted by GARCH before correction. The results show that regression prediction is very accurate for residual prediction, which significantly reduces the error of the GARCH model and makes up for the lack of consideration of external factors in the GARCH model. Therefore, the comprehensive model can accurately grasp the volatility of stock prices and the influence of external factors on stock prices. The prediction accuracy is high.

This paper introduces the idea of error correction into the study of stock price forecasting to establish a stock price forecasting model that integrates GARCH and regression methods. Firstly, a generalized autoregressive conditional heteroscedasticity prediction model is established. Secondly, an error regression prediction model is constructed using the error sequence as a sample, and the subsequent points of the sequence are predicted. Finally, the error forecast value is used to correct the preliminary forecast value of the stock price to obtain the corrected stock price forecast value. The analysis of the Shanghai Composite Index sample data shows that the corrected prediction accuracy has been significantly improved, which verifies the model's effectiveness.

#### GARCH forecast results.

Date | Actual value | GARCH forecast (_{t} |
Error/% |
---|---|---|---|

2020/10/21 | 2317.275 | 2328.8085 | 0.50% |

2020/10/24 | 2370.333 | 2317.3251 | −2.24% |

2020/10/25 | 2409.672 | 2368.1104 | −1.72% |

2020/10/26 | 2427.48 | 2409.1882 | −0.75% |

2020/10/27 | 2435.614 | 2425.5667 | −0.41% |

2020/10/28 | 2473.41 | 2434.8203 | −1.56% |

2020/10/31 | 2468.25 | 2,471.70 | 0.14% |

2020/11/1 | 2470.019 | 2467.2555 | −0.11% |

2020/11/2 | 2,504.11 | 2468.4613 | −1.42% |

2020/11/3 | 2508.09 | 2502.9791 | −0.20% |

2020/11/4 | 2528.294 | 2506.6032 | −0.86% |

2020/11/7 | 2509.799 | 2,527.08 | 0.69% |

2020/11/8 | 2503.836 | 2508.3703 | 0.18% |

2020/11/9 | 2524.919 | 2502.5857 | −0.88% |

2020/11/10 | 2,479.54 | 2523.5189 | 1.77% |

2020/11/11 | 2,481.08 | 2478.2691 | −0.11% |

2020/11/14 | 2528.714 | 2479.7309 | −1.94% |

#### Principal component loading matrix.

Independent variable | 1st principal component | 2nd principal component | 3rd principal component |
---|---|---|---|

X1 | 0.617 | −0.3035 | −0.7261 |

X2 | 0.5031 | 0.8616 | 0.0674 |

X3 | 0.6052 | −0.4069 | 0.6842 |

#### Stationarity test performance table.

variable | ADF statistics | Significance level (critical value) |
---|---|---|

Lnɛi | −28.79395 | (1%)–3.436782 |

(5%)–2.864269 | ||

(10%)–2.568275 |

#### CFt sequence descriptive statistics.

N | 984 |
---|---|

Mean | −0.00091 |

Std Deviation | 0.019474 |

Maximum | 0.1255 |

Minimum | −0.0842 |

Skewness | 0.188468 |

Kurtosis | 6.830535 |

Jarque-Bera | 607.4183 |

Probability | 0 |

#### Regression equation residual prediction results.

Date | Actual value | GARCH residuals/% | Regression prediction residual/% | After correction/% |
---|---|---|---|---|

2020/11/8 | 2503.836 | 0.18 | 0.34 | −0.16 |

2020/11/9 | 2524.919 | −0.88 | −0.23 | −0.65 |

2020/11/10 | 2479.536 | 1.77 | 0.63 | 114 |

2020/11/11 | 2481.084 | −0.32 | −0.11 | −0.21 |

2020/11/14 | 2528.714 | −1.94 | −1.01 | −0.93 |

MAPE/% | 0.64 | 0.35 | ||

MSPE/% | 0.38 | 0.2 |

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Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and 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learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model