Economic prediction method and system based on principal component regression model

Abstract

The invention provides an economic prediction method and system based on a principal component regression model. According to the method, the advantages of principal component analysis and multiple regression are fused, and the defects existing in statistical method prediction are overcome by using the principal component analysis method, so that influence factors of economic development are better mined, and economic data are accurately predicted.

Description

Technical Field

[0001] The invention relates to an economic forecasting method and system based on a principal component regression model, and belongs to the technical field of economics and computer science. Background Art

[0002] With the development of society and the advancement of science and technology, economic data, as one of the most basic data, can reflect the development status and infrastructure construction of a region. The stability of economic forecasting models and the accuracy of forecast results play a vital role in social development planning. However, in actual social development, economic data is affected by many factors, resulting in low forecasting accuracy of many forecasting models.

[0003] Existing economic forecasting models mainly include time series forecasting models, statistical method forecasting models, and qualitative forecasting models. Time series models are mainly based on historical data for forecasting, and often lack consideration of economic theory, resulting in poor forecasting results when there is not enough historical data or the data quality is not high. Statistical method forecasting models may experience information overload when processing large amounts of data, making it difficult to identify which factors are the key variables affecting economic changes. Qualitative forecasting methods rely on the forecaster's experience and judgment, and may lack objectivity and accuracy. Summary of the invention

[0004] In view of the above problems, the present invention proposes an economic forecasting method and system based on the principal component regression model to overcome the shortcomings of statistical method forecasting, so as to better explore the influencing factors of economic development and accurately predict economic data.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] In a first aspect, an embodiment of the present invention provides an economic forecasting method based on a principal component regression model, which includes:

[0007] Collect historical economic data and its influencing factors as basic data;

[0008] Preprocessing the basic data and classifying them according to different time scales and data types;

[0009] Perform feature engineering and standardization on the preprocessed and classified data, and select target feature indicators with high relevance to economic forecasting;

[0010] The principal component analysis method is used to perform dimensionality reduction processing on the target characteristic index to reduce the amount of characteristic data and retain important information;

[0011] Based on multiple linear regression, the principal components after dimensionality reduction were selected as independent variables to construct a regression model;

[0012] Training the regression model, wherein the effect and prediction accuracy of the prediction model are evaluated through residual analysis based on historical data;

[0013] Output prediction results based on the trained model.

[0014] Based on the above method, optionally, the preprocessing of the basic data includes:

[0015] The Z-scor method is used to detect outliers in the data set, and its calculation formula is:

[0016]

[0017] Where X is a single observation, μ is the mean of the sample in which the observation is located, and σ is the standard deviation of the sample;

[0018] Use Newton interpolation to fill in the outliers, and use Newton interpolation to fit the curve to ensure that the interpolation polynomial and the fitted function have the same function value and high-order derivative value at the known points. The defined Newton interpolation function is:

[0019] P n (x)=f(x0)+f[x0,x1](x-x0)+f[x0,x1,x2](x-x0)(x-x1)+…+f[x0,x1,…,x n ](x-x0)…(xx n-1 )

[0020] Among them, f[x0,x1,…,x n ] is the original function f(x) with respect to x0,x1,…,x n The n-order difference quotient of n The relationship between (x) and the original function f(x) is:

[0021] f(x)=P n (x)+R n (x)

[0022] Among them, R n (x) is the remainder;

[0023] The data is standardized, and the specific formula is:

[0024]

[0025] Among them, x ij is the jth observed value of the ith influencing factor, zx ij is the jth observation value of the i-th influencing factor after standardization, is the mean value of the i-th influencing factor, σ iis the variance of the i-th influencing factor.

[0026] Based on the above method, optionally, the feature engineering and standardization processing of the preprocessed and classified data includes:

[0027] Ridge regression is used to perform feature selection on preprocessed and classified data. The specific formula is:

[0028]

[0029] Among them, β is the vector parameter of the model, y i is the target variable for the ith observation, X i is the feature vector of the i-th observation, n is the number of samples, p is the number of features, and λ is the regularization parameter used to control the strength of regularization;

[0030] Perform max-min normalization on the selected features.

[0031] Based on the above method, optionally, the target characteristic indicators highly correlated with economic forecasts are selected, including:

[0032] The Spearman rank correlation coefficient is used to evaluate the correlation between historical economic data and its influencing factor data. The specific steps are as follows;

[0033] (1) Convert data into levels and process them appropriately during calculations;

[0034] (2) Calculate the level difference between the influencing factors and the historical data of the model to be predicted. The formula is:

[0035] d i =r xi -r yi

[0036] Among them, r xi and r yi Represent the levels of two variables respectively;

[0037] (3) Calculate the sum of squares of grade differences:

[0038]

[0039] (4) Calculate the Spearman rank correlation coefficient:

[0040]

[0041] Where n is the total number of observations; Spearman's rank coefficient r s The value range is -1 to 1. The stronger the positive correlation, the s The closer it is to 1, the stronger the negative correlation. sThe closer it is to -1.

[0042] Based on the above method, optionally, the principal component analysis method is used to perform dimension reduction processing on the target feature index, including:

[0043] Compute the covariance matrix:

[0044]

[0045] in, is the mean of the ith index after standardization, is the mean of the mth index after standardization, and the eigenvalue and eigenvector of the matrix are calculated;

[0046] Solve for the principal components:

[0047]

[0048] Where p is the number of eigenvalues ​​of the covariance matrix, λ1,λ2,λ3,…,λp are the eigenvalues, and v1,v2,v3,…,vp are the corresponding eigenvectors;

[0049] Calculate the contribution rate of the i-th principal component. The calculation formula is:

[0050]

[0051] Among them, C i is the contribution rate of the ith principal component.

[0052] Based on the above method, optionally, the regression model of the multiple linear regression analysis is:

[0053]

[0054] Where x1, x2, ..., x m is the independent variable that affects the dependent variable y, β1,…,β m are the correlation coefficients corresponding to each independent variable, β0 is the intercept term, and ε is the error term.

[0055] Based on the above method, optionally, the test of model fit includes:

[0056] Residual analysis and residual distribution test, wherein the residual distribution test includes residual autocorrelation test and model prediction accuracy assessment.

[0057] In a second aspect, an embodiment of the present invention further provides an economic forecasting system based on a principal component regression model, which includes:

[0058] Data acquisition module, used to collect historical economic data and its influencing factors as basic data;

[0059] A preprocessing module, used for preprocessing the basic data and classifying them according to different time scales and data types;

[0060] Feature screening module, which is used to perform feature engineering and standardization on preprocessed and classified data, and select target feature indicators with high relevance to economic forecasting;

[0061] A dimension reduction processing module is used to perform dimension reduction processing on the target feature index by using principal component analysis method to reduce the amount of feature data and retain important information;

[0062] The model building module is used to build a regression model based on multiple linear regression by selecting the principal components after dimensionality reduction as independent variables;

[0063] A model training module, used to train the regression model, wherein the effect and prediction accuracy of the prediction model are evaluated through residual analysis based on historical data;

[0064] The prediction module is used to output prediction results based on the trained model.

[0065] The economic forecasting method and system based on the principal component regression model provided by the present invention combine the advantages of principal component analysis and multivariate regression, and use the principal component analysis method to overcome the shortcomings of statistical method prediction, so as to better explore the influencing factors of economic development and accurately predict economic data. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] The accompanying drawings herein are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the present invention, and together with the specification are used to explain the principles of the present invention. In addition, these drawings and text descriptions are not intended to limit the scope of the present invention in any way, but to illustrate the concept of the present invention for those skilled in the art by reference to specific embodiments.

[0067] Figure 1 A schematic flow chart of an economic forecasting method based on a principal component regression model provided by one embodiment of the present invention;

[0068] Figure 2 A real-time flow chart of an economic forecasting method based on a principal component regression model provided by one embodiment of the present invention;

[0069] Figure 3 A schematic diagram of the structure of an economic forecasting system based on a principal component regression model provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0070] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In the absence of conflict, the following embodiments and features in the embodiments can be combined with each other.

[0071] Economic forecasting can help governments and enterprises make more scientific decisions. By predicting future economic trends, the government can formulate corresponding fiscal and monetary policies to maintain stable economic growth. At the same time, since economic data and power data are strongly correlated, economic forecasting helps the power system to better plan power generation and transmission strategies. Therefore, the development of an economic forecasting model has important practical significance for the development of the economy and society and the stability of the power system. Although there are some economic forecasting methods, they often have certain limitations and fail to consider the joint influence of multiple factors, especially the strong correlation between economic data and power system data.

[0072] Existing economic forecasting models mainly include time series forecasting models, statistical method forecasting models, and qualitative forecasting models. Time series forecasting models can reveal trends, cyclical and seasonal patterns in data and are used for forecasting and predictive analysis. However, these models are sensitive to noise and outliers, require certain assumptions to be met, such as data stationarity, and have limited forecasting accuracy. Statistical method forecasting models are based on certain mathematical and statistical assumptions. These models can provide accurate forecasts when processing large amounts of data, but they often assume that there is a linear relationship between variables, are sensitive to outliers, and are limited in their application to multi-classification problems. Qualitative forecasting models rely on the experience and intuition of experts. These methods are very useful when data is insufficient or influencing factors are complex, but are susceptible to subjective factors, lack quantitative precision, and are easily limited by personal knowledge, experience, and ability.

[0073] In view of the above problems, the present invention aims to provide a new economic forecasting method, which combines the advantages of principal component analysis and multivariate regression, and uses the principal component analysis method to overcome the shortcomings of statistical method prediction, so as to better explore the influencing factors of economic development and accurately predict economic data. The following non-limiting description of the specific implementation scheme is given through several examples or embodiments.

[0074] like Figure 1 As shown, an embodiment of the present invention provides an economic forecasting method based on a principal component regression model, comprising the following steps:

[0075] Step S101: Collect historical economic data and its influencing factor data as basic data.

[0076] Specifically, the historical economic data of a certain region and its influencing factors data can be used as basic data.

[0077] In some embodiments, historical economic data and its influencing factors are shown in the following table:

[0078] type Influencing factors Economic development factors Historical GDP data, fixed asset investment, scientific and technological research and development investment, industrial added value, etc. Industrial structure factors Value added, employment, fixed asset investment, etc. of the primary, secondary and tertiary industries Energy structure factors Consumption and proportion of various energy sources such as coal, oil, natural gas, electricity, and renewable energy

[0079] Step S102: pre-process the basic data and classify them according to different time scales and data types.

[0080] Specifically, by preprocessing the basic data, the accuracy and effectiveness of the data can be improved.

[0081] Furthermore, preprocessing the basic data may specifically include:

[0082] The Z-scor method is used to detect outliers in the data set, and its calculation formula is:

[0083]

[0084] Where X is a single observation, μ is the mean of the sample in which the observation is located, and σ is the standard deviation of the sample;

[0085] Use Newton interpolation to fill in the outliers, and use Newton interpolation to fit the curve to ensure that the interpolation polynomial and the fitted function have the same function value and high-order derivative value at the known points. The defined Newton interpolation function is:

[0086] P n (x)=f(x0)+f[x0,x1](x-x0)+f[x0,x1,x2](x-x0)(x-x1)+…+f[x0,x1,…,x n ](x-x0)…(xx n-1 )

[0087] Among them, f[x0,x1,…,x n ] is the original function f(x) with respect to x0,x1,…,x n The n-order difference quotient of n The relationship between (x) and the original function f(x) is:

[0088] f(x)=P n (x)+R n (x)

[0089] Among them, R n (x) is the remainder;

[0090] The data is standardized, and the specific formula is:

[0091]

[0092] Among them, x ij is the jth observed value of the ith influencing factor, zx ij is the jth observation value of the i-th influencing factor after standardization, is the mean value of the i-th influencing factor, σ i is the variance of the i-th influencing factor.

[0093] Step S103: Perform feature engineering and standardization on the preprocessed and classified data, and select target feature indicators with high relevance to economic forecasting.

[0094] Specifically, feature engineering is the process of transforming raw data into features suitable for machine learning models, and standardization is the step of adjusting features to the same scale to improve the performance and convergence speed of the model.

[0095] In some embodiments, feature engineering and standardization are performed on the preprocessed and classified data, including:

[0096] Ridge regression is used to perform feature selection on preprocessed and classified data. The specific formula is:

[0097]

[0098] Among them, β is the vector parameter of the model, y i is the target variable for the ith observation, X i is the feature vector of the i-th observation, n is the number of samples, p is the number of features, and λ is the regularization parameter used to control the strength of regularization;

[0099] Perform max-min normalization on the selected features.

[0100] The formula for max-min normalization is:

[0101]

[0102] Among them, x' is the original feature data, x max is the maximum value of the feature data, x min is the minimum value of the feature data. Through the maximum-minimum normalization process, the feature can be scaled to the range of [0,1].

[0103] In some embodiments, since there are many variables in the prediction process, Ridge regression is selected to perform feature selection. Further, using Ridge regression to select target feature indicators with high correlation with economic forecasting may specifically include:

[0104] The Spearman rank correlation coefficient is used to evaluate the correlation between historical economic data and its influencing factor data. The specific steps are as follows;

[0105] (1) Convert data into levels and process them appropriately during calculations;

[0106] (2) Calculate the level difference between the influencing factors and the historical data of the model to be predicted. The formula is:

[0107] d i =r xi -r yi

[0108] Among them, r xi and r yi Represent the levels of two variables respectively;

[0109] (3) Calculate the sum of squares of grade differences:

[0110]

[0111] (4) Calculate the Spearman rank correlation coefficient:

[0112]

[0113] Where n is the total number of observations; Spearman's rank coefficient r s The value range is -1 to 1. The stronger the positive correlation, the s The closer it is to 1, the stronger the negative correlation. s The closer it is to -1.

[0114] Step S104: Use principal component analysis to perform dimensionality reduction processing on the target feature index to reduce the amount of feature data and retain important information.

[0115] Specifically, Principal Component Analysis (PCA) is a commonly used dimensionality reduction technique, which is mainly used to reduce the dimension of data set features while retaining the main information of the data as much as possible. In high-dimensional data analysis, PCA helps eliminate redundancy, remove noise, and improve the interpretability of data.

[0116] The specific implementation process of using principal component analysis to reduce the dimension of target feature indicators is as follows:

[0117] Compute the covariance matrix:

[0118]

[0119] in, is the mean of the ith index after standardization, is the mean of the mth index after standardization, and the eigenvalue and eigenvector of the matrix are calculated;

[0120] Solve for the principal components:

[0121]

[0122] Where p is the number of eigenvalues ​​of the covariance matrix, λ1,λ2,λ3,…,λp are the eigenvalues, and v1,v2,v3,…,vp are the corresponding eigenvectors;

[0123] Calculate the contribution rate of the i-th principal component. The calculation formula is:

[0124]

[0125] Among them, C i is the contribution rate of the ith principal component.

[0126] Based on the contribution rate, the principal components after dimensionality reduction can be determined.

[0127] Step S105: Based on multiple linear regression, the principal components after dimensionality reduction are selected as independent variables to construct a regression model.

[0128] Specifically, the regression model of the multiple linear regression analysis is:

[0129]

[0130] Where x1, x2, ..., x m is the independent variable that affects the dependent variable y, β1,…,β m are the correlation coefficients corresponding to each independent variable, β0 is the intercept term, and ε is the error term.

[0131] The parameters β0, β1, …, β in the regression model m The least squares method is used for estimation, that is, the estimated value should be selected Make When j = 0, 1, 2, ..., m, the error sum of squares reaches the minimum. The calculation formula of the error sum of squares Q is:

[0132]

[0133] To this end,

[0134]

[0135] have to:

[0136]

[0137] After sorting, it is transformed into the following normal equations:

[0138]

[0139] The matrix form of the normal equations is:

[0140] X T Xβ=X T Y

[0141] When the matrix X has full column rank, X T X is a reversible square matrix, and the solution is:

[0142]

[0143] Substitute β back into the original regression model to get the estimated value of y:

[0144]

[0145] Step S106: training the regression model, wherein the effect and prediction accuracy of the prediction model are evaluated through residual analysis based on historical data.

[0146] After the regression model is constructed, the actual data of the principal components obtained by the above steps can be used for model training. In order to ensure the effectiveness of the training model, the effect and prediction accuracy of the prediction model are evaluated through residual analysis based on historical data.

[0147] Furthermore, the test of model fit includes: residual analysis and residual distribution test, and the residual distribution test includes residual autocorrelation test and model prediction accuracy assessment.

[0148] Among them, (1) residual analysis

[0149]

[0150] Among them, y t is the observed value, is the model prediction value.

[0151] (2) Residual distribution test

[0152] On the basis of residual analysis, the residual distribution is evaluated by drawing a residual histogram to test whether the residual distribution satisfies the normal distribution. This step is very important for correlation testing.

[0153] Residual autocorrelation test

[0154] Check whether the model adequately captures the time series characteristics of the data, and check whether the residuals show time series autocorrelation based on the residual distribution test.

[0155] Model prediction accuracy evaluation:

[0156] The root mean square error is used to test the accuracy of the model prediction. Based on the residual analysis, the residual sum of squares is calculated as follows:

[0157]

[0158] The formula for calculating the root mean square error is:

[0159]

[0160] Among them, the smaller the root mean square error value, the smaller the difference between the predicted value and the observed value, which means that the prediction accuracy of the model is higher; the larger the root mean square error value, the greater the difference between the predicted value and the observed value, which means that the prediction accuracy of the model is lower.

[0161] Step S107: Output prediction results based on the trained model.

[0162] After training the final model, actual economic forecasts can be made based on it. Figure 2 shown.

[0163] Through the above scheme, the advantages of principal component analysis and multiple regression are integrated, and the principal component analysis method is used to overcome the shortcomings of statistical method prediction, so as to better explore the influencing factors of economic development and accurately predict economic data.

[0164] In addition, an embodiment of the present invention provides an economic forecasting system based on a principal component regression model. Figure 3 As shown, the system includes:

[0165] The data acquisition module 31 is used to collect historical economic data and its influencing factor data as basic data;

[0166] A preprocessing module 32, used to preprocess the basic data and classify them according to different time scales and data types;

[0167] The feature screening module 33 is used to perform feature engineering and standardization on the preprocessed and classified data, and select target feature indicators with high relevance to economic forecasting;

[0168] A dimension reduction processing module 34 is used to perform dimension reduction processing on the target feature index by using a principal component analysis method to reduce the amount of feature data and retain important information;

[0169] A model building module 35 is used to build a regression model based on multiple linear regression by selecting the principal components after dimensionality reduction as independent variables;

[0170] A model training module 36 is used to train the regression model, wherein the effect and prediction accuracy of the prediction model are evaluated by residual analysis based on historical data;

[0171] The prediction module 37 is used to output prediction results based on the trained model.

[0172] Among them, regarding the specific implementation methods of each module of the above-mentioned economic forecasting system based on the principal component regression model, reference can be made to the corresponding contents in the aforementioned method embodiments, which will not be repeated here.

[0173] It can be understood that the same or similar parts of the above embodiments can be referenced to each other, and the contents not described in detail in some embodiments can refer to the same or similar contents in other embodiments.

[0174] It should be noted that, in the description of the present invention, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance. In addition, in the description of the present invention, unless otherwise specified, the meaning of "plurality" refers to at least two.

[0175] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code that includes one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present invention belong.

[0176] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0177] A person skilled in the art may understand that all or part of the steps in the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0178] In addition, each functional unit in each embodiment of the present invention may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium. The above-mentioned storage medium may be a read-only memory, a disk or an optical disk, etc.

[0179] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0180] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. An economic forecasting method based on a principal component regression model, characterized in that: include: Collect historical economic data and its influencing factors as basic data; The basic data are preprocessed and classified according to different time scales and data types: Perform feature engineering and standardization on the preprocessed and classified data, and select target feature indicators with high relevance to economic forecasting; The principal component analysis method is used to perform dimensionality reduction processing on the target characteristic index to reduce the amount of characteristic data and retain important information; Based on multiple linear regression, the principal components after dimensionality reduction are selected as independent variables to construct a regression model: Training the regression model, wherein the effect and prediction accuracy of the prediction model are evaluated through residual analysis based on historical data; Output prediction results based on the trained model.

2. The method according to claim 1, characterized in that The preprocessing of the basic data comprises: The Z-scor method is used to detect outliers in the data set, and its calculation formula is: Where X is a single observation, μ is the mean of the sample in which the observation is located, and σ is the standard deviation of the sample; Use Newton interpolation to fill in the outliers, and use Newton interpolation to fit the curve to ensure that the interpolation polynomial and the fitted function have the same function value and high-order derivative value at the known points. The defined Newton interpolation function is: P n (x) = f(x0) + f[x0, x1](x-x0) + f[x0, x1, x2](x-x0)(x-x1) +... + f[x0, x1,..., x n ](x-x0)...(xx n-1 ) where f[x0, x1, ..., x n ] is the original function f(x) with respect to x0, x1, ..., x n The n-order difference quotient of n The relationship between (x) and the original function f(x) is: f(x)=P n (x)+R n (x) Among them, R n (x) is the remainder; The data is standardized, and the specific formula is: Among them, x ij is the jth observed value of the ith influencing factor, zx ij is the jth observation value of the i-th influencing factor after standardization, is the mean value of the i-th influencing factor, σ i is the variance of the i-th influencing factor.

3. The method according to claim 2, characterized in that The feature engineering and standardization processing of the preprocessed and classified data includes: Ridge regression is used to perform feature selection on preprocessed and classified data. The specific formula is: Among them, β is the vector parameter of the model, y i is the target variable for the ith observation, X i is the eigenvector of the ith observation, n is the number of samples, p is the number of features, and α is the regularization parameter used to control the strength of regularization; Perform max-min normalization on the selected features.

4. The method according to claim 3, characterized in that The target characteristic indicators selected that are highly correlated with economic forecasts include: The Spearman rank correlation coefficient is used to evaluate the correlation between historical economic data and its influencing factor data. The specific steps are as follows; (1) Convert data into levels and process them appropriately during calculations; (2) Calculate the level difference between the influencing factors and the historical data of the model to be predicted. The formula is: d i ＝r xi -r yi Among them, r xi and r yi Represent the levels of two variables respectively; (3) Calculate the sum of squares of grade differences: (4) Calculate the Spearman rank correlation coefficient: Where n is the total number of observations; Spearman's rank coefficient r s The value range is -1 to 1. The stronger the positive correlation, the s The closer it is to 1, the stronger the negative correlation. s The closer it is to -1.

5. The method according to claim 4, characterized in that The principal component analysis method is used to perform dimension reduction processing on the target feature index, including: Compute the covariance matrix: in, is the mean of the ith index after standardization, is the mean of the mth index after standardization, and the eigenvalue and eigenvector of the matrix are calculated; Solve for the principal components: Where p is the number of eigenvalues ​​of the covariance matrix, λ1, λ2, λ3, ..., λp are the eigenvalues, and v1, v2, v3, ..., vp are the eigenvectors corresponding to them; Calculate the contribution rate of the i-th principal component. The calculation formula is: Among them, C i is the contribution rate of the ith principal component.

6. The method according to claim 5, characterized in that The regression model of multiple linear regression analysis is: Where x1, x2, ..., x m is the independent variable that affects the dependent variable y, β1,…,β m are the correlation coefficients corresponding to each independent variable, β0 is the intercept term, and ε is the error term.

7. The method according to claim 6, characterized in that Tests of model fit include: Residual analysis and residual distribution test, wherein the residual distribution test includes residual autocorrelation test and model prediction accuracy assessment.

8. An economic forecasting system based on a principal component regression model, characterized in that: include: Data acquisition module, used to collect historical economic data and its influencing factors as basic data; The preprocessing module is used to preprocess the basic data and classify them according to different time scales and data types: Feature screening module, which is used to perform feature engineering and standardization on preprocessed and classified data, and select target feature indicators with high relevance to economic forecasting; A dimension reduction processing module is used to perform dimension reduction processing on the target feature index by using principal component analysis method to reduce the amount of feature data and retain important information; The model building module is used to build a regression model based on multiple linear regression by selecting the principal components after dimensionality reduction as independent variables; A model training module, used to train the regression model, wherein the effect and prediction accuracy of the prediction model are evaluated through residual analysis based on historical data; The prediction module is used to output prediction results based on the trained model.

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