# Support Vector Machine-Based Nonlinear Model and Its Application in Regional Economic Forecasting

Authors: Yili Hu; Zhiyong Wang
Journal: Wireless Communications and Mobile Computing
 (2022)

---

## Abstract

The regional economic potential is affected by too many entities and large dynamic changes in the economic structure, resulting in large errors in the prediction obtained by the traditional economic potential development prediction method. Therefore, this paper puts forward the regional economic development potential prediction model with the concept of decision domain, solves the nonlinear characteristics of regional economic impact indicators by using the traditional support vector machine, and obtains the economic prediction data. The decision domain method is introduced in the decision-making process to construct the decision domain of training economic-related data sets. The experimental results show that compared with other prediction models, the model proposed in this paper has higher regional economic prediction accuracy, 2% higher than the baseline method, can quickly and accurately predict the potential trend of regional economic development, and has important application value.


---

## Body

## 1. Introduction

A regional economy is a huge system composed of many interrelated elements with certain causal relationships. There are many factors affecting regional economic development, including natural resource factors, employment factors, environmental factors, technological factors, and institutional factors, thus making the regional economic system a dynamic, nonlinear, and complex giant system [1]. Coupled with the uncertainty of the movement of factors inside and outside the system, the regional macroeconomy shows fluctuations around its general trend in the process of its own operation, and it is difficult to make reliable and accurate forecasts. In the case of China’s macroeconomy, making economic forecasts and decisions has become even more complicated as all aspects of the economic system are being established and improved [2].Accurate forecasting is the basis for correct decision-making, and how to forecast accurately to achieve good forecasting results depends largely on the forecasting methods and techniques used. A lot of research work has been done by researchers on such a difficult topic as forecasting, which focuses on two main aspects: on the one hand, new theories are constantly used to explore new forecasting methods and their applications; on the other hand, technologies such as computers and artificial intelligence are combined with forecasting techniques to research and develop intelligent forecasting support systems, which can be used by general personnel to make convenient forecasting [3].Most of the various macroeconomic forecasting models established on the basis of econometrics are linear models. While these linear models play a great role, they also gradually reveal their shortcomings, i.e., it is difficult to grasp the nonlinear phenomena in the macroeconomic system, thus inevitably causing an increase in forecasting errors [4]. To make up for the shortcomings, the economics community has improved the linear models—such as building segmented linear models or linear models with time-varying parameters, the results are often unsatisfactory, in which case, people are forced to look for a nonlinear tool for economic forecasting modeling.In recent years, with the improvement of computer processing power and the development of optimization theory, some nonlinear methods with artificial intelligence have been proposed for economic forecasting, among which neural network methods have gained wider application because they can approximate nonlinear functions with arbitrary accuracy [5]. A large number of experiments have proved that neural networks are much more accurate than traditional econometric methods for economic forecasting, but neural networks have their own disadvantages that are difficult to overcome: (1) they tend to be trapped in local optimum; (2) they require a large number of training samples and a large number of repeated experiments; (3) there is no clear standard for the setting of control parameters, so there are still some defects when neural networks are applied to economic system forecasting.Support vector machine (SVM) is a recently emerging machine learning method, including SVR (support vector regression) and SVC (support vector classification), which can solve practical problems such as small samples, nonlinearity, and high dimensionality and has been applied more successfully in the fields of pattern recognition and regression prediction, especially in solving small samples, and it has been applied more successfully in the fields of pattern recognition and regression forecasting, especially in solving small samples and nonlinearities, which makes it have advantages in regional economic forecasting that other methods cannot match [6].This paper will construct the index system of regional economic forecasting from different perspectives and then apply the support vector machine method to construct the nonlinear model of regional economic forecasting, and through the optimal solution of the model, the influence of parameters on the model in the training process of support vector machine is discussed in detail, and the effectiveness and superiority of the support vector machine method in the field of regional economic forecasting are tested through the comparative analysis of the forecasting results with the neural network method. The research of this paper enriches and extends the current research [7]. The research of this paper enriches and expands the current research content of regional economic forecasting, and its conclusions can provide scientific reference basis for local governments to formulate economic planning and carry out effective economic regulation and control.


## 2. Related Work

Economic forecasting research has produced many theories and methods after nearly half a century of development, and some foreign scholars have conducted a detailed review of the research on economic forecasting in recent years. [8] provides an in-depth summary of the results of economic forecasting in the past 25 years based on the analysis of various forecasting models and makes a meaningful discussion on the development direction of future economic forecasting research in the context of the improvement of existing computing power and the increase of data volume. In contrast, [9] reviews the development of economic forecasting in the past 25 years from the perspective of subjective factors of forecasting judgment and argues that the subjective judgment factors of forecasters will play an increasingly important role in future economic forecasting models. [10] analyzes the role of various components in economic forecasting (including the accuracy and rationality of the model, the time span of the data, the role of the forecaster’s judgment, and the interaction among the components) in a more comprehensive manner and emphasizes the need to integrate various components for comprehensive analysis in future economic forecasting studies.The economic structure and development trend of the regional economic system were analyzed, and econometric models such as demand-oriented macroeconomic system model of regional economic growth, production function model, and time series model were established and verified by examples with relevant statistics of economic development of Zhejiang Province [11]. The human resource factor is introduced into the production function to establish a small-scale joint macroeconomic equation model for China [12]. The development of macroeconomic econometric models in China for more than 20 years is reviewed [13]. Using orthogonal polynomials to reduce more independent variables to fewer independent variables and then establishing general multiple regression equations for economic forecasting to analyze the effects of independent variables on dependent variables at different time periods [14], the optimal regression model based on the least squares criterion (abbreviated as the La OR model) is proposed in response to the shortcomings of the generalization ability that is not guaranteed in the current regression function, combined with the research results of statistical learning theory. Compared with previous models, the La OR model integrates regression error and confidence range and is expected to effectively reduce the expected risk of the regression function.In [15], by drawing on the system dynamics approach, a tax economic system dynamics model was established using the basic theories of taxation and macroeconomics, and the operation of the tax economic system in China in the 1990s was simulated [16]. The exponential smoothing method is applied to economic forecasting, and the method of determining the smoothing constants and initial statistics is improved [17]. The ARIMA model was used to study the structure of economic time series, on which different forms of structural time series models were developed, and the structural time series models were used to forecast the economic time series of total retail sales of consumer goods, narrow money supply (M1), and gross domestic product (GDP) in China. [18] provides an in-depth study of ANN and traditional statistical models, including a nonseasonal single exponential smoothing model, an ARMA model, a nonseasonal exponential smoothing model, a combined forecasting model, and a natural forecasting model, as well as an approach based on subjective judgment. [19] applied neural networks to tax forecasting and conducted two empirical studies. Firstly, neural networks were applied alone for forecasting and compared with traditional statistical methods such as moving average and ARIMA models, and the forecasting results showed that neural networks have higher forecasting accuracy. And in another experiment, he used traditional statistical method models to assist the structure selection of ANN, and the experimental results proved that such a combination of forecasting effects is more advantageous than applying ANN methods alone. [20] has made meaningful exploration of the application of SVM in the field of macroeconomic forecasting, and this paper will build on their research to investigate in depth the issues of model construction and parameter selection of support vector machines in regional economic forecasting.


### 2.1. Support Vector Machine-Based Nonlinear Prediction Model

#### 2.1.1. Regression Problem

For definition regression problem, given the training set(1)D=xi,yii=1,2,⋯,n,where xi∈RN,yi∈R,i=1,2,⋯,n. Assuming that the training set is an independent identically distributed sample of points selected according to some distribution Fx,y over RN×R, try to find a real-valued function Fx so as to use y=Fx to infer the y∈R value corresponding to either input x∈RN and to make the expected risk for the training set
(2)Rf=∫Lx,y,fdFx,y,min., where Lx,y,f is the given loss function.Obviously, the regression problem is very similar to the classification problem, but the difference lies in the range of values of the outputy. In the classification problem, the variable y takes only “+1” and “-1” values (of course, it can also take consecutive integers in multiclass problems), while in the regression problem, the variable y can take any real value.To resolve the difference in the range of values of the dependent variabley, SVM can be used in regression problems by introducing an optional loss function.


#### 2.1.2. Support Vector Machine Regression Prediction Model

The objective function of the regression problem is different from the SVM classification in that the SVM regression has only one class of sample points, and the optimal hyperplane is sought not to separate the two classes of samples the most, but to minimize the total deviation of all sample points from the hyperplane. In this case, the sample points are between the two dashed lines in Figure1, and finding the optimal regression hyperplane is equivalent to finding the maximum interval, which is similar to the SVM.Figure 1
Flow chart of the forecasting based on SVM.SVR uses the following equation to estimate the function.(3)y=fx=ωφx+b,where φx is a nonlinear mapping from the input space RN to the high-dimensional feature space F. A linear regression function is constructed in the high-dimensional feature space to implement the nonlinear regression problem in the original space. To ensure the smoothness of the fitted curve, ω and b can be trained by solving the following optimization problem.
(4)minL=12ω2+C∑i=1nξi∗+ξi(5)s.t.yi−ω·x+b≤ε+ξi∗ω·x+b−yi≤ε+ξiξi,ξi∗≥0,i=1,2,⋯,nWith the introduction of Lagrange multipliers and kernel functions, the pairwise problem of the above equation is(6)Wαi,αi∗=−12∑i=1n∑j=1nαi−αi∗αj−αj∗Kxi,xj−ε∑i=1nαi+αi∗+∑i=1nyiαi∗−αi,(7)s.t.∑i=1nαi−αi∗=00≤αi,αi∗≤C,i=1,2,⋯,nFinally, the support vector regression estimation function can be found as follows.(8)fx=∑xi∈SVαi−αi∗Kx,xi+b∗.Based on the KKT condition, only some of the coefficientsαi−αi∗ are nonzero, and the errors of the training samples are greater than or equal to ε. These training samples are the support vectors.Algorithm 1 inε−support vector regression machine
(1)
The training setD=xi,yii=1,2,⋯n, where xi∈RN,yi∈R,i=1,2,⋯n(2)
Choose appropriate nonnegative numbersε and C(3)
Choose appropriate kernel functions and kernel function parameters(4)
Construct and solve the optimization problem (equation (6)) and (equation (7)) to obtain the optimal solutions α^,α∧∗, and α^=α∧1,α∧2,⋯,α∧nT,α∧∗=α∧1∗,α∧2∗,⋯,α∧n∗T(5)
Construct the decision function(9)fx=∑xi∈SVα^i−α^i∗Kx,xi+b∧∗,where b∧∗ is calculated as follows: choose α^i or α^k∗ in the open interval (0, C/n), and if α^i is chosen, then
(10)b∧∗=yj−∑xi∈SVα^i−α^i∗Kx,xi+ε.If the selection isα^k∗, then
(11)y^i=fxi,xi2,⋯,xim.


#### 2.1.3. Support Vector Machine Regression Solution Algorithm

In both Algorithm 1 and Algorithm 2, the solution of the optimization problem (convex quadratic programming) is mentioned, and then, the SVR regression is estimated. This method greatly improves the speed of computation.The specific steps are as follows.(1)
All combinations ofαi,αi∗ are drawn sequentially for optimization, and the objective function decreases until it converges to a minimum when any pair of αi,αi∗ can no longer be optimizedThe general process of prediction using SVM is as follows.(1)
Select appropriate evaluation indicators and establish an indicator system based on the characteristics of the study object(2)
Selecting a continuous time series of historical sample data(3)
Standardize the sample data to construct a training sample set and a test sample set(4)
Selecting appropriate SVR types, kernel function forms, and values of relevant parameters(5)
Use the training samples to establish the objective function, select a suitable optimization algorithm to solve the corresponding planning problem, and obtain the Lagrange multiplierαi,αi∗,b∗(6)
Substitute the obtained parameters into the estimation function (equation (8)) to establish the prediction model and use the test sample to calculate the predicted values at the future moment [21, 22](7)
Calculate the error of the function, and when the absolute value of the error is less than a predetermined value, end the learning process; otherwise, return to continue learningThe process can be represented in Figure1.


### 2.2. Regional Economic Data and Indicators

Regional economic forecasting is the analysis of economic growth influencing factors and historical regional economic development of a region, and then the analysis of regional economic growth trends and status using scientific statistical methods and techniques, and then the forecast of the economic development potential of the region [23, 24]. The regional economic development potential is disturbed by factors such as regional fixed asset investment, regional total retail sales of consumer goods, foreign trade import and export, energy consumption, and environmental protection input. These disturbed factors are represented by x1,x2,⋯,xi,⋯,xm, xi is used to describe the ith disturbed factor, and y is used to describe the economic level of the region; then, the expression of regional economic development potential is
(12)yi=xi1xi2⋯xim.Then, the mathematical model of regional economic potential forecast in yeari can be obtained as shown as follows:
(13)y^i=fxi1,xi2,⋯,xim.(1)
Setxi to be the stability coefficient of the data of the ith economic region and build the matrix of total economic growth of different industries(14)W=w11w12⋯w1nw21w22⋯w2n⋮⋮⋮⋮wm1wm2⋯wmn,wherewij is the total economic growth of the previous i years for the jth industry that needs to be evaluated for GDP growth
(2)
Establish a matrix of residual totals for different industries(15)S=s11s12⋯s1ns21s22⋯s2n⋮⋮⋮⋮sm1sm2⋯smn,wheresij is the total number of sales in the previous i years for the jth industry for which the GDP growth assessment is required
(3)
Calculate the mean value of the ratio of the growth totals of different industries to obtain the coefficient of the residual weight of the economic growth assessment created by theith industry:(16)εi=Wiei1×1+ei2×1+2+⋯+ein×n−1+i2×di1+di2+⋯+dinS.According to the above formula, it is possible to obtain the residual coefficient components of the economic growth assessment weights created by different industriesε=ε1,ε2,⋯,εnT.By calculating the mean value of the residual coefficients of the economic growth assessment weights of different industries, it is possible to evaluate the economic growth with the following formula:(17)δ=∑i=1nεi,thereby describing the economic growth assessment.


## 2.1. Support Vector Machine-Based Nonlinear Prediction Model

### 2.1.1. Regression Problem

For definition regression problem, given the training set(1)D=xi,yii=1,2,⋯,n,where xi∈RN,yi∈R,i=1,2,⋯,n. Assuming that the training set is an independent identically distributed sample of points selected according to some distribution Fx,y over RN×R, try to find a real-valued function Fx so as to use y=Fx to infer the y∈R value corresponding to either input x∈RN and to make the expected risk for the training set
(2)Rf=∫Lx,y,fdFx,y,min., where Lx,y,f is the given loss function.Obviously, the regression problem is very similar to the classification problem, but the difference lies in the range of values of the outputy. In the classification problem, the variable y takes only “+1” and “-1” values (of course, it can also take consecutive integers in multiclass problems), while in the regression problem, the variable y can take any real value.To resolve the difference in the range of values of the dependent variabley, SVM can be used in regression problems by introducing an optional loss function.


### 2.1.2. Support Vector Machine Regression Prediction Model

The objective function of the regression problem is different from the SVM classification in that the SVM regression has only one class of sample points, and the optimal hyperplane is sought not to separate the two classes of samples the most, but to minimize the total deviation of all sample points from the hyperplane. In this case, the sample points are between the two dashed lines in Figure1, and finding the optimal regression hyperplane is equivalent to finding the maximum interval, which is similar to the SVM.Figure 1
Flow chart of the forecasting based on SVM.SVR uses the following equation to estimate the function.(3)y=fx=ωφx+b,where φx is a nonlinear mapping from the input space RN to the high-dimensional feature space F. A linear regression function is constructed in the high-dimensional feature space to implement the nonlinear regression problem in the original space. To ensure the smoothness of the fitted curve, ω and b can be trained by solving the following optimization problem.
(4)minL=12ω2+C∑i=1nξi∗+ξi(5)s.t.yi−ω·x+b≤ε+ξi∗ω·x+b−yi≤ε+ξiξi,ξi∗≥0,i=1,2,⋯,nWith the introduction of Lagrange multipliers and kernel functions, the pairwise problem of the above equation is(6)Wαi,αi∗=−12∑i=1n∑j=1nαi−αi∗αj−αj∗Kxi,xj−ε∑i=1nαi+αi∗+∑i=1nyiαi∗−αi,(7)s.t.∑i=1nαi−αi∗=00≤αi,αi∗≤C,i=1,2,⋯,nFinally, the support vector regression estimation function can be found as follows.(8)fx=∑xi∈SVαi−αi∗Kx,xi+b∗.Based on the KKT condition, only some of the coefficientsαi−αi∗ are nonzero, and the errors of the training samples are greater than or equal to ε. These training samples are the support vectors.Algorithm 1 inε−support vector regression machine
(1)
The training setD=xi,yii=1,2,⋯n, where xi∈RN,yi∈R,i=1,2,⋯n(2)
Choose appropriate nonnegative numbersε and C(3)
Choose appropriate kernel functions and kernel function parameters(4)
Construct and solve the optimization problem (equation (6)) and (equation (7)) to obtain the optimal solutions α^,α∧∗, and α^=α∧1,α∧2,⋯,α∧nT,α∧∗=α∧1∗,α∧2∗,⋯,α∧n∗T(5)
Construct the decision function(9)fx=∑xi∈SVα^i−α^i∗Kx,xi+b∧∗,where b∧∗ is calculated as follows: choose α^i or α^k∗ in the open interval (0, C/n), and if α^i is chosen, then
(10)b∧∗=yj−∑xi∈SVα^i−α^i∗Kx,xi+ε.If the selection isα^k∗, then
(11)y^i=fxi,xi2,⋯,xim.


### 2.1.3. Support Vector Machine Regression Solution Algorithm

In both Algorithm 1 and Algorithm 2, the solution of the optimization problem (convex quadratic programming) is mentioned, and then, the SVR regression is estimated. This method greatly improves the speed of computation.The specific steps are as follows.(1)
All combinations ofαi,αi∗ are drawn sequentially for optimization, and the objective function decreases until it converges to a minimum when any pair of αi,αi∗ can no longer be optimizedThe general process of prediction using SVM is as follows.(1)
Select appropriate evaluation indicators and establish an indicator system based on the characteristics of the study object(2)
Selecting a continuous time series of historical sample data(3)
Standardize the sample data to construct a training sample set and a test sample set(4)
Selecting appropriate SVR types, kernel function forms, and values of relevant parameters(5)
Use the training samples to establish the objective function, select a suitable optimization algorithm to solve the corresponding planning problem, and obtain the Lagrange multiplierαi,αi∗,b∗(6)
Substitute the obtained parameters into the estimation function (equation (8)) to establish the prediction model and use the test sample to calculate the predicted values at the future moment [21, 22](7)
Calculate the error of the function, and when the absolute value of the error is less than a predetermined value, end the learning process; otherwise, return to continue learningThe process can be represented in Figure1.


## 2.1.1. Regression Problem

For definition regression problem, given the training set(1)D=xi,yii=1,2,⋯,n,where xi∈RN,yi∈R,i=1,2,⋯,n. Assuming that the training set is an independent identically distributed sample of points selected according to some distribution Fx,y over RN×R, try to find a real-valued function Fx so as to use y=Fx to infer the y∈R value corresponding to either input x∈RN and to make the expected risk for the training set
(2)Rf=∫Lx,y,fdFx,y,min., where Lx,y,f is the given loss function.Obviously, the regression problem is very similar to the classification problem, but the difference lies in the range of values of the outputy. In the classification problem, the variable y takes only “+1” and “-1” values (of course, it can also take consecutive integers in multiclass problems), while in the regression problem, the variable y can take any real value.To resolve the difference in the range of values of the dependent variabley, SVM can be used in regression problems by introducing an optional loss function.


## 2.1.2. Support Vector Machine Regression Prediction Model

The objective function of the regression problem is different from the SVM classification in that the SVM regression has only one class of sample points, and the optimal hyperplane is sought not to separate the two classes of samples the most, but to minimize the total deviation of all sample points from the hyperplane. In this case, the sample points are between the two dashed lines in Figure1, and finding the optimal regression hyperplane is equivalent to finding the maximum interval, which is similar to the SVM.Figure 1
Flow chart of the forecasting based on SVM.SVR uses the following equation to estimate the function.(3)y=fx=ωφx+b,where φx is a nonlinear mapping from the input space RN to the high-dimensional feature space F. A linear regression function is constructed in the high-dimensional feature space to implement the nonlinear regression problem in the original space. To ensure the smoothness of the fitted curve, ω and b can be trained by solving the following optimization problem.
(4)minL=12ω2+C∑i=1nξi∗+ξi(5)s.t.yi−ω·x+b≤ε+ξi∗ω·x+b−yi≤ε+ξiξi,ξi∗≥0,i=1,2,⋯,nWith the introduction of Lagrange multipliers and kernel functions, the pairwise problem of the above equation is(6)Wαi,αi∗=−12∑i=1n∑j=1nαi−αi∗αj−αj∗Kxi,xj−ε∑i=1nαi+αi∗+∑i=1nyiαi∗−αi,(7)s.t.∑i=1nαi−αi∗=00≤αi,αi∗≤C,i=1,2,⋯,nFinally, the support vector regression estimation function can be found as follows.(8)fx=∑xi∈SVαi−αi∗Kx,xi+b∗.Based on the KKT condition, only some of the coefficientsαi−αi∗ are nonzero, and the errors of the training samples are greater than or equal to ε. These training samples are the support vectors.Algorithm 1 inε−support vector regression machine
(1)
The training setD=xi,yii=1,2,⋯n, where xi∈RN,yi∈R,i=1,2,⋯n(2)
Choose appropriate nonnegative numbersε and C(3)
Choose appropriate kernel functions and kernel function parameters(4)
Construct and solve the optimization problem (equation (6)) and (equation (7)) to obtain the optimal solutions α^,α∧∗, and α^=α∧1,α∧2,⋯,α∧nT,α∧∗=α∧1∗,α∧2∗,⋯,α∧n∗T(5)
Construct the decision function(9)fx=∑xi∈SVα^i−α^i∗Kx,xi+b∧∗,where b∧∗ is calculated as follows: choose α^i or α^k∗ in the open interval (0, C/n), and if α^i is chosen, then
(10)b∧∗=yj−∑xi∈SVα^i−α^i∗Kx,xi+ε.If the selection isα^k∗, then
(11)y^i=fxi,xi2,⋯,xim.


## 2.1.3. Support Vector Machine Regression Solution Algorithm

In both Algorithm 1 and Algorithm 2, the solution of the optimization problem (convex quadratic programming) is mentioned, and then, the SVR regression is estimated. This method greatly improves the speed of computation.The specific steps are as follows.(1)
All combinations ofαi,αi∗ are drawn sequentially for optimization, and the objective function decreases until it converges to a minimum when any pair of αi,αi∗ can no longer be optimizedThe general process of prediction using SVM is as follows.(1)
Select appropriate evaluation indicators and establish an indicator system based on the characteristics of the study object(2)
Selecting a continuous time series of historical sample data(3)
Standardize the sample data to construct a training sample set and a test sample set(4)
Selecting appropriate SVR types, kernel function forms, and values of relevant parameters(5)
Use the training samples to establish the objective function, select a suitable optimization algorithm to solve the corresponding planning problem, and obtain the Lagrange multiplierαi,αi∗,b∗(6)
Substitute the obtained parameters into the estimation function (equation (8)) to establish the prediction model and use the test sample to calculate the predicted values at the future moment [21, 22](7)
Calculate the error of the function, and when the absolute value of the error is less than a predetermined value, end the learning process; otherwise, return to continue learningThe process can be represented in Figure1.


## 2.2. Regional Economic Data and Indicators

Regional economic forecasting is the analysis of economic growth influencing factors and historical regional economic development of a region, and then the analysis of regional economic growth trends and status using scientific statistical methods and techniques, and then the forecast of the economic development potential of the region [23, 24]. The regional economic development potential is disturbed by factors such as regional fixed asset investment, regional total retail sales of consumer goods, foreign trade import and export, energy consumption, and environmental protection input. These disturbed factors are represented by x1,x2,⋯,xi,⋯,xm, xi is used to describe the ith disturbed factor, and y is used to describe the economic level of the region; then, the expression of regional economic development potential is
(12)yi=xi1xi2⋯xim.Then, the mathematical model of regional economic potential forecast in yeari can be obtained as shown as follows:
(13)y^i=fxi1,xi2,⋯,xim.(1)
Setxi to be the stability coefficient of the data of the ith economic region and build the matrix of total economic growth of different industries(14)W=w11w12⋯w1nw21w22⋯w2n⋮⋮⋮⋮wm1wm2⋯wmn,wherewij is the total economic growth of the previous i years for the jth industry that needs to be evaluated for GDP growth
(2)
Establish a matrix of residual totals for different industries(15)S=s11s12⋯s1ns21s22⋯s2n⋮⋮⋮⋮sm1sm2⋯smn,wheresij is the total number of sales in the previous i years for the jth industry for which the GDP growth assessment is required
(3)
Calculate the mean value of the ratio of the growth totals of different industries to obtain the coefficient of the residual weight of the economic growth assessment created by theith industry:(16)εi=Wiei1×1+ei2×1+2+⋯+ein×n−1+i2×di1+di2+⋯+dinS.According to the above formula, it is possible to obtain the residual coefficient components of the economic growth assessment weights created by different industriesε=ε1,ε2,⋯,εnT.By calculating the mean value of the residual coefficients of the economic growth assessment weights of different industries, it is possible to evaluate the economic growth with the following formula:(17)δ=∑i=1nεi,thereby describing the economic growth assessment.


## 3. Analysis of Experimental Results

In order to verify the validity of the regional economic development potential prediction model analyzed in this paper, relevant experiments should be conducted. The experimental sample data of this paper is obtained from the regional economic GDP data of a certain region for 5 years, and the results of GDP prediction and comparison between the predicted and actual values of the region using this model are depicted in Table1 and Figure 2, respectively [25, 26]. The MATLAB 7.0 simulation software was used to complete the experiments.Table 1
Prediction results using the model of this paper.
Particular yearPredicted GDP/100 million yuanActual GDP/100 million yuanError/%20012347.22371.11.9720022625.42577.32.620033016.63056.1-0.6720043603.83641.1-0.6520054417.14401.60.28Figure 2
Comparison of the predicted and actual values of the model.Analyzing Table1 and Figure 2, we can see that the predicted economic growth of the regional economy in the last five years is well fitted, and the GDP value of the region predicted by the model of this paper has a high consistency with the actual value, and the method of this paper can achieve satisfactory prediction accuracy for the regional economy, which indicates that the model designed in this paper is feasible.In order to further verify the superiority of this paper’s model, the time series model, ant colony search model, and this paper’s model were used to predict the economic development potential of the experimental region, and the detailed results are depicted in Figure3.Figure 3
Prediction effect of different prediction models.From Figure4, we can see that the training and testing errors of the two types of SVRs are very close, with the difference between the predicted values being no more than 0.05% at the highest and almost equal at the lowest. The average relative error of the ν−SVR model is 1.57%, which is lower than the average relative error of the ε−SVR of 1.58%, and the ν−SVR is relatively better. However, the results of both types of SVR applications in this paper demonstrate their superior learning and generalization performance, and both of them can be used as the final models, and it will be discussed which of them is superior in further data testing. In view of this, they are applied in this paper to forecast the economic development level of Chongqing in 2006, and the forecast results are compared with the data in the 2006 statistical bulletin of Chongqing.Figure 4
Clustering and trend analysis of different economic data.


## 4. Conclusion

In this paper, the concepts involved in the support vector machine regression problem are discussed, the loss functions are introduced in detail, and theε−SVR model and ν−SVR model are derived based on the principles of support vector classification, and the algorithms for solving the optimization problem in the model are discussed, with emphasis on the SMO algorithm, which is more widely used at present. Finally, a general procedure of SVM-based nonlinear prediction model is given.



---

*Source: 3387543-2022-05-06.xml*