# Research on Freight Development of Guangdong Province Based on Grey Theory Model

Authors: Lianhua Liu; Aili Xie; Hai Ping
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

Logistics and economic development complement each other. The comprehensive competitiveness of Guangdong provincial economy ranks first in China. Under the influence of COVID-19, the freight development of Guangdong Province has been affected, but there is still lack of quantitative research. It is significant to explore the trend of economic development through the freight development of Guangdong Province. Based on the grey theory model, this paper uses six freight indexes to research freight development of Guangdong Province. Under the assumption that COVID-19 did not happen, we predicted the development value of freight index of Guangdong Province from January to December in 2020 and studied the influence based on the comparison between the predicted value and actual value. The empirical study shows three impact characteristics: stage characteristics, structural characteristics, and entity transmission characteristics. COVID-19 has a negative impact on the development of total freight volume, highway freight volume, waterway freight volume, and air freight volume in Guangdong Province. The influence values were −23.001%, −29.344%, −11.296%, and −3.838%. But, the freight volumes of railway and pipeline were positively affected by 14.343% and 13.057%, respectively, due to their continuity and substitution to other transportation modes. To further explore the abate measures of COVID-19 impact on Guangdong’s freight development, the grey correlation model is introduced to study the correlation factors of freight development of Guangdong Province. Through the research of the related factors, this paper puts forward some measures to promote the freight development of Guangdong Province in the postepidemic era.


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## Body

## 1. Introduction

Guangdong Province is the South Gate of China, located in the South China Sea shipping hub position, since the Qin and Han Dynasties have become the starting point of the maritime Silk Road. The comprehensive competitiveness of Guangdong provincial economy ranks first in China. Since 1989, Guangdong’s GDP has ranked first in China for 32 consecutive years, becoming the largest economic province in China. In 2020, Guangdong Province’s GDP reached 11.08 trillion yuan, accounting for one-eighth of China’s economy. The nine cities in the Pearl River Delta of Guangdong Province join hands with Hong Kong and Macao to build the bay area of Guangdong, Hong Kong, and Macao and become one of the four bay areas in the world side by side with New York Bay area, San Francisco Bay area, and Tokyo Bay area. The developments of economy and logistics complement each other. The rapid economic development of Guangdong Province promotes the improvement of logistics development level [1–4], which further supports the economic development of Guangdong Province.The COVID-19 outbreak as a public health emergency has a negative impact on the economy from multiple channels. It also has a direct impact on the logistics economy. The epidemic situation affects the demand and supply of the logistics market. It affects the development of logistics enterprises through the operation of logistics and indirectly transmits to the field of logistics through the impact on domestic real economy and foreign trade. In the postepidemic period, the relevant supporting policies need a certain industry and time transmission, so COVID-19’s impact on the logistics industry is characterized by multiple channels and multiple spatial and temporal superposition. Guangdong Province as an important node of the global supply chain, the total freight volume, road freight volume, railway freight volume, waterway freight volume, air freight volume, and pipeline freight volume has been affected by COVID-19.In order to study the impact of COVID-19 on freight transportation in Guangdong Province and explore mitigation measures, this paper intends to use the grey prediction model GM (1, 1) to analyze the impact and introduce the grey correlation model to conduct a quantitative study on the correlation degree of the factors affecting the freight development of Guangdong Province. According to the correlation factors of the freight development of Guangdong Province, this paper puts forward some measures to promote the freight development of Guangdong Province in the postepidemic era.


## 2. Literature Review

### 2.1. Research Progress on Forecasting Freight Development

In recent years, logistics development prediction has become a hot issue for scholars. The methods commonly used by scholars include exponential smoothing [5–7], linear model [8], BP neural network method [5–9], multiple regression analysis [5, 9], seasonal autoregressive model [10–13], discrete wavelet technology [14], vector autoregressive method [15], and Markov chain theory [16], which are widely used in the prediction of logistics and freight development. In addition to conventional prediction methods, scholars also innovate prediction methods, such as a genetic algorithm and backpropagation (GA-BP) prediction model (optimized backpropagation neural network model using genetic algorithm), which are used to predict freight volume demand with small error [17]. Scholars use L-OD logistics demand forecasting method and construct a new model of double constraint gravity model to forecast logistics distribution, which achieves good forecasting effect. The state travel demand model (STDM) [18] is introduced to forecasting freight development, and a new hybrid multicriteria decision-making model combining Delphi, analytic network process (ANP), and quality function deployment (QFD) in fuzzy environment is applied to freight forecasting [19].


### 2.2. Application of GM in Forecasting Freight

Grey system theory is an effective method of studying and modeling systems consisting of small sample sizes that contain a limited amount of information and is widely used in many fields. The valuable information is extracted by processing the known information. This is further used to explore the evolution laws of the system and thus establish a prediction model. As there are many factors influencing the freight development of Guangdong Province, e.g., environmental factors of transportation and logistics, regional economic environment, government policy, and science and technology environment, it can be regarded as a grey system. Thus, it can be described using a grey model (GM). The GM (1, 1) is the most generally used grey model. GM (1, 1) used to predict the freight volume achieved satisfactory results [5, 9, 20–24].To sum up, the grey prediction model is widely used in logistics development and freight volume prediction. Therefore, it is scientific and feasible to use the grey prediction model in the quantitative research of Guangdong freight development:(1)
The innovation of this paper is the prediction of impact value refined to month which is a more precise observation of COVID-19’s impact on Guangdong’s freight development.(2)
Practical significance: through quantitative and accurate research on the monthly impact value of freight development in Guangdong Province, we can grasp the situation of economic operation in Guangdong Province from the side and promote the formulation and implementation of relevant economic stimulus policies, which has certain management practical significance.


## 2.1. Research Progress on Forecasting Freight Development

In recent years, logistics development prediction has become a hot issue for scholars. The methods commonly used by scholars include exponential smoothing [5–7], linear model [8], BP neural network method [5–9], multiple regression analysis [5, 9], seasonal autoregressive model [10–13], discrete wavelet technology [14], vector autoregressive method [15], and Markov chain theory [16], which are widely used in the prediction of logistics and freight development. In addition to conventional prediction methods, scholars also innovate prediction methods, such as a genetic algorithm and backpropagation (GA-BP) prediction model (optimized backpropagation neural network model using genetic algorithm), which are used to predict freight volume demand with small error [17]. Scholars use L-OD logistics demand forecasting method and construct a new model of double constraint gravity model to forecast logistics distribution, which achieves good forecasting effect. The state travel demand model (STDM) [18] is introduced to forecasting freight development, and a new hybrid multicriteria decision-making model combining Delphi, analytic network process (ANP), and quality function deployment (QFD) in fuzzy environment is applied to freight forecasting [19].


## 2.2. Application of GM in Forecasting Freight

Grey system theory is an effective method of studying and modeling systems consisting of small sample sizes that contain a limited amount of information and is widely used in many fields. The valuable information is extracted by processing the known information. This is further used to explore the evolution laws of the system and thus establish a prediction model. As there are many factors influencing the freight development of Guangdong Province, e.g., environmental factors of transportation and logistics, regional economic environment, government policy, and science and technology environment, it can be regarded as a grey system. Thus, it can be described using a grey model (GM). The GM (1, 1) is the most generally used grey model. GM (1, 1) used to predict the freight volume achieved satisfactory results [5, 9, 20–24].To sum up, the grey prediction model is widely used in logistics development and freight volume prediction. Therefore, it is scientific and feasible to use the grey prediction model in the quantitative research of Guangdong freight development:(1)
The innovation of this paper is the prediction of impact value refined to month which is a more precise observation of COVID-19’s impact on Guangdong’s freight development.(2)
Practical significance: through quantitative and accurate research on the monthly impact value of freight development in Guangdong Province, we can grasp the situation of economic operation in Guangdong Province from the side and promote the formulation and implementation of relevant economic stimulus policies, which has certain management practical significance.


## 3. Research Methods

### 3.1. Introduction of GM (1, 1)

The differential equation of grey system theory is called GM. G stands for grey, M stands for model, and GM (1, 1) is a one-order and one-variable differential equation model. The modeling process and mechanism of GM (1, 1) are as follows:(1)X0=x01,x02,x3,…,x0n.(1)
Record the original data sequence as a nonnegative sequence, whereX0 is a nonnegative sequence, X0k≥0,k=1,2,…,n.(2)
Generate a cumulative data sequenceX1:(2)X1=x11,x12,x13,…,x1n,wherex1k=∑i=1kx0i, k=1,2,…,n. Z1is the adjacent mean generating sequence of X1:(3)Z1=z11,z12,z13,…,z1n,whereZ1k=0.5x1k+0.5x1k−1,k=1,2,…,n.(3)
Establish GM(1,1):(4)x0k+aZ1k=b.in which “a” and “b” are parameters, which are development grey number and endogenous control grey number, respectively.(4)
Solve the parameters “a” and “b”:Ifa=abT is a parameter column and(5)Y=x02x03⋮x0N,B=z121z131⋮⋮z1n1,then find the least square estimation coefficient sequence of differential equationx0k+az1k=b, satisfying condition a^=BTB−1BTY.(5)
Establish a prediction model.Establish the whitening equation corresponding to the grey differential equation, as the following formula:(6)dx1dt+ax1=b.As mentioned above, the time response sequence of GM (1, 1) grey differential equationx0k+az1k=b is the following formula:(7)x^1k+1=x01−bae−ak+ba,k=1,2,3,…,n.The predicted values generated by restoration are as follows:(8)x^0k+1=x^1k+1−x^1k,k=1,2,3,…,n.


### 3.2. Grey Prediction Model (GM (1, 1)) Test

#### 3.2.1. Modeling Rationality Test

Firstly, the modeling rationality of the original sequencex0 is tested, and the grade ratioλk is used to represent(9)λk=x0k+1x0k,where k=1,2,3,…,n. When all λk∈e−2/n+1,e2/n+1,, the GM (1,1) can be used in the x0 series for satisfactory prediction modeling.


#### 3.2.2. Grey System Model Prediction Accuracy Test

(1) Residual Error Test. After modeling with GM (1, 1), the predicted value sequence is as follows: (10)X^0K=x^01,x^01,…,x^0n.By calculating the seriesX0K and x^0K, the following GM (1, 1) modeling rationality residual test index is obtained.①
Absolute residual is(11)εk=x0k−x^0k.②
Relative residual is(12)Δk=εkx0k.③
Average residual is(13)Δk¯=1n∑i=1nΔk.④
Average accuracy is(14)ρ0=1−Δk¯×100%.Residual test standards are as shown in Table1.Table 1
Grade reference table of grey system model parameters.
Accuracy classRelative residuals (Δk)Mean variance ratio (C)Probability of small error (P)Correlation degree (γ0i)Good0.010.350.950.90Qualification0.050.450.850.80Barely qualified0.10.500.700.70Disqualification0.20.650.700.60(2) Posterior Variance Test. Suppose X0is the original sequence, X^0is the simulation error sequence, and ε0is the absolute residual sequence. Test standards are shown in Table 1.①
Mean value ofX0 is(15)x¯=1n∑k=1nx0k.②
Variance ofX0 is(16)S1=1n∑k=1nx0k−x¯2.③
Mean of absolute residuals is(17)ε¯=1n∑k=1nεk.④
Absolute residual variance is(18)S2=1n∑k=1nεk−ε¯2.⑤
Ratio of variance is(19)C=S2S1.⑥
Probability of small error is(20)P=pεk−ε¯<0.6745S1,(21)S0=0.6745S1.


### 3.3. Grey Correlation Degree

Correlation degree refers to the measurement of the correlation between the factors of the two systems that change with time or different objects. Grey system theory puts forward the concept of grey correlation analysis for each subsystem and intends to seek the numerical relationship between each subsystem in the system through certain methods or measure the influence of each subfactor in the system on the main factor. Grey correlation analysis provides a quantitative measurement for the development and change trend of a system, which is suitable for dynamic process analysis.The calculation steps of grey correlation degree are as follows:(1)
Establish a raw data matrixXi for each index:(22)Xi=xi1,xi2,…,xik.Here,xik represents the original data of i factor in year k.(2)
Calculate initialization transformation of matrixXi′:(23)Xi′=xi1xi1,xi2xi1,…,xikxi1=xi′1,xi′2,…,xi′k.(3)
Calculate the difference sequenceΔ0ik. The difference sequence occurs between the main factor sequence data and the measure factors:(24)Δ0ik=x0k−xi′k,k=1,2,…,n,i=1,2,…,m,Δ0ik=Δ0i1,Δ0i2,…,Δ0ik.(4)
The correlation coefficientξ0ik and grey correlation degree γ0i are calculated:(25)ξ0ik=miniminkΔ0ik+ϕmaximaxkΔ0ikΔ0ik+ϕmaximaxkΔ0ik,whereφis the resolution coefficient, which improves the significance of the difference between the correlation coefficients, φ∈0,1, and the general value is 0.5. The grey correlation degree is shown as follows:(26)γ0i=1n∑k=1nξ0ik.In summary, the relevant parameters of the grey system model level index [20] reference table are shown in Table 1.


## 3.1. Introduction of GM (1, 1)

The differential equation of grey system theory is called GM. G stands for grey, M stands for model, and GM (1, 1) is a one-order and one-variable differential equation model. The modeling process and mechanism of GM (1, 1) are as follows:(1)X0=x01,x02,x3,…,x0n.(1)
Record the original data sequence as a nonnegative sequence, whereX0 is a nonnegative sequence, X0k≥0,k=1,2,…,n.(2)
Generate a cumulative data sequenceX1:(2)X1=x11,x12,x13,…,x1n,wherex1k=∑i=1kx0i, k=1,2,…,n. Z1is the adjacent mean generating sequence of X1:(3)Z1=z11,z12,z13,…,z1n,whereZ1k=0.5x1k+0.5x1k−1,k=1,2,…,n.(3)
Establish GM(1,1):(4)x0k+aZ1k=b.in which “a” and “b” are parameters, which are development grey number and endogenous control grey number, respectively.(4)
Solve the parameters “a” and “b”:Ifa=abT is a parameter column and(5)Y=x02x03⋮x0N,B=z121z131⋮⋮z1n1,then find the least square estimation coefficient sequence of differential equationx0k+az1k=b, satisfying condition a^=BTB−1BTY.(5)
Establish a prediction model.Establish the whitening equation corresponding to the grey differential equation, as the following formula:(6)dx1dt+ax1=b.As mentioned above, the time response sequence of GM (1, 1) grey differential equationx0k+az1k=b is the following formula:(7)x^1k+1=x01−bae−ak+ba,k=1,2,3,…,n.The predicted values generated by restoration are as follows:(8)x^0k+1=x^1k+1−x^1k,k=1,2,3,…,n.


## 3.2. Grey Prediction Model (GM (1, 1)) Test

### 3.2.1. Modeling Rationality Test

Firstly, the modeling rationality of the original sequencex0 is tested, and the grade ratioλk is used to represent(9)λk=x0k+1x0k,where k=1,2,3,…,n. When all λk∈e−2/n+1,e2/n+1,, the GM (1,1) can be used in the x0 series for satisfactory prediction modeling.


### 3.2.2. Grey System Model Prediction Accuracy Test

(1) Residual Error Test. After modeling with GM (1, 1), the predicted value sequence is as follows: (10)X^0K=x^01,x^01,…,x^0n.By calculating the seriesX0K and x^0K, the following GM (1, 1) modeling rationality residual test index is obtained.①
Absolute residual is(11)εk=x0k−x^0k.②
Relative residual is(12)Δk=εkx0k.③
Average residual is(13)Δk¯=1n∑i=1nΔk.④
Average accuracy is(14)ρ0=1−Δk¯×100%.Residual test standards are as shown in Table1.Table 1
Grade reference table of grey system model parameters.
Accuracy classRelative residuals (Δk)Mean variance ratio (C)Probability of small error (P)Correlation degree (γ0i)Good0.010.350.950.90Qualification0.050.450.850.80Barely qualified0.10.500.700.70Disqualification0.20.650.700.60(2) Posterior Variance Test. Suppose X0is the original sequence, X^0is the simulation error sequence, and ε0is the absolute residual sequence. Test standards are shown in Table 1.①
Mean value ofX0 is(15)x¯=1n∑k=1nx0k.②
Variance ofX0 is(16)S1=1n∑k=1nx0k−x¯2.③
Mean of absolute residuals is(17)ε¯=1n∑k=1nεk.④
Absolute residual variance is(18)S2=1n∑k=1nεk−ε¯2.⑤
Ratio of variance is(19)C=S2S1.⑥
Probability of small error is(20)P=pεk−ε¯<0.6745S1,(21)S0=0.6745S1.


## 3.2.1. Modeling Rationality Test

Firstly, the modeling rationality of the original sequencex0 is tested, and the grade ratioλk is used to represent(9)λk=x0k+1x0k,where k=1,2,3,…,n. When all λk∈e−2/n+1,e2/n+1,, the GM (1,1) can be used in the x0 series for satisfactory prediction modeling.


## 3.2.2. Grey System Model Prediction Accuracy Test

(1) Residual Error Test. After modeling with GM (1, 1), the predicted value sequence is as follows: (10)X^0K=x^01,x^01,…,x^0n.By calculating the seriesX0K and x^0K, the following GM (1, 1) modeling rationality residual test index is obtained.①
Absolute residual is(11)εk=x0k−x^0k.②
Relative residual is(12)Δk=εkx0k.③
Average residual is(13)Δk¯=1n∑i=1nΔk.④
Average accuracy is(14)ρ0=1−Δk¯×100%.Residual test standards are as shown in Table1.Table 1
Grade reference table of grey system model parameters.
Accuracy classRelative residuals (Δk)Mean variance ratio (C)Probability of small error (P)Correlation degree (γ0i)Good0.010.350.950.90Qualification0.050.450.850.80Barely qualified0.10.500.700.70Disqualification0.20.650.700.60(2) Posterior Variance Test. Suppose X0is the original sequence, X^0is the simulation error sequence, and ε0is the absolute residual sequence. Test standards are shown in Table 1.①
Mean value ofX0 is(15)x¯=1n∑k=1nx0k.②
Variance ofX0 is(16)S1=1n∑k=1nx0k−x¯2.③
Mean of absolute residuals is(17)ε¯=1n∑k=1nεk.④
Absolute residual variance is(18)S2=1n∑k=1nεk−ε¯2.⑤
Ratio of variance is(19)C=S2S1.⑥
Probability of small error is(20)P=pεk−ε¯<0.6745S1,(21)S0=0.6745S1.


## 3.3. Grey Correlation Degree

Correlation degree refers to the measurement of the correlation between the factors of the two systems that change with time or different objects. Grey system theory puts forward the concept of grey correlation analysis for each subsystem and intends to seek the numerical relationship between each subsystem in the system through certain methods or measure the influence of each subfactor in the system on the main factor. Grey correlation analysis provides a quantitative measurement for the development and change trend of a system, which is suitable for dynamic process analysis.The calculation steps of grey correlation degree are as follows:(1)
Establish a raw data matrixXi for each index:(22)Xi=xi1,xi2,…,xik.Here,xik represents the original data of i factor in year k.(2)
Calculate initialization transformation of matrixXi′:(23)Xi′=xi1xi1,xi2xi1,…,xikxi1=xi′1,xi′2,…,xi′k.(3)
Calculate the difference sequenceΔ0ik. The difference sequence occurs between the main factor sequence data and the measure factors:(24)Δ0ik=x0k−xi′k,k=1,2,…,n,i=1,2,…,m,Δ0ik=Δ0i1,Δ0i2,…,Δ0ik.(4)
The correlation coefficientξ0ik and grey correlation degree γ0i are calculated:(25)ξ0ik=miniminkΔ0ik+ϕmaximaxkΔ0ikΔ0ik+ϕmaximaxkΔ0ik,whereφis the resolution coefficient, which improves the significance of the difference between the correlation coefficients, φ∈0,1, and the general value is 0.5. The grey correlation degree is shown as follows:(26)γ0i=1n∑k=1nξ0ik.In summary, the relevant parameters of the grey system model level index [20] reference table are shown in Table 1.


## 4. Construction of GM (1, 1)

### 4.1. Data Source and Description

The data are from the monthly open statistics of Guangdong Provincial Bureau of Statistics from 2013 to 2020. The data content includes six groups of data: total freight volume, truck freight volume, railway freight volume, waterway freight volume, air freight volume, and pipeline freight volume of Guangdong Province. For the convenience of calculation, total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume are expressed. The annual freight development of Guangdong Province is counted, covering the six freight indexes. The original data to predict the development of freight of Guangdong Province in 2020 are shown in Table2.Table 2
Monthly data of freight indicators of Guangdong Province from 2013 to 2020 (unit: million tons) (%).
YearTotal freight volume (F)Railway freight volume (R)Truck freight volume (T)Water freight volume (W)Air cargo volume (A)Pipeline freight volume (P)AmountRatioAmountRatioAmountRatioAmountRatioAmountRatio20133065.44122.383.9922176.4370.999688.5122.4601.320.04376.812.50620143612.49112.093.1032636.1972.974781.2521.6261.440.04081.542.25720153792.21104.022.7432828.8774.597780.9320.5931.480.03976.932.02920163743.48106.232.8382727.3772.857828.9322.1431.600.04379.322.11920173984.6975.721.9002886.1972.432939.0423.5661.650.04182.092.06020184265.7877.641.8203063.0471.8051023.5123.9942.210.05299.412.33020194459.7581.921.8373192.3171.5801083.7124.3002.370.05398.992.22020203547.5177.672.1892313.5665.2161036.5729.2202.380.067117.353.308Data source: according to the website data of Guangdong Provincial Bureau of Statistics.


### 4.2. Rationality of GM (1, 1) Construction

The rationality of model construction was tested in advance. On the basis of the original data sequence, the stage ratioλk is calculated according to formula (10).


#### 4.2.1. Calculation of the Grade Ratioλk

The grade ratio is calculated as follows:(27)λkF=0.8486,0.9526,1.0130,0.9395,0.9341,0.9565,λkR=1.0918,1.0776,0.9792,1.4029,0.9753,0.9478,λkT=0.8256,0.9319,1.0372,0.9450,0.9423,0.9595,λkW=0.8813,1.0004,0.9421,0.8827,0.9175,0.9445,λkA=0.9167,0.9730,0.9250,0.9697,0.7466,0.9325,λkP=0.9420,1.0599,0.9699,0.9663,0.8258,1.0042.


#### 4.2.2. Judgment of the Grade Ratio

λk∈e−2/n+1,e2/n+1, when n = 7,λk∈0.7788,1.2840. If λ(k) in the above range, x0k is suitable for GM (1,1). λkF∈0.8486,1.0130, λkT∈0.8256,1.0372, λkW∈0.8813,1.0004,andλkP∈0.8258,1.0559,wherek=2,3,4,5,6,7, and the grade ratios are in0.7788,1.2840; hence,XF0XT0,XW0, and XP0 can be modeled by GM (1,1). The values of grey development coefficient “-a” are 0.0429, 0.0364, 0.0752, and 0.0539, respectively, i.e., less than 0.3, which are suitable for medium- and long-term prediction.However,λkR∈0.9478,1.4029andλkA∈0.7446,1.0442. There is a grade ratio not in the region, which is not available for XR0and XA0modeled in GM (1, 1) directly. Therefore, it is necessary to do translation transformation on the data, and the translated data are XR0′and XA0′, as follows:(28)XR0′=202.38,192.09,184.02,186.23,155.72,157.64,161.92,XA0′=2.12,2.24,2.28,2.40,2.45,3.01,3.17.The grade ratios ofXR0′and XA0′are calculated:(29)λ′kR=1.0536,1.0439,0.9881,1.1959,0.9878,0.9736,λ′kR∈0.9736,1.1959,K=2,3,4,5,6,7,λ′kA=0.9464,0.9825,0.9500,0.9796,0.8140,0.9495,λ′kA∈0.8140,0.9825,K=2,3,4,5,6,7.The grade ratios ofXR0′and XA0′ are in the rank of λkand∈0.7788,1.2840. The values of grey development coefficient “−a” are −0.0435 and −0.0784, which are less than 0.3. So XR0′and XA0′ are suitable for medium- and long-term prediction.


### 4.3. Construction of GM (1, 1)

According to the original sequence, the accumulated sequence is generated and the differential equation is constructed. On the basis of solving the values of “a” and “b,” the time response sequence is obtained, as formulas (30)–(35). The predicted values are calculated according to the time response sequence, shown in Tables 3 and 4.(30)X^1k+1F=X01F−bae−ak+ba=81237.44e0.0429k−78172.00,(31)X^1k+1R=X0′1R−bae−ak+ba=4713.89−4511.51e−0.0435k,(32)X^1k+1T=X01T−bae−ak+ba=71059.66e0.03637k−6888311.00,(33)X^1k+1W=X01W−bae−ak+ba=9522.20e0.0752k−8833.69,(34)X^1k+1A=X0′1A−bae−ak+ba=25.8654e0.0784k−23.7454,(35)X^1k+1P=X01P−bae−ak+ba=1357.82e0.0539k−1281.01.Table 3
Actual value and forecast value of the freight development index in Guangdong Province (unit: million tons).
YearTotal freight volume (F)Railway freight volume (R)Truck freight volume (T)XF0X^FXR0′X^RXT0′X^T20133065.443065.44202.38202.382176.432176.5520143612.493561.51192.09192.042636.192632.3720153792.213717.65184.02183.872828.872729.8820163743.483880.63186.23176.042727.372831.0120173984.694050.76155.72168.552886.192935.8820184265.784228.35157.64161.373063.043044.6420194459.754413.72161.92154.503192.313157.43Source: according to the calculation criteria.Table 4
Actual value and forecast value of the freight development index in Guangdong Province (unit: million tons).
YearWater freight volume (W)Air cargo volume (A)Pipeline freight volume (P)XW0X^WXA0′X^AXP0X^P2013688.51688.512.122.1276.8176.812014781.25744.062.242.1181.5475.142015780.93802.202.282.2876.9379.292016828.93864.882.402.4779.3283.682017939.04932.462.452.6782.0988.3120181023.511005.323.012.8999.4193.2020191083.711083.883.0173.1298.9998.35Source: according to the calculation criteria.


### 4.4. Validation of Modeling Accuracy of GM (1, 1) of Freight Volume in Guangdong Province

According to the modeling results of GM (1, 1), we will test the accuracy of the model by the residual test and posterior test.


#### 4.4.1. Residual Test

The residual test is carried out to test the accuracy of GM (1, 1) in forecasting the freight volume of Guangdong Province. The predicted value of total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume is compared with the original data.εkF, εkR, εkT, εkW, εkA, and εkP and ΔkF, ΔkR, ΔkT, ΔkW, ΔkA, and ΔkPare calculated according to formulas (11)–(14), and the results are shown in Tables 5 and 6.Table 5
Residual test results of GM (1,1) of freight volume in Guangdong Province.
YearTotal freight volume (F)Railway freight volume (R)Truck freight volume (T)εkFΔkFεkRΔkRεkTΔkT20130.0000.0000.0000.0000.1200.0002014−50.9800.014−0.0500.000−3.8200.0012015−74.5600.020−0.1500.001−98.9900.0352016137.1500.037−10.1900.055103.6400.038201766.0700.01712.8300.08249.6900.0172018−37.4300.0093.7300.024−18.4000.0062019−46.0300.010−7.4200.046−34.8800.011Source: according to the calculation criteria.Table 6
Residual test results of GM (1,1) of freight volume in Guangdong Province.
YearWater freight volume (W)Air cargo volume (A)Pipeline freight volume (P)εkWΔkWεkAΔkAεkPΔkP20130.0000.0000.0000.0000.0000.0002014−37.1900.048−0.1300.058−0.0780.078201521.2700.0270.0000.0000.0310.031201635.9500.0430.0700.0290.0550.0552017−6.5800.0070.2200.0900.0760.0762018−18.1900.018−0.1200.040−0.0620.06220190.1700.0000.1030.034−0.0060.006Source: according to the calculation criteria.(36)ΔkF≤0.05,ΔkF¯=0.0152<0.05,ρF0=1−ΔkF¯∗100%=98.48%>90%,ΔkR≤0.05,ΔkR¯=0.0297<0.05,ρR0=1−ΔkR¯∗100%=97.03%>90%,ΔkT≤0.05,ΔkT¯=0.0155<0.05,ρT0=1−ΔkT¯∗100%=98.45%>90%,ΔkW≤0.05,ΔkW¯=0.02548<0.05,ρW0=1−ΔkW¯∗100%=97.96%>90%,ΔkA≤0.05,ΔkA¯=0.0359<0.05,ρA0=1−ΔkA¯∗100%=96.41%>90%,ΔkP≤0.05,ΔkP¯=0.0441<0.05,ρP0=1−ΔkC¯∗100%=95.59%>90%.To sum up, GM (1, 1) has a good accuracy in modeling and forecasting the freight development index of Guangdong Province and can pass the residual test.


#### 4.4.2. Posterior Error Test

In order to further test the accuracy of GM (1,1) in forecasting the development of freight volume in Guangdong Province, a posteriori test is carried out. According to formulas (15)–(18), the original sequence’s variance of XF0, XR0′, XT0, XW0, XA0′, and XP0 is calculated, and the results are as follows:(37)S1F=456.316,S1R=18.535,S1T=329.434,S1W=143.907,S1A=0.365,S1P=9.902.The absolute residual sequence’s variance ofεkF, εkR, εkT, εkW, εkA, and εkp is calculated, and the results are as follows:(38)S2F=76.211,S2R=7.497,S2T=64.003,S2W=24.194,S2A=0.124,S2P=4.885.According to formula (19), calculate the ratio of variance of the freight index. The results are as follows:(39)CF=0.167,CR=0.404,CT=0.194,CW=0.168,CA=0.365,CP=0.493.CP is less than 0.5, so the posterior error test is barely qualified. CR and CA are greater than 0.35 and less than 0.45, respectively, and the posterior error test result is qualified. CF, CT, and CWare less than 0.35, and hence, the posterior error test result is good.Calculate the probability of small error according to formulas (20) and (21). The results are as follows:(40)S0F=307.785,S0R=12.502,S0T=222.203,S0W=97.065,S0A=0.246,S0P=6.679,εkF−ε¯F=0.826,50.154,73.734,137.976,66.896,36.604,45.204,P=1>0.95,εkR−ε¯R=0.179,0.129,0.029,10.011,13.009,3.909,7.241,P=85.7>0.8,εkT−ε¯T=0.497,3.443,98.613,104.017,50.067,18.023,34.503,P=1>0.95,εkW−ε¯W=0.653,36.537,21.923,36.603,5.927,17.537,0.823,P=1>0.95εkA−ε¯A=0.020,0.150,0.020,0.050,0.200,0.140,0.083,P=1>0.95,εkP−ε¯P=0.044,6.356,2.404,4.404,6.264,6.166,0.596,P=1>0.95.To sum up, the six indicators of freight development in Guangdong Province, total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume, all meet the requirements of posterior error test standardC<0.5, 0.8<P, which indicate that the accuracy of the model is qualified.


## 4.1. Data Source and Description

The data are from the monthly open statistics of Guangdong Provincial Bureau of Statistics from 2013 to 2020. The data content includes six groups of data: total freight volume, truck freight volume, railway freight volume, waterway freight volume, air freight volume, and pipeline freight volume of Guangdong Province. For the convenience of calculation, total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume are expressed. The annual freight development of Guangdong Province is counted, covering the six freight indexes. The original data to predict the development of freight of Guangdong Province in 2020 are shown in Table2.Table 2
Monthly data of freight indicators of Guangdong Province from 2013 to 2020 (unit: million tons) (%).
YearTotal freight volume (F)Railway freight volume (R)Truck freight volume (T)Water freight volume (W)Air cargo volume (A)Pipeline freight volume (P)AmountRatioAmountRatioAmountRatioAmountRatioAmountRatio20133065.44122.383.9922176.4370.999688.5122.4601.320.04376.812.50620143612.49112.093.1032636.1972.974781.2521.6261.440.04081.542.25720153792.21104.022.7432828.8774.597780.9320.5931.480.03976.932.02920163743.48106.232.8382727.3772.857828.9322.1431.600.04379.322.11920173984.6975.721.9002886.1972.432939.0423.5661.650.04182.092.06020184265.7877.641.8203063.0471.8051023.5123.9942.210.05299.412.33020194459.7581.921.8373192.3171.5801083.7124.3002.370.05398.992.22020203547.5177.672.1892313.5665.2161036.5729.2202.380.067117.353.308Data source: according to the website data of Guangdong Provincial Bureau of Statistics.


## 4.2. Rationality of GM (1, 1) Construction

The rationality of model construction was tested in advance. On the basis of the original data sequence, the stage ratioλk is calculated according to formula (10).


### 4.2.1. Calculation of the Grade Ratioλk

The grade ratio is calculated as follows:(27)λkF=0.8486,0.9526,1.0130,0.9395,0.9341,0.9565,λkR=1.0918,1.0776,0.9792,1.4029,0.9753,0.9478,λkT=0.8256,0.9319,1.0372,0.9450,0.9423,0.9595,λkW=0.8813,1.0004,0.9421,0.8827,0.9175,0.9445,λkA=0.9167,0.9730,0.9250,0.9697,0.7466,0.9325,λkP=0.9420,1.0599,0.9699,0.9663,0.8258,1.0042.


### 4.2.2. Judgment of the Grade Ratio

λk∈e−2/n+1,e2/n+1, when n = 7,λk∈0.7788,1.2840. If λ(k) in the above range, x0k is suitable for GM (1,1). λkF∈0.8486,1.0130, λkT∈0.8256,1.0372, λkW∈0.8813,1.0004,andλkP∈0.8258,1.0559,wherek=2,3,4,5,6,7, and the grade ratios are in0.7788,1.2840; hence,XF0XT0,XW0, and XP0 can be modeled by GM (1,1). The values of grey development coefficient “-a” are 0.0429, 0.0364, 0.0752, and 0.0539, respectively, i.e., less than 0.3, which are suitable for medium- and long-term prediction.However,λkR∈0.9478,1.4029andλkA∈0.7446,1.0442. There is a grade ratio not in the region, which is not available for XR0and XA0modeled in GM (1, 1) directly. Therefore, it is necessary to do translation transformation on the data, and the translated data are XR0′and XA0′, as follows:(28)XR0′=202.38,192.09,184.02,186.23,155.72,157.64,161.92,XA0′=2.12,2.24,2.28,2.40,2.45,3.01,3.17.The grade ratios ofXR0′and XA0′are calculated:(29)λ′kR=1.0536,1.0439,0.9881,1.1959,0.9878,0.9736,λ′kR∈0.9736,1.1959,K=2,3,4,5,6,7,λ′kA=0.9464,0.9825,0.9500,0.9796,0.8140,0.9495,λ′kA∈0.8140,0.9825,K=2,3,4,5,6,7.The grade ratios ofXR0′and XA0′ are in the rank of λkand∈0.7788,1.2840. The values of grey development coefficient “−a” are −0.0435 and −0.0784, which are less than 0.3. So XR0′and XA0′ are suitable for medium- and long-term prediction.


## 4.2.1. Calculation of the Grade Ratioλk

The grade ratio is calculated as follows:(27)λkF=0.8486,0.9526,1.0130,0.9395,0.9341,0.9565,λkR=1.0918,1.0776,0.9792,1.4029,0.9753,0.9478,λkT=0.8256,0.9319,1.0372,0.9450,0.9423,0.9595,λkW=0.8813,1.0004,0.9421,0.8827,0.9175,0.9445,λkA=0.9167,0.9730,0.9250,0.9697,0.7466,0.9325,λkP=0.9420,1.0599,0.9699,0.9663,0.8258,1.0042.


## 4.2.2. Judgment of the Grade Ratio

λk∈e−2/n+1,e2/n+1, when n = 7,λk∈0.7788,1.2840. If λ(k) in the above range, x0k is suitable for GM (1,1). λkF∈0.8486,1.0130, λkT∈0.8256,1.0372, λkW∈0.8813,1.0004,andλkP∈0.8258,1.0559,wherek=2,3,4,5,6,7, and the grade ratios are in0.7788,1.2840; hence,XF0XT0,XW0, and XP0 can be modeled by GM (1,1). The values of grey development coefficient “-a” are 0.0429, 0.0364, 0.0752, and 0.0539, respectively, i.e., less than 0.3, which are suitable for medium- and long-term prediction.However,λkR∈0.9478,1.4029andλkA∈0.7446,1.0442. There is a grade ratio not in the region, which is not available for XR0and XA0modeled in GM (1, 1) directly. Therefore, it is necessary to do translation transformation on the data, and the translated data are XR0′and XA0′, as follows:(28)XR0′=202.38,192.09,184.02,186.23,155.72,157.64,161.92,XA0′=2.12,2.24,2.28,2.40,2.45,3.01,3.17.The grade ratios ofXR0′and XA0′are calculated:(29)λ′kR=1.0536,1.0439,0.9881,1.1959,0.9878,0.9736,λ′kR∈0.9736,1.1959,K=2,3,4,5,6,7,λ′kA=0.9464,0.9825,0.9500,0.9796,0.8140,0.9495,λ′kA∈0.8140,0.9825,K=2,3,4,5,6,7.The grade ratios ofXR0′and XA0′ are in the rank of λkand∈0.7788,1.2840. The values of grey development coefficient “−a” are −0.0435 and −0.0784, which are less than 0.3. So XR0′and XA0′ are suitable for medium- and long-term prediction.


## 4.3. Construction of GM (1, 1)

According to the original sequence, the accumulated sequence is generated and the differential equation is constructed. On the basis of solving the values of “a” and “b,” the time response sequence is obtained, as formulas (30)–(35). The predicted values are calculated according to the time response sequence, shown in Tables 3 and 4.(30)X^1k+1F=X01F−bae−ak+ba=81237.44e0.0429k−78172.00,(31)X^1k+1R=X0′1R−bae−ak+ba=4713.89−4511.51e−0.0435k,(32)X^1k+1T=X01T−bae−ak+ba=71059.66e0.03637k−6888311.00,(33)X^1k+1W=X01W−bae−ak+ba=9522.20e0.0752k−8833.69,(34)X^1k+1A=X0′1A−bae−ak+ba=25.8654e0.0784k−23.7454,(35)X^1k+1P=X01P−bae−ak+ba=1357.82e0.0539k−1281.01.Table 3
Actual value and forecast value of the freight development index in Guangdong Province (unit: million tons).
YearTotal freight volume (F)Railway freight volume (R)Truck freight volume (T)XF0X^FXR0′X^RXT0′X^T20133065.443065.44202.38202.382176.432176.5520143612.493561.51192.09192.042636.192632.3720153792.213717.65184.02183.872828.872729.8820163743.483880.63186.23176.042727.372831.0120173984.694050.76155.72168.552886.192935.8820184265.784228.35157.64161.373063.043044.6420194459.754413.72161.92154.503192.313157.43Source: according to the calculation criteria.Table 4
Actual value and forecast value of the freight development index in Guangdong Province (unit: million tons).
YearWater freight volume (W)Air cargo volume (A)Pipeline freight volume (P)XW0X^WXA0′X^AXP0X^P2013688.51688.512.122.1276.8176.812014781.25744.062.242.1181.5475.142015780.93802.202.282.2876.9379.292016828.93864.882.402.4779.3283.682017939.04932.462.452.6782.0988.3120181023.511005.323.012.8999.4193.2020191083.711083.883.0173.1298.9998.35Source: according to the calculation criteria.


## 4.4. Validation of Modeling Accuracy of GM (1, 1) of Freight Volume in Guangdong Province

According to the modeling results of GM (1, 1), we will test the accuracy of the model by the residual test and posterior test.


### 4.4.1. Residual Test

The residual test is carried out to test the accuracy of GM (1, 1) in forecasting the freight volume of Guangdong Province. The predicted value of total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume is compared with the original data.εkF, εkR, εkT, εkW, εkA, and εkP and ΔkF, ΔkR, ΔkT, ΔkW, ΔkA, and ΔkPare calculated according to formulas (11)–(14), and the results are shown in Tables 5 and 6.Table 5
Residual test results of GM (1,1) of freight volume in Guangdong Province.
YearTotal freight volume (F)Railway freight volume (R)Truck freight volume (T)εkFΔkFεkRΔkRεkTΔkT20130.0000.0000.0000.0000.1200.0002014−50.9800.014−0.0500.000−3.8200.0012015−74.5600.020−0.1500.001−98.9900.0352016137.1500.037−10.1900.055103.6400.038201766.0700.01712.8300.08249.6900.0172018−37.4300.0093.7300.024−18.4000.0062019−46.0300.010−7.4200.046−34.8800.011Source: according to the calculation criteria.Table 6
Residual test results of GM (1,1) of freight volume in Guangdong Province.
YearWater freight volume (W)Air cargo volume (A)Pipeline freight volume (P)εkWΔkWεkAΔkAεkPΔkP20130.0000.0000.0000.0000.0000.0002014−37.1900.048−0.1300.058−0.0780.078201521.2700.0270.0000.0000.0310.031201635.9500.0430.0700.0290.0550.0552017−6.5800.0070.2200.0900.0760.0762018−18.1900.018−0.1200.040−0.0620.06220190.1700.0000.1030.034−0.0060.006Source: according to the calculation criteria.(36)ΔkF≤0.05,ΔkF¯=0.0152<0.05,ρF0=1−ΔkF¯∗100%=98.48%>90%,ΔkR≤0.05,ΔkR¯=0.0297<0.05,ρR0=1−ΔkR¯∗100%=97.03%>90%,ΔkT≤0.05,ΔkT¯=0.0155<0.05,ρT0=1−ΔkT¯∗100%=98.45%>90%,ΔkW≤0.05,ΔkW¯=0.02548<0.05,ρW0=1−ΔkW¯∗100%=97.96%>90%,ΔkA≤0.05,ΔkA¯=0.0359<0.05,ρA0=1−ΔkA¯∗100%=96.41%>90%,ΔkP≤0.05,ΔkP¯=0.0441<0.05,ρP0=1−ΔkC¯∗100%=95.59%>90%.To sum up, GM (1, 1) has a good accuracy in modeling and forecasting the freight development index of Guangdong Province and can pass the residual test.


### 4.4.2. Posterior Error Test

In order to further test the accuracy of GM (1,1) in forecasting the development of freight volume in Guangdong Province, a posteriori test is carried out. According to formulas (15)–(18), the original sequence’s variance of XF0, XR0′, XT0, XW0, XA0′, and XP0 is calculated, and the results are as follows:(37)S1F=456.316,S1R=18.535,S1T=329.434,S1W=143.907,S1A=0.365,S1P=9.902.The absolute residual sequence’s variance ofεkF, εkR, εkT, εkW, εkA, and εkp is calculated, and the results are as follows:(38)S2F=76.211,S2R=7.497,S2T=64.003,S2W=24.194,S2A=0.124,S2P=4.885.According to formula (19), calculate the ratio of variance of the freight index. The results are as follows:(39)CF=0.167,CR=0.404,CT=0.194,CW=0.168,CA=0.365,CP=0.493.CP is less than 0.5, so the posterior error test is barely qualified. CR and CA are greater than 0.35 and less than 0.45, respectively, and the posterior error test result is qualified. CF, CT, and CWare less than 0.35, and hence, the posterior error test result is good.Calculate the probability of small error according to formulas (20) and (21). The results are as follows:(40)S0F=307.785,S0R=12.502,S0T=222.203,S0W=97.065,S0A=0.246,S0P=6.679,εkF−ε¯F=0.826,50.154,73.734,137.976,66.896,36.604,45.204,P=1>0.95,εkR−ε¯R=0.179,0.129,0.029,10.011,13.009,3.909,7.241,P=85.7>0.8,εkT−ε¯T=0.497,3.443,98.613,104.017,50.067,18.023,34.503,P=1>0.95,εkW−ε¯W=0.653,36.537,21.923,36.603,5.927,17.537,0.823,P=1>0.95εkA−ε¯A=0.020,0.150,0.020,0.050,0.200,0.140,0.083,P=1>0.95,εkP−ε¯P=0.044,6.356,2.404,4.404,6.264,6.166,0.596,P=1>0.95.To sum up, the six indicators of freight development in Guangdong Province, total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume, all meet the requirements of posterior error test standardC<0.5, 0.8<P, which indicate that the accuracy of the model is qualified.


## 4.4.1. Residual Test

The residual test is carried out to test the accuracy of GM (1, 1) in forecasting the freight volume of Guangdong Province. The predicted value of total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume is compared with the original data.εkF, εkR, εkT, εkW, εkA, and εkP and ΔkF, ΔkR, ΔkT, ΔkW, ΔkA, and ΔkPare calculated according to formulas (11)–(14), and the results are shown in Tables 5 and 6.Table 5
Residual test results of GM (1,1) of freight volume in Guangdong Province.
YearTotal freight volume (F)Railway freight volume (R)Truck freight volume (T)εkFΔkFεkRΔkRεkTΔkT20130.0000.0000.0000.0000.1200.0002014−50.9800.014−0.0500.000−3.8200.0012015−74.5600.020−0.1500.001−98.9900.0352016137.1500.037−10.1900.055103.6400.038201766.0700.01712.8300.08249.6900.0172018−37.4300.0093.7300.024−18.4000.0062019−46.0300.010−7.4200.046−34.8800.011Source: according to the calculation criteria.Table 6
Residual test results of GM (1,1) of freight volume in Guangdong Province.
YearWater freight volume (W)Air cargo volume (A)Pipeline freight volume (P)εkWΔkWεkAΔkAεkPΔkP20130.0000.0000.0000.0000.0000.0002014−37.1900.048−0.1300.058−0.0780.078201521.2700.0270.0000.0000.0310.031201635.9500.0430.0700.0290.0550.0552017−6.5800.0070.2200.0900.0760.0762018−18.1900.018−0.1200.040−0.0620.06220190.1700.0000.1030.034−0.0060.006Source: according to the calculation criteria.(36)ΔkF≤0.05,ΔkF¯=0.0152<0.05,ρF0=1−ΔkF¯∗100%=98.48%>90%,ΔkR≤0.05,ΔkR¯=0.0297<0.05,ρR0=1−ΔkR¯∗100%=97.03%>90%,ΔkT≤0.05,ΔkT¯=0.0155<0.05,ρT0=1−ΔkT¯∗100%=98.45%>90%,ΔkW≤0.05,ΔkW¯=0.02548<0.05,ρW0=1−ΔkW¯∗100%=97.96%>90%,ΔkA≤0.05,ΔkA¯=0.0359<0.05,ρA0=1−ΔkA¯∗100%=96.41%>90%,ΔkP≤0.05,ΔkP¯=0.0441<0.05,ρP0=1−ΔkC¯∗100%=95.59%>90%.To sum up, GM (1, 1) has a good accuracy in modeling and forecasting the freight development index of Guangdong Province and can pass the residual test.


## 4.4.2. Posterior Error Test

In order to further test the accuracy of GM (1,1) in forecasting the development of freight volume in Guangdong Province, a posteriori test is carried out. According to formulas (15)–(18), the original sequence’s variance of XF0, XR0′, XT0, XW0, XA0′, and XP0 is calculated, and the results are as follows:(37)S1F=456.316,S1R=18.535,S1T=329.434,S1W=143.907,S1A=0.365,S1P=9.902.The absolute residual sequence’s variance ofεkF, εkR, εkT, εkW, εkA, and εkp is calculated, and the results are as follows:(38)S2F=76.211,S2R=7.497,S2T=64.003,S2W=24.194,S2A=0.124,S2P=4.885.According to formula (19), calculate the ratio of variance of the freight index. The results are as follows:(39)CF=0.167,CR=0.404,CT=0.194,CW=0.168,CA=0.365,CP=0.493.CP is less than 0.5, so the posterior error test is barely qualified. CR and CA are greater than 0.35 and less than 0.45, respectively, and the posterior error test result is qualified. CF, CT, and CWare less than 0.35, and hence, the posterior error test result is good.Calculate the probability of small error according to formulas (20) and (21). The results are as follows:(40)S0F=307.785,S0R=12.502,S0T=222.203,S0W=97.065,S0A=0.246,S0P=6.679,εkF−ε¯F=0.826,50.154,73.734,137.976,66.896,36.604,45.204,P=1>0.95,εkR−ε¯R=0.179,0.129,0.029,10.011,13.009,3.909,7.241,P=85.7>0.8,εkT−ε¯T=0.497,3.443,98.613,104.017,50.067,18.023,34.503,P=1>0.95,εkW−ε¯W=0.653,36.537,21.923,36.603,5.927,17.537,0.823,P=1>0.95εkA−ε¯A=0.020,0.150,0.020,0.050,0.200,0.140,0.083,P=1>0.95,εkP−ε¯P=0.044,6.356,2.404,4.404,6.264,6.166,0.596,P=1>0.95.To sum up, the six indicators of freight development in Guangdong Province, total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume, all meet the requirements of posterior error test standardC<0.5, 0.8<P, which indicate that the accuracy of the model is qualified.


## 5. Impact of COVID-19 on Freight Development of Guangdong Province

The results of the rationality test of model construction, residual test, and posteriori test proved that GM (1, 1) is feasible to forecast the freight development of Guangdong Province in 2020. Due to the particularity of railway transportation and air transportation, after eliminating the influence ofC value, the prediction results are shown in Table 7.Table 7
Forecast freight volume value of Guangdong Province in 2020 (unit: million ton).
YearTotal freight volumeRailway freight volumeTruck, freight volumeWater freight volumeAir cargo volumePipeline freight volume20204607.22267.9273274.3921168.5722.475103.797Source: according to the calculation criteria.In order to reflect COVID-19’s monthly impact on Guangdong Province’s freight development, further explore the monthly forecast value of freight volume in Guangdong Province of 2020:(1)
Calculate the ratio of each month in different years to the freight volume of that year.Record the freight development data of Guangdong Province from 2013 to 2019 as matrix ofAF7×12, AR7×12, AT7×12, AW7×12, AA7×12, andAP7×12, and calculate the ratio of monthly freight volume (akj) to the total freight volume of the year (x0k) and record it as Rkj, where R is ratio, k is year, and j is month:(41)Rkj=akjx0k,k=1,2,3,…,7,j=1,2,3,…,12.(2)
Calculate the average freight ratio of the same month in different years:(42)Rj¯=17∑k=17rkj,k=1,2,3,…,7,j=1,2,3,…,12.According to formulas (35)–(41), we can calculateRjF¯, RjR¯, RjT¯, RjW¯, RjA¯, and RjP¯ from January to December, as shown in Table 8.(3)
Calculate monthly forecast value as follows:(43)a^kj=Rj¯x^0kk=1,2,3,…,9,j=1,2,3,…,12.(4)
Calculate the influence value I as follows:(44)Ikj=akj−a^ija^ij×100%,(45)Ik=x0k−x^0kx^0k×100%.Table 8
Average ratio of monthly freight (unit: %).
JanFebMarAprMayJunJulAugSepOctNovDecRjF¯7.3786.3647.5608.0328.2518.3578.5298.5718.7949.0959.3049.766RjR¯8.3796.9658.4298.0738.5968.0898.3678.2998.3588.5108.7099.225RjT¯7.1176.2217.4847.9898.2298.3418.5948.6348.8379.2209.3699.965RjW¯7.9866.5987.5768.1098.2828.4588.3898.3758.7228.8629.2719.372RjA¯7.7156.5377.7628.0518.3408.3118.4708.4708.6788.9229.1639.582RjP¯8.0557.2808.1578.2368.2628.3128.3598.7658.6098.5678.6778.720Source: according to the calculation criteria.According to formulas (41)–(45), the monthly forecast value and impact of freight development in Guangdong Province from January to December 2020 are calculated, as shown in Tables 9 and 10 and Figure 1.Table 9
COVID-19’s impact of freight development in Guangdong Province (unit, million ton; %).
MonthTotal freight volumeRailway freight volumeTruck freight volumeActual valuePredictive valueImpact degreeActual valuePredictive valueImpact degreeActual valuePredictive valueImpact degreeJan250.750339.903−26.2295.5405.692−2.668158.130233.029−32.142Feb135.680293.208−53.7265.4804.73115.82970.980203.705−65.155Mar223.620348.316−35.8006.2705.7259.511132.740245.071−45.836Apr267.320370.044−27.7605.9805.4849.048170.170261.582−34.946May298.390380.134−21.5046.9105.83918.336191.570269.464−28.907Jun308.350385.032−19.9166.7805.49523.387204.060273.113−25.284Jul314.180392.930−20.0427.2605.68327.744211.690281.402−24.773Aug329.530394.878−16.5496.6505.63717.964215.540282.716−23.761Sep332.890405.139−17.8336.9605.67822.586220.050289.356−23.952Oct349.210419.023−16.6616.3605.78010.029237.200301.893−21.429Nov364.490428.661−14.9706.9905.91618.163245.020306.762−20.127Dec373.100449.955−17.0816.4906.2663.568256.410326.298−21.418Total impact4607.2223547.510−23.00177.6767.92714.3432313.5603274.392−29.344Source: according to the calculation criteria.Table 10
COVID-19’s impact of freight development in Guangdong Province (unit: million ton; %).
MonthWater freight volumeAir cargo volumePipeline freight volumeActual valuePredictive valueImpact degreeActual valuePredictive valueImpact degreeActual valuePredictive valueImpact degreeJan78.54093.318−15.8360.1900.191−0.4938.3408.361−0.248Feb53.02077.100−31.2320.1100.162−32.0116.0807.556−19.533Mar76.20088.529−13.9260.1800.192−6.3088.2308.467−2.798Apr82.36094.757−13.0830.1800.199−9.6628.6408.5491.065May91.33096.785−5.6360.2000.206−3.1058.3908.575−2.161Jun87.89098.840−11.0790.2100.2062.0879.4108.6289.068Jul86.63098.033−11.6320.2000.210−4.5918.4108.677−3.075Aug95.00097.869−2.9320.2000.210−4.59312.1409.09833.432Sep94.440101.925−7.3440.2400.21511.74511.2008.93625.332Oct93.680103.560−9.5400.2200.221−0.36711.7508.89332.131Nov99.080108.343−8.5500.2200.227−2.99413.1809.00746.332Dec98.400109.513−10.1480.2300.237−3.01711.5809.05127.948Total impact1036.5701168.572−11.2962.3802.475−3.838117.350103.79713.057Source: according to the calculation criteria.Figure 1
The impact of freight development in Guangdong Province.According to Tables9 and 10 and Figure 1, reflecting the influence of COVID-19, there are three characteristics of freight transport development of Guangdong Province in 2020, which are stage characteristics, structural characteristics, and entity conduction.


### 5.1. Stage Characteristics

The first stage is the direct impact stage. Freight transport in Guangdong Province is stagnant during January and February. Affected by the epidemic situation, most logistics enterprises shut down except emergency logistics, and some logistics transportation channels were interrupted. The risk mainly comes from the disconnection of logistics supply and demand and the interruption of logistics channel. COVID-19 had the greatest impact on freight development in Guangdong at that time. The negative impact value of freight volume of various forms of transportation reached the peak in February. The impact value of total freight volume is −53.726%, that of truck freight volume is −65.155%, that of water freight volume is −31.232%, that of air cargo volume is −32.011%, and that of pipeline freight volume is −19.533%. However, the impact of railway is positive, and the stagnation of other transportation promotes the actual value of railway freight volume to be higher than the predicted value, and the impact value is 15.829%.The second stage is the stage of entity conduction. The impact value of each subindex of Guangdong freight volume from March to May is reduced. This stage mainly focuses on the period from March to May 2020. The main impact of this stage is the uneven structure of the type and quantity of freight demand business in Guangdong Province and the short-term mismatch between supply and demand. The development of Guangdong’s port freight industry has changed from explosive logistics demand in the early stage of the full resumption of manufacturing and circulation industries to the gradual emergence of real economic difficulties and the decline of logistics demand with the spread of the global epidemic.The third stage is the policy digestion stage. This stage is mainly after May 2020; the state has issued relevant policies to support the recovery and development of the real economy and logistics industry, such as providing freeway and other measures to promote further recovery of freight. The role of policy has a certain lag and conductivity. The development of freight transportation in Guangdong Province is affected by the favorable policies and the recovery of logistics demand of the upstream manufacturing industry, which can be shown in turn in the postepidemic period. COVID-19’s impact on freight development in Guangdong showed a gradual reduction. The risk points in this period mainly focus on the recovery of logistics industry, the scale of logistics investment, and the choice of new development mode.


### 5.2. Structural Characteristics

The impact of the epidemic on the development of freight transportation in Guangdong Province has structural characteristics. In the same period, the impact of the epidemic on the internal subbusiness sectors of freight transportation in Guangdong Province is different. The overall impact value of the epidemic on freight transportation was −23.001%, and the most affected mode was truck transportation (−29.344%), followed by waterway transportation (−11.296%) and air transportation (−3.838%). At the beginning of the outbreak, the railway operation remained sustainable. Due to the suspension of road transport enterprises, a large number of goods were transferred to railway transportation. Pipeline transportation can be carried out without people. The epidemic has little impact on its production and operation. Therefore, the impact of COVID-19 on the railway transportation and pipeline transportation is positive. The influence values were 14.343 and 13.057, respectively. In summary, the development structure of freight transport in Guangdong has been characterized by structural development under the influence of COVID-19.


### 5.3. Characteristics of Solid Conduction

Freight industry is a derivative industry. The demand of freight industry is mainly affected by the secondary industry and commodity circulation industry and is mainly affected by manufacturing industry, import and export trade, domestic trade, and manufacturing industry. As an auxiliary industry of the national economy, freight industry is an important support for the development of industrial economy. The crisis of the freight industry will be transmitted in reverse, resulting in damage to the real economy. During the epidemic period, due to traffic control, road restrictions, blocked logistics channels, staff unable to rework and resume production on time, and unsatisfied conditions for resumption of production, some freight enterprises were unable to provide normal freight service, which affected the resumption of some industrial enterprises and could not guarantee the logistics of raw materials and finished products.


## 5.1. Stage Characteristics

The first stage is the direct impact stage. Freight transport in Guangdong Province is stagnant during January and February. Affected by the epidemic situation, most logistics enterprises shut down except emergency logistics, and some logistics transportation channels were interrupted. The risk mainly comes from the disconnection of logistics supply and demand and the interruption of logistics channel. COVID-19 had the greatest impact on freight development in Guangdong at that time. The negative impact value of freight volume of various forms of transportation reached the peak in February. The impact value of total freight volume is −53.726%, that of truck freight volume is −65.155%, that of water freight volume is −31.232%, that of air cargo volume is −32.011%, and that of pipeline freight volume is −19.533%. However, the impact of railway is positive, and the stagnation of other transportation promotes the actual value of railway freight volume to be higher than the predicted value, and the impact value is 15.829%.The second stage is the stage of entity conduction. The impact value of each subindex of Guangdong freight volume from March to May is reduced. This stage mainly focuses on the period from March to May 2020. The main impact of this stage is the uneven structure of the type and quantity of freight demand business in Guangdong Province and the short-term mismatch between supply and demand. The development of Guangdong’s port freight industry has changed from explosive logistics demand in the early stage of the full resumption of manufacturing and circulation industries to the gradual emergence of real economic difficulties and the decline of logistics demand with the spread of the global epidemic.The third stage is the policy digestion stage. This stage is mainly after May 2020; the state has issued relevant policies to support the recovery and development of the real economy and logistics industry, such as providing freeway and other measures to promote further recovery of freight. The role of policy has a certain lag and conductivity. The development of freight transportation in Guangdong Province is affected by the favorable policies and the recovery of logistics demand of the upstream manufacturing industry, which can be shown in turn in the postepidemic period. COVID-19’s impact on freight development in Guangdong showed a gradual reduction. The risk points in this period mainly focus on the recovery of logistics industry, the scale of logistics investment, and the choice of new development mode.


## 5.2. Structural Characteristics

The impact of the epidemic on the development of freight transportation in Guangdong Province has structural characteristics. In the same period, the impact of the epidemic on the internal subbusiness sectors of freight transportation in Guangdong Province is different. The overall impact value of the epidemic on freight transportation was −23.001%, and the most affected mode was truck transportation (−29.344%), followed by waterway transportation (−11.296%) and air transportation (−3.838%). At the beginning of the outbreak, the railway operation remained sustainable. Due to the suspension of road transport enterprises, a large number of goods were transferred to railway transportation. Pipeline transportation can be carried out without people. The epidemic has little impact on its production and operation. Therefore, the impact of COVID-19 on the railway transportation and pipeline transportation is positive. The influence values were 14.343 and 13.057, respectively. In summary, the development structure of freight transport in Guangdong has been characterized by structural development under the influence of COVID-19.


## 5.3. Characteristics of Solid Conduction

Freight industry is a derivative industry. The demand of freight industry is mainly affected by the secondary industry and commodity circulation industry and is mainly affected by manufacturing industry, import and export trade, domestic trade, and manufacturing industry. As an auxiliary industry of the national economy, freight industry is an important support for the development of industrial economy. The crisis of the freight industry will be transmitted in reverse, resulting in damage to the real economy. During the epidemic period, due to traffic control, road restrictions, blocked logistics channels, staff unable to rework and resume production on time, and unsatisfied conditions for resumption of production, some freight enterprises were unable to provide normal freight service, which affected the resumption of some industrial enterprises and could not guarantee the logistics of raw materials and finished products.


## 6. Research on the Related Factors of Freight Development in Guangdong Province

The grey prediction model GM (1, 1) can scientifically measure the impact of COVID-19 on the development of freight transport in Guangdong. From the perspective of system theory, the development of freight transportation in Guangdong Province is the output of logistics system and the product of adapting to the economic environment and regional development of Guangdong Province. Therefore, in order to explore the countermeasures of the development of freight transportation in Guangdong Province in the postepidemic period, we should also analyze the environmental factors. To sum up, this paper will use the grey correlation model to study the related factors of freight development in Guangdong Province.


### 6.1. Construction of the Index System

Scholars in the study of freight development factors divide them mainly into the regional economic factors, logistics environmental factors, and industrial factors for quantitative index selection; this paper, considering the scientificity, rationality, comprehensiveness, and comparability of the index construction, divides the related factors of the freight development of Guangdong Province into economic factors, transportation factors, science and technology factors, and policy factors, as shown in Table11.Table 11
Index system of influencing factors of freight development in Guangdong Province.
First level indicatorsSecond level indicatorsVariableCharacteristicRegional economy factorsGross domestic productX11Positive correlationProportion of added value of secondary industryX12Positive correlationTotal investment in fixed assetsX13Positive correlationPer capita disposable personal incomeX14Positive correlationTotal retail sales of social consumptionX15Positive correlationTotal imports and exportsX16Positive correlationBalance of domestic and foreign currency deposits of financial institutionsX17Positive correlationScience and technology factorsNumber of Internet broadband access usersX21Positive correlationInternal expenditure of R&D fundsX22Positive correlationNumber of employees of R&DX23Positive correlationEducation expenditureX24Positive correlationExpenditure on science and technologyX25Positive correlationGovernment policy factorsRevenueX31Positive correlationTransportation expenditureX32Positive correlationTransportation environment factorsNumber of employees in transportation, storage, and post industryX41Positive correlationLength of railroad lines in serviceX42Positive correlationNet tonnage of carrying vesselX43Positive correlationTonnage of truckX44Positive correlationOil pipeline mileageX45Positive correlationTransport planeX46Positive correlation


### 6.2. Calculation of Grey Correlation Degree of Influencing Factors

Based on the freight development of Guangdong Province from 2011 to 2019, total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume are the main factor sequence data of the system. The historical data ofX11−X46 index factors are regarded as subfactor series data, and the grey correlation resolution coefficient is 0.5 based on experience. The data involved are from the public data of the Guangdong Statistical Yearbook in 2013–2019. The grey correlation degree of influencing factors of freight development in Guangdong Province is calculated as given in formulas (24)–(26) and AVGγ0i=avgγ0iF+γ0iR+γ0iT+γ0iW+γ0iA+γ0iP, and the calculation results are shown in Tables 12–14.Table 12
Grey correlation results of freight development in Guangdong Province (1).
VariableX11X12X13X14X15X16X17γ0iF0.8960.7620.8070.9250.9000.7740.818γ0iR0.7470.9160.6890.8060.7370.9030.708γ0iT0.8940.7470.8160.9040.8970.7580.829γ0iW0.9300.7520.7980.9030.9170.7610.824γ0iW0.9210.7260.7980.8710.8840.7330.848γ0iA0.8380.8660.7400.9240.8230.8790.773AVGγ0i0.8710.7950.7750.8890.8600.8010.800Source: according to the calculation criteria.Table 13
Grey correlation results of freight development in Guangdong Province (2).
VariableX21X22X23X24X25X31X32γ0iF0.8500.8230.8900.8700.5860.8480.816γ0iR0.7490.7060.7790.7440.5990.7120.806γ0iT0.8480.8190.8820.8670.5900.8590.824γ0iW0.8850.8250.9330.8990.5760.8580.770γ0iW0.9170.8310.9120.9130.5580.8770.743γ0iA0.8310.7640.8810.8240.5790.7810.785AVGγ0i0.8470.7950.8800.8530.5820.8230.791Source: according to the calculation criteria.Table 14
Grey correlation results of freight development in Guangdong Province (3).
VariableX41X42X43X44X45X46γ0iF0.9160.9470.8080.9150.9080.902γ0iR0.8070.7850.8780.7900.7900.777γ0iT0.8940.9230.7890.9010.9030.887γ0iW0.8970.9190.8030.9300.8940.935γ0iW0.8640.8760.7670.9060.8290.942γ0iA0.9500.9220.8700.9110.8850.883AVGγ0i0.8880.8950.8190.8920.8680.888Source: according to the calculation criteria.The closer the value to 1, the higher the correlation between the self-factor sequence data and the main factor sequence data. According to the calculation results of correlation degree of Tables12–14, AVGR042>AVGR044>AVGR014>AVGR041=AVGR046>AVGR023>AVGR011>AVGR045>AVGR015>AVGR024>AVGR021>AVGR031>AVGR043>AVGR043>AVGR016>AVGR017>AVGR012=AVGR022>AVGR032>AVGR013>AVGR025; there are 15 factors with AVGR0i; there are 15 factors with AVGR0i greater than or equal to 0.8, indicating that the vast majority of factors are highly related to the development of freight transportation in Guangdong Province, including operating mileage of railway, tonnage of trucks, disposable income, deposit balance of financial institutions, number of employees in transportation, warehousing and postal industry, transport aircraft, R&D personnel, GDP, mileage of oil pipeline, total retail sales of consumer goods, financial expenditure on education, Internet broadband access users, general budget revenue, tonnage of cargo ships, and total import and export, which are most closely related to the development of freight transportation in Guangdong Province, ranking in the top 15 with the correlation degree greater than 0.8. The relevance degree of the added value of the secondary industry in the proportion of GDP is greater than 0.7, and its closeness with the freight development of Guangdong Province cannot be ignored. The relevance degree of science and technology financial expenditure is only 0.582, and its relevance with the freight development of Guangdong Province can be ignored.


### 6.3. Analysis of Grey Correlation Results

By using the grey correlation analysis method, we can objectively and reasonably reflect the influence degree of relevant influencing factors on the freight development of Guangdong Province and provide a quantifiable research perspective for the analysis of the relationship between regional economic factors, scientific and technological environment factors, government policy factors, transportation environment factors, and the freight development of Guangdong Province:(1)
The regional economic environment plays an important role in the freight development Guangdong Province.The average value of the six factors of regional economy (AVGR01i) is 0.827, and the value of four factors is greater than 0.8, which reflects that the economic environment is closely related to the freight development of Guangdong Province. The regional economic environment represents the demand of the freight market in the port market and reflects the impact of the economic environment on the demand of the port freight market; it also reflects the industrial transmission effect of the logistics industry affected by the real economy.(2)
The development of freight transportation in Guangdong Province should pay attention to the environmental factors of science and technology.The value of science and technology environment factor (AVGR02i) is 0.791. There is a certain degree of correlation between R&D personnel and the level of regional science and technology in Guangdong Province and the development of freight transportation in Guangdong Province, which means that the promotion and development of information technology have greatly promoted the development of freight transportation in Guangdong Province. R&D practitioners reflect the information technology talents, education expenditure reflects the strength of regional talent cultivation, and the amount of Internet broadband access reflects the basic environment of science and technology. The above three factors are greater than 0.8, which shows that the development of freight transportation in Guangdong Province is constrained by the basic conditions of the development of information technology and the cultivation of information talents. However, the government’s financial expenditure on science and technology has no direct correlation with the freight development of Guangdong Province, and its correlation coefficient is only 0.582.(3)
Government policy factors guide freight development in Guangdong Province.The value of government policy factor (AVGR03i) is 0.807. The government’s financial capacity and the intensity of transportation expenditure are closely related to the development of freight transportation in Guangdong Province. The amount of government’s financial revenue and the intensity of transportation expenditure are helpful to improve the conditions of transportation infrastructure in Guangdong Province.(4)
The transportation environment factors directly affect the development of freight in Guangdong Province.The value of environmental factors of transportation (AVGR04i) is 0.875. The development of freight transportation in Guangdong Province is closely related to environmental factors of transportation. The correlation degree between the environmental factors of transportation and the freight development of Guangdong Province is greater than 0.8. The operating mileage of railway and oil pipeline reflects the overall infrastructure of freight industry. The number of employees in transportation, warehousing, and postal industry reflects the human resource factors of logistics industry. The number of trucks, ships, and aircraft reflects the basic equipment conditions of logistics. The above indicators are closely related to the freight development of Guangdong Province.


## 6.1. Construction of the Index System

Scholars in the study of freight development factors divide them mainly into the regional economic factors, logistics environmental factors, and industrial factors for quantitative index selection; this paper, considering the scientificity, rationality, comprehensiveness, and comparability of the index construction, divides the related factors of the freight development of Guangdong Province into economic factors, transportation factors, science and technology factors, and policy factors, as shown in Table11.Table 11
Index system of influencing factors of freight development in Guangdong Province.
First level indicatorsSecond level indicatorsVariableCharacteristicRegional economy factorsGross domestic productX11Positive correlationProportion of added value of secondary industryX12Positive correlationTotal investment in fixed assetsX13Positive correlationPer capita disposable personal incomeX14Positive correlationTotal retail sales of social consumptionX15Positive correlationTotal imports and exportsX16Positive correlationBalance of domestic and foreign currency deposits of financial institutionsX17Positive correlationScience and technology factorsNumber of Internet broadband access usersX21Positive correlationInternal expenditure of R&D fundsX22Positive correlationNumber of employees of R&DX23Positive correlationEducation expenditureX24Positive correlationExpenditure on science and technologyX25Positive correlationGovernment policy factorsRevenueX31Positive correlationTransportation expenditureX32Positive correlationTransportation environment factorsNumber of employees in transportation, storage, and post industryX41Positive correlationLength of railroad lines in serviceX42Positive correlationNet tonnage of carrying vesselX43Positive correlationTonnage of truckX44Positive correlationOil pipeline mileageX45Positive correlationTransport planeX46Positive correlation


## 6.2. Calculation of Grey Correlation Degree of Influencing Factors

Based on the freight development of Guangdong Province from 2011 to 2019, total freight volume, railway freight volume, truck freight volume, water freight volume, air cargo volume, and pipeline freight volume are the main factor sequence data of the system. The historical data ofX11−X46 index factors are regarded as subfactor series data, and the grey correlation resolution coefficient is 0.5 based on experience. The data involved are from the public data of the Guangdong Statistical Yearbook in 2013–2019. The grey correlation degree of influencing factors of freight development in Guangdong Province is calculated as given in formulas (24)–(26) and AVGγ0i=avgγ0iF+γ0iR+γ0iT+γ0iW+γ0iA+γ0iP, and the calculation results are shown in Tables 12–14.Table 12
Grey correlation results of freight development in Guangdong Province (1).
VariableX11X12X13X14X15X16X17γ0iF0.8960.7620.8070.9250.9000.7740.818γ0iR0.7470.9160.6890.8060.7370.9030.708γ0iT0.8940.7470.8160.9040.8970.7580.829γ0iW0.9300.7520.7980.9030.9170.7610.824γ0iW0.9210.7260.7980.8710.8840.7330.848γ0iA0.8380.8660.7400.9240.8230.8790.773AVGγ0i0.8710.7950.7750.8890.8600.8010.800Source: according to the calculation criteria.Table 13
Grey correlation results of freight development in Guangdong Province (2).
VariableX21X22X23X24X25X31X32γ0iF0.8500.8230.8900.8700.5860.8480.816γ0iR0.7490.7060.7790.7440.5990.7120.806γ0iT0.8480.8190.8820.8670.5900.8590.824γ0iW0.8850.8250.9330.8990.5760.8580.770γ0iW0.9170.8310.9120.9130.5580.8770.743γ0iA0.8310.7640.8810.8240.5790.7810.785AVGγ0i0.8470.7950.8800.8530.5820.8230.791Source: according to the calculation criteria.Table 14
Grey correlation results of freight development in Guangdong Province (3).
VariableX41X42X43X44X45X46γ0iF0.9160.9470.8080.9150.9080.902γ0iR0.8070.7850.8780.7900.7900.777γ0iT0.8940.9230.7890.9010.9030.887γ0iW0.8970.9190.8030.9300.8940.935γ0iW0.8640.8760.7670.9060.8290.942γ0iA0.9500.9220.8700.9110.8850.883AVGγ0i0.8880.8950.8190.8920.8680.888Source: according to the calculation criteria.The closer the value to 1, the higher the correlation between the self-factor sequence data and the main factor sequence data. According to the calculation results of correlation degree of Tables12–14, AVGR042>AVGR044>AVGR014>AVGR041=AVGR046>AVGR023>AVGR011>AVGR045>AVGR015>AVGR024>AVGR021>AVGR031>AVGR043>AVGR043>AVGR016>AVGR017>AVGR012=AVGR022>AVGR032>AVGR013>AVGR025; there are 15 factors with AVGR0i; there are 15 factors with AVGR0i greater than or equal to 0.8, indicating that the vast majority of factors are highly related to the development of freight transportation in Guangdong Province, including operating mileage of railway, tonnage of trucks, disposable income, deposit balance of financial institutions, number of employees in transportation, warehousing and postal industry, transport aircraft, R&D personnel, GDP, mileage of oil pipeline, total retail sales of consumer goods, financial expenditure on education, Internet broadband access users, general budget revenue, tonnage of cargo ships, and total import and export, which are most closely related to the development of freight transportation in Guangdong Province, ranking in the top 15 with the correlation degree greater than 0.8. The relevance degree of the added value of the secondary industry in the proportion of GDP is greater than 0.7, and its closeness with the freight development of Guangdong Province cannot be ignored. The relevance degree of science and technology financial expenditure is only 0.582, and its relevance with the freight development of Guangdong Province can be ignored.


## 6.3. Analysis of Grey Correlation Results

By using the grey correlation analysis method, we can objectively and reasonably reflect the influence degree of relevant influencing factors on the freight development of Guangdong Province and provide a quantifiable research perspective for the analysis of the relationship between regional economic factors, scientific and technological environment factors, government policy factors, transportation environment factors, and the freight development of Guangdong Province:(1)
The regional economic environment plays an important role in the freight development Guangdong Province.The average value of the six factors of regional economy (AVGR01i) is 0.827, and the value of four factors is greater than 0.8, which reflects that the economic environment is closely related to the freight development of Guangdong Province. The regional economic environment represents the demand of the freight market in the port market and reflects the impact of the economic environment on the demand of the port freight market; it also reflects the industrial transmission effect of the logistics industry affected by the real economy.(2)
The development of freight transportation in Guangdong Province should pay attention to the environmental factors of science and technology.The value of science and technology environment factor (AVGR02i) is 0.791. There is a certain degree of correlation between R&D personnel and the level of regional science and technology in Guangdong Province and the development of freight transportation in Guangdong Province, which means that the promotion and development of information technology have greatly promoted the development of freight transportation in Guangdong Province. R&D practitioners reflect the information technology talents, education expenditure reflects the strength of regional talent cultivation, and the amount of Internet broadband access reflects the basic environment of science and technology. The above three factors are greater than 0.8, which shows that the development of freight transportation in Guangdong Province is constrained by the basic conditions of the development of information technology and the cultivation of information talents. However, the government’s financial expenditure on science and technology has no direct correlation with the freight development of Guangdong Province, and its correlation coefficient is only 0.582.(3)
Government policy factors guide freight development in Guangdong Province.The value of government policy factor (AVGR03i) is 0.807. The government’s financial capacity and the intensity of transportation expenditure are closely related to the development of freight transportation in Guangdong Province. The amount of government’s financial revenue and the intensity of transportation expenditure are helpful to improve the conditions of transportation infrastructure in Guangdong Province.(4)
The transportation environment factors directly affect the development of freight in Guangdong Province.The value of environmental factors of transportation (AVGR04i) is 0.875. The development of freight transportation in Guangdong Province is closely related to environmental factors of transportation. The correlation degree between the environmental factors of transportation and the freight development of Guangdong Province is greater than 0.8. The operating mileage of railway and oil pipeline reflects the overall infrastructure of freight industry. The number of employees in transportation, warehousing, and postal industry reflects the human resource factors of logistics industry. The number of trucks, ships, and aircraft reflects the basic equipment conditions of logistics. The above indicators are closely related to the freight development of Guangdong Province.


## 7. Conclusions and Suggestions

This paper makes a quantitative study on the development trend of freight transport in Guangdong from the perspective of freight volume. However, the research needs to be further expanded to fully reflect the overall situation of freight development in Guangdong Province, such as the study of freight market price factors and the change of supply-demand relationship. The empirical study shows the COVID-19 has a certain impact on the freight development of Guangdong, which has the following characteristics: stage characteristics, structural characteristics, and physical transmission characteristics; the total freight volume of Guangdong is affected by −23.001%, and the truck transportation is affected by −29.344%, with −11.296% for water transportation and −3.838% for air transportation. Due to the continuity of transportation and the substitution for other transportation modes, the freight volume of railway and pipeline transportation is affected by 14.343% and 13.057%, respectively.To further explore the abate measures of COVID-19 impact on Guangdong’s freight development, the grey correlation model is introduced to study the correlation factors of freight development of Guangdong Province. This paper selects four factors including regional economic environment, science and technology environment, government policy, and transportation and logistics environment, covering 20 subfactors. Through the research, it is found that the average correlation degree of the four factors is greater than 0.7 and the order of correlation degrees is as follows: transportation and logistics environment factors, government policy factors, and science and technology environment factors.Through the research on the related factors of freight development of Guangdong Province, this paper puts forward the following measures to promote the freight development in Guangdong Province in the postepidemic era: first, pay attention to improving the freight infrastructure equipment in Guangdong Province, improve the efficiency of infrastructure equipment operation, and improve the connection ability of transportation modes, such as sea rail combined transportation, sea air combined transportation, and sea land combined transportation. Second, the government continues to invest in transportation infrastructure and introduces relevant measures, such as reducing and exempting tolls, operating taxes, and so on. Third, strengthen the linkage between freight development and economy, pay attention to the trend of economic development, and timely adjust the strategy of freight development and operation. Fourth, pay attention to strengthening the construction and application of information technology and intelligent technology in freight operation and improve the intelligent and digital degree of freight operation process.



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*Source: 5401499-2021-07-21.xml*