# A Nonlinear Stochastic Matrix Model for the Analysis of the Association between International Trade Growth and Environmental Change

Authors: Xinmei Zhang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

This study uses a nonlinear stochastic matrix for an in-depth analysis of the association between international trade growth and environmental change. First, for a class of uncertain stochastic nonlinear time-lag systems, this study investigates its time-lag-related robust stochastic stabilization problem. A memory-free state feedback controller for the system is then obtained to ensure the effectiveness of the system performance. This makes the system more general and the corresponding theoretical results less conservative. Finally, numerical examples are given to further verify the validity and feasibility of the results. The “tariff measure” based on the magnitude of adverse changes in trade policy is not an accurate measure of trade policy uncertainty; the stochastic volatility method measures trade policy uncertainty by including tariff fluctuations that have been communicated in advance in the trade policy uncertainty indicator and fail to identify the different commodities that occur during the current trade friction. The trade policy uncertainty index constructed through textual analysis of newspapers can better reflect the trade policy uncertainty during this trade friction between China and the United States, and the rich time-varying nature can also reflect the alternating changes of tension and détente in economic and trade relations over some time. The analysis of the mechanism reveals that exporters have fewer emission reduction facilities than nonexporters but significantly lower energy consumption intensity for coal and water than nonexporters, reasoning that the mechanism by which exporters are more environmentally friendly than nonexporters lies in their cleaner energy use mix. Following the conclusions of this study, relevant policy recommendations are put forward, specifically the use of more efficient energy sources in the production process and more investment in energy efficiency and emission reduction to combat pollution.


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## Body

## 1. Introduction

The development of international trade has a long history and trade issues are an important topic of research in international economics. International trade has enabled many emerging countries to achieve rapid economic growth. In addition to rapid economic growth, international trade has also brought about problems such as profit distribution, trade barriers, changes in factors and product prices, and environmental pollution. The impact of international trade on the environment is a topic, on which academics are still divided [1]. However, the pro-free trade view is that the transfer of industries from developed countries will also reduce pollution levels in developing countries through technological spillovers, or that environmental standards and green barriers to imports from developed countries will actively induce exporters in developing countries to reduce environmental pollution. In the current context of the rapid development of international trade, green trade barriers are becoming increasingly common in developed countries, green coordination has become the basis for the development of international trade, and various coordination plans issued by the state also advocate the vigorous development of green coordination mode [2]. The development of international trade and green coordination is an important part of the development of green coordination.The development of international trade and green coordination is a contradictory relationship of interdependence, mutual promotion, and mutual constraints. The level of green coordination performance still differs greatly from that of developed countries, and the coordination industry, as a basic industry for the construction and development of a country’s economy, is known as the “accelerator” for national economic growth, while the traditional coordination model is relatively sloppy, unable to integrate into the wave of circular economy and green development, and there are also problems such as high coordination costs, serious energy consumption, and low operational efficiency [3]. The scientific measurement and correct judgment of China’s labor supply and employment situation are not only faced with the application of analytical methods but also with the shortcomings of the underlying data and publicly released data. The current survey data on labor force employment situation mainly serves the construction of comprehensive statistical indicators such as labor force participation rate, employment rate, and unemployment rate, which is far from sufficient for in-depth study of the overall employment situation of the working-age population in the country. The analysis needs to be conducted on the basis of existing data, combined with raw sample data such as the population census. The development of international trade and fierce trade competition will push the coordination industry to improve operational efficiency and reduce energy consumption, to develop into a modern, green, and professional coordination mode with high added value, and the rapid development of green coordination will provide a better service guarantee for international trade activities [4]. Therefore, this study studies the mutual influence relationship between international trade and green coordination performance, which is of great practical significance for driving the growth of China’s foreign trade volume, improving the development level of the coordination industry, and enhancing China’s economic strength.International trade is an important source of a material basis for economic development; with the rapid development of society, more and more countries participate in international trade to meet their own development needs; with the development of international trade, participation in international trade in goods and services is more and more, so that the structure of international trade in commodities is constantly changing, and energy is related to the development of social economy, so in international trade, energy products have become the most common trade commodities, such as oil and natural gas. The production and consumption of energy have a special nature, and the global energy reserves are not evenly distributed, but the development of each country is inseparable from energy, so countries with insufficient energy need to import from countries with sufficient energy, which makes international energy trade occur [5]. Countries are at different levels of development and are at different stages of economic development, which makes them have different energy needs. Therefore, depending on their stage of economic development, countries must choose the countries that meet their development and develop a reasonable trade strategy to meet their economic development needs and ensure their political security. The study of the complexity of financial markets can, on the one hand, help market investors to grasp market information and assist market regulators to implement effective regulatory measures, and on the other hand, it can help market investors to understand and become familiar with the general principles of financial asset price formation, providing a theoretical basis for the optimal allocation of financial assets and the management of financial market risks. As a complex dynamical system, this study presents an empirical study of financial market linkages, portfolio optimization, and financial risk management from the perspectives of fractal analysis theory, stochastic matrix theory, and complex network theory.


## 2. Related Works

The selection of trade partners according to their own development needs and the formulation of trade policies conducive to the country’s development before engaging in international trade are of great importance to national economic development and political security [6]. Senturk et al. explored the competitive relationship between oil-importing countries based on complex network theory and analyzed the evolution and transmission of oil trade competition patterns in conjunction with measures of competitive intensity [7]. Leitao et al. analyzed the overall topological characteristics of the global oil international trade network and the evolution of the network structure and used random matrix theory to analyze the complex spatio-temporal dynamics from the national level. The evolution of market adaptability of international oil trade is analyzed from the perspective of demand side [8]. A complex network approach was used to construct the unweighted and weighted complex networks for the 2010 gas trade. The structural characteristics of the unweighted and weighted networks were analyzed and found to be power law and cluster based [9]. The social network analysis method was used to analyze the relevant indicators of the international crude oil trade network such as network density, centrality, and core nodes. It was found that world economic conditions and international market prices have a significant impact on the network density of the international crude oil trade network; the trading partners of crude oil-importing countries are more concentrated, and the major crude oil-producing and consuming countries are the main core countries [10].Destek et al. found that international trade volume and coordination efficiency are mutually influential and vary in the same direction, and overall, increased trade volume can improve regional coordination supply capacity, and improve coordination efficiency can also promote the development of international trade [11]. They found that there is a significant positive relationship between coordination performance and international trade and that customs clearance efficiency, coordination infrastructure, and import and export cargo turnaround time indicators are the main factors affecting the development of international trade, and finally suggested that the less environmental restrictions are conducive to improving the efficiency of coordination operations [12]. It is argued that the source of trade policy uncertainty is that the current tariff rate applied to imported goods is lower than the potential maximum tariff rate, and when the international trade environment deteriorates, the importing country may impose taxes on imported goods at the potential maximum tariff rate, and since enterprises need to pay higher sunk costs to enter the export market, trade policy uncertainty in the importing country may bring potential losses to exporters, which in turn hinders the expansion of international trade [13]. To counter this problem, the governments of different countries can sign trade agreements to reduce the risk of potential exporters entering the export market and increase the export possibilities of enterprises.First, the theories related to the development level of international trade are elaborated, leading to the theory of sustainable development of international trade adapted to the development of today’s world, followed by the introduction of the concept of green coordination, its main contents, and the basic theory of green coordination performance. International trade, also known as commerce, is the trading of goods and services across national borders, generally consisting of import trade and export trade, and can therefore also be called import and export trade. International trade is also known as world trade. Import and export trade can regulate the utilization rate of domestic production factors, improve the international supply and demand relationship, adjust the economic structure, and increase fiscal revenue, etc. The relationship between international trade and green coordination performance is first analyzed qualitatively, then international trade indicators are used to regress on green coordination performance to find the international trade indicators that affect green coordination performance, and an impact degree model is constructed based on grey correlation analysis to analyze the degree of impact of international trade indicators on green coordination performance in each region. Finally, the correlation between green coordination performance indicators and the level of international trade development in each region is analyzed and ranked, and the main indicators that have a greater impact on international trade in each region are analyzed in conjunction with the actual situation, based on which practical countermeasures are proposed to promote the development of green coordination to better serve international trade.


## 3. Nonlinear Random Matrix Model of International Trade Growth and Environmental Change Correlation Analysis

### 3.1. Nonlinear Stochastic Matrix Model Design

With the rapid development of science and technology, stochastic factors exist in many practical systems; therefore, we must conduct theoretical research on the change process of some stochastic phenomena. Further, we must consider multiple random variables, and the starting point of the problem is not an independent sample of random variables but an infinite number of random variables to make a specific observation. In this case, we must use a family of random variables to delineate the full statistical pattern of this random phenomenon. In general, we refer to the family of random variables as the stochastic process.(1)Cμk=λkμk−b.Random matrix theory predicts that all eigenvalues fall within the range, and if there are eigenvalues of the empirical correlation matrixC that lie outside the interval, then this means that the empirical eigenvalues lie outside the range of the RMT and contain part of the true information. In addition, if the empirical intercorrelation matrix C has the same properties as the random matrix R, it indicates that the matrix C contains randomly existing elements; if the properties of the empirical intercorrelation matrix C exhibit different properties from those of the random matrix R, then it means that the elements of the matrix C are nonrandomly existing and contain real information.The constituent elements of the characteristic vectoru obeyed the standard normal distribution N (0, 1) are defined as follows:(2)Pu=12πeu2/4.Complex network theory achieves the analysis of the nature of the market and the linkage behavior of the financial market by constructing a network of relationships between financial markets [14]. A network of financial markets consists of a combination of linkage coefficients between financial variables, where the individual variables within the market are referred to as vertices and the linkage relationships between variables form the edges of the network, with the weights of the edges being measured by the linkage coefficients between them. As the value of the number of interrelationships may be negative, to meet the measurement requirements of the construction algorithm, the number of interrelationships is usually converted into a distance measure so that the weights are all non-negative, as shown in Figure 1.Figure 1
Nonlinear random matrix model.Currently, two methods, phase adjustment processing and random rearrangement of the data are generally used to identify the causes of multifractals and to be able to analyze the magnitude of the impact of these two causes on multifractal features. The random rearrangement of the two identification methods focuses on the multifractal features caused by long-term memory features, which work by causing the long-term memory features in the original time series to be corrupted, while ensuring that the original probability distribution features remain unchanged. In this way, there is no memory, but there is the same probability distribution between the original sequence and the randomly rearranged sequence, and the time series is characterized by a single fractal state, which means that the multiple fractal features are caused by the long-term memory features it has after the time series has been rearranged. Green logistics is a scientific concept of logistics development based on the general principles of economics and founded on the theory of sustainable development, the theory of ecological economics, the theory of ecological ethics, and the theory of internalisation of external costs and the assessment of logistics performance. At the same time, green logistics is also a logistics activity that can inhibit the pollution of the environment from logistics activities, reduce resource consumption, and use advanced logistics technology to plan and implement operational processes such as transportation, warehousing, loading and unloading, distribution processing, packaging, and distribution.The phase adjustment process focuses on the multifractal features caused by the thick-tailed probability distribution, which is used to determine the cause of the multifractal features by removing the original distribution characteristics of the data. Alternatively, the phase adjustment process can be used for multiple fractal features caused by thick-tailed distributions of probability density functions, where the nonGaussian nature of the series is weakened, provided that the correlation of the series does not change, and the correlation coefficient index after the phase adjustment process will be independent of each other and theq value. If the multifractal characteristics are caused by both long-term memory features and thick-tailed distributions, then the data series after processing with phase adjustment and random rearrangement shows weakened multifractal characteristics.Coordination transport is one of the most important functional elements of coordination activities, and the exhaust emissions and fuel consumption generated during its delivery are the main causes of environmental pollution caused by coordination activities, so the key to implementing green coordination lies in improving transport issues. First, suitable transport routes and means of transport should be chosen to avoid emptying, roundabout, convection, or repeated transport and effectively increase the actual loading rate of transport vehicles. Second, the internal combustion engine technology of transport vehicles should be continuously improved, and the use of clean fuels should be encouraged to achieve the goal of energy saving and emission reduction. The operational characteristics as well as the shape between smart logistics and traditional logistics are different. The basic characteristics of wisdom logistics are expressed in the efficient development of logistics, networked logistics organisation, shared logistics information, intelligent logistics operation, green logistics development, intensive logistics services, integrated logistics operation, and regional logistics integration. Moreover, the social transaction cost of intelligent logistics is low, resource allocation efficiency is high, industrial value-added value is excellent, spatial layout flexibility is strong, and network construction has given rise to a new industrial ecology, development mode, and technological innovation. Finally, the leakage of goods during coordination transportation should be prevented, causing serious pollution to the environment [15]. The differential moving average autoregressive model is mainly used to fit time series with smooth properties or time series that can be transformed to have smooth properties and a time series fitting method is widely used by scholars at present. The central idea is to make the unstable original series smooth through the differential operator, where m is the total number of differential operations.(3)Fx1,x2,…,xm,t1,t2,…,tm,h1,h2,…,hm=Fx1,…xm−1−1,t1,…tm−1,h1,…hm−1.There are two methods for testing the smooth characteristics of a time series: one is to choose between the statistical properties of the autocorrelation graph and the time-series graph and the other is to test the hypothesis test following the test statistic. The former test is more intuitive and simpler but is susceptible to subjective consciousness and subjective experience, thus the latter hypothesis testing method is still required to assist.The graphical test of stability is based on the principle that a time series with a wide smoothness has a constant variance and a constant mean and is an artificial and subjective test for the smoothness of a series based on a time-series graph. A smooth time-series graph will show that the time series has been fluctuating up and down around a fixed value and that the fluctuation range has clear boundaries. A common test for smoothness is the unit root test, which states that if the series has the property of being smooth, then the characteristic roots of the series should all lie within the unit circle. Commonly used tests are the DF test, the ADF test, and the PP test. The ADF test is a modification of the DF test, that is, the augmented PDF test, referred to as the ADF test. Similarly, the DF test is a special case of the ADF test when the autocorrelation coefficient is 1, so the two can be combined into the ADF test.(4)pk=∑t=1nxt−xxt−k+x∑t=1nxt−x3.A model with good properties should be able to reasonably configure the fitting accuracy and the number of parameters. Guided by the basic idea of this criterion, the relative merits of a model fitting result can be considered from two aspects: on the one hand, from the unknown parameters of the fitted model, usually, the number of variables and the difficulty of parameter estimation are proportional; that is, the more variables in the model, the difficulty of parameter estimation will increase [16]. The greater the number of variables in the model, the greater the difficulty of parameter estimation and the greater the unknown risk, as shown in Figure 2. On the other hand, the likelihood function, which is used to measure the goodness of fit of the model, is proportional to the accuracy of the fit.Figure 2
Multiple fractal characteristics of the original sequence, random rearrangement, and phase adjustment.With the extent of exploitation of resources and the development of the economy and society, environmental economics has become a focal point of economic development in all countries. Due to the increasing pressure on the world's energy resources, especially the decreasing amount of nonrenewable energy sources, people's awareness of environmental protection is increasing and energy conservation and emission reduction are being given high priority. The importance of comparative trade policy uncertainty measurement is not only reflected in academic research but also has an important reference value for socio-economic actors to make decisions.


### 3.2. Analysis of the Link between International Trade Growth and Environmental Change

A complex network is a graph consisting of some nodes and the edges connecting them. A network can be classified as directed or undirected, considering whether the connected edges between the nodes have a direction. When considering whether the edges in the network are weighted or not, the network can be divided into weighted and unweighted networks. If both the direction and the weight of the edges are considered, then the network can be divided into directed and undirected, weighted and unweighted networks. n a directionless unweighted network, the edges between nodes have no direction, the edges only represent the relationship between the nodes, and the edges do not have weights; that is, the edges are of the same thickness [17]. In an undirected weighted network, the edges are not directional, but the edges are weighted, and the thickness of the line represents the weight of the edge. In a directional unweighted network, the edges are directional, but the edges do not have weights. Environmental protection generally refers to the general term for all kinds of actions taken by human beings to solve real or potential environmental problems, harmonise the relationship between human beings and the environment, protect the living environment of human beings, and guarantee the sustainable development of economy and society. The methods and means include engineering and technology, administration and management, as well as economics, publicity, and education.In a directed weighted network, the edges between nodes have both direction and weight, and the line between nodes shows the transferability between nodes, while the thickness of the line shows the strength of the relationship. From a statistical perspective, a network is a holistic system in which there are many interacting individuals. In this study, the study of the conventional energy trade relationship network takes into account both the direction of conventional energy flow, that is, the directionality of the edges and the trade volume of conventional energy, that is, the weight of the edges, so the conventional energy trade relationship network constructed in this study is a complex network with directional power, which better reflects the difference in energy demand of each country in the whole conventional energy trade market and more intuitively reflects the whole trade network’s structural characteristics.In a conventional energy trade network, if the point strength and intensity distribution of the nodes are greater, then the greater the trade volume of energy traded by that country with other countries. According to previous research, complex networks are widespread in real life, and most complex networks are distributed as power-law distributions, where a power-law distribution means that the influence on something is often a small number of factors. In energy international trade networks, there are fewer nodes with larger weights and more nodes with fewer weights. In the following study, the incoming intensity is used to analyze whether the incoming intensity conforms to the power-law distribution characteristics. First, the incoming strength of each network is ranked from the top to the bottom to obtain the ordinal numberR. The function of fitting the ordinal number R to the incoming strength of nodes in double logarithmic coordinates is shown in Figure 3. In the logistics process, the environmental damage caused by logistics is suppressed and the logistics environment is cleaned up so that the logistics resources are fully utilised. Green logistics makes the best use of logistics resources. From a management point of view, green logistics refers to the process of green economic management activities to achieve customer satisfaction, connect green demand subjects and green supply subjects, and overcome the space and time constraints of green goods and services effectively and quickly.Figure 3
Intensity distribution fitting function.In a complex network, the intermediary centrality of a node indicates how often the node appears on the shortest path throughout the network. In a conventional energy trade network, the greater the intermediary centrality of a node, the greater the country’s role in the transmission of energy through the network, that is, its ability to transit and control [18]. If the country is influenced by prices or other factors, the impact on the energy network is greater. To better analyze the degree, to which each trading country is positioned as a hub in the energy network, the intermediary centrality indicator is used for the study. The intermediary centrality of a node is defined as follows:(5)GBi=∑j,kgjj−1,k+1gkk−1,j+1.In a complex network, the distance between two nodes is the minimum number of edges that one of the nodes passes through to the other node, and the average path length is the average distance between two nodes in the whole network. The larger the average path length of the network, the less efficient the circulation of the network is; conversely, the more efficient the network is. In a conventional energy trade network, the more efficient the network is, the more efficient the energy flows in the trade market and the more efficient the exchange between countries. The average route length of the network is defined as follows:(6)L=1NN−1∑i=1N∑j=1N−1lij.The response to a standard deviation increases in the growth rate of international trade volume is 0.073. In the first period, the income growth rate of language service industry is significantly positive [19]. In turn, the impulse response in the upper right-hand corner of Figure 4 shows that a one standard deviation increase in the growth rate of language services revenue results in a significantly positive response to the growth rate of international trade of 0.032 in the first period, followed by an alternating decline and rebound, both of which are insignificant and decay to zero. This suggests that the relationship between international trade and the language services industry is mutually influential.Figure 4
Impulse response of the model.In terms of the level of economic development, among the three indicators, the added value of the coordination industry as a proportion of GDP has a relatively large weight of 0.0962, indicating that this indicator is more important to the development of the economy and green coordination, which can directly reflect the contribution of the coordination industry to the regional national economy [20]. In terms of the level of infrastructure, the intensity of investment in exhaust gas control equipment has a greater weight than the mileage density of the coordination industry network, indicating that the improvement of infrastructure equipment related to environmental control is more conducive to promoting the development of green coordination [21]. Trade frictions are those that arise in the balance of trade in international trade between countries in the course of trade transactions, generally a persistent surplus in one country and a deficit in another, or trade activities in one country that touch or harm the industries of another. Friction exists not only between developed and developing countries, between developing countries, but also between developed countries. In terms of operation and management, the entropy weight of the proportion of coordination employees is the largest, with a weight of 0.0854, reflecting the importance of human input to coordination operations and green coordination development. In terms of environment and energy consumption, the weight of the comprehensive recycling rate of waste materials is the largest, with a weight of 0.1434, indicating that the green transformation capacity of the region is more important for environmental protection.


### 3.3. Experimental Design

Figure5 presents the impulse response plots when measuring economic fluctuations in terms of the year-on-year GDP growth rate, subject only to the imposed sign constraint on structural shocks. Compared to the baseline identification results in the previous section, the corresponding set of impulse response functions does not contract significantly when the constraint is progressively applied, and it is still not possible to make a judgment on the causal relationship between trade policy uncertainty and economic volatility from the current impulse response function plots. In addition, in the benchmark identification results, the sign constraint on structural shocks can already identify the causal relationship between exchange rate and capital account policy uncertainty and economic volatility through the impulse response plots, but when economic volatility is measured by the year-on-year GDP growth rate. The sign constraint on shocks alone cannot lead to this conclusion; therefore, in the subsequent robustness tests, this study will continue to impose a significant shock, Therefore, in the subsequent robustness check, we will continue to impose significant shock constraints to test the robustness of the benchmark identification results in the previous section.Figure 5
Impulse with structural shock sign constraint.When imposing a more relaxed constraint, that is, assigning a value toθ using the 60% quantile, it can already be seen from the impulse response plots that a positive trade policy uncertainty shock leads to an increase in GDP y-o-y growth, while a positive GDP y-o-y growth shock leads to an increase in trade policy uncertainty in the short run, but the impact, overall, is uncertain, and with GDP, the effect of a year-on-year growth rate shock on trade policy uncertainty is not clear. When θ is assigned a value using the 75th percentile, the result that a positive trade policy uncertainty shock leads to a larger GDP like-for-like growth rate does not change significantly; moreover, a positive GDP like-for-like growth rate shock still leads to a rise in trade policy uncertainty in the short run, while it leads to a fall in trade policy uncertainty overall, as shown in Figure 6.Figure 6
Parameter estimation of volatility.While the use of recursive constraints in the shock identification process can help researchers efficiently identify structural shocks in SVAR models, the economics behind them cannot be applied to the full empirical analysis. All particles have a velocity, a position, and a corresponding adaptation value that determine the direction of movement; the global optimal solution to the problem and the corresponding adaptation are searched for until the global optimal solution to the problem is optimized and the corresponding value is found by group collaboration. From a theoretical point of view, the main trade strategies for developing countries are primary export strategies, export substitution strategies, import substitution strategies, and export-oriented strategies. The choice and implementation of the correct economic development strategy are major decisions for developing countries on how to use foreign trade to develop their national economies. In order to ensure that trade development strategies are in line with national conditions and the international environment, so as to better serve the overall development strategy of the national economy and promote the economic development of the nation, it is necessary to carefully study the principles of trade development strategies and carefully analyze the factors affecting the choice of trade strategies in order to formulate trade development strategies that are more in line with the national conditions and thus more effectively promote the development of the national economy. The greatest advantage of this algorithm over other biological evolutionary intelligence algorithms is that it is easy to design and converges quickly.


## 3.1. Nonlinear Stochastic Matrix Model Design

With the rapid development of science and technology, stochastic factors exist in many practical systems; therefore, we must conduct theoretical research on the change process of some stochastic phenomena. Further, we must consider multiple random variables, and the starting point of the problem is not an independent sample of random variables but an infinite number of random variables to make a specific observation. In this case, we must use a family of random variables to delineate the full statistical pattern of this random phenomenon. In general, we refer to the family of random variables as the stochastic process.(1)Cμk=λkμk−b.Random matrix theory predicts that all eigenvalues fall within the range, and if there are eigenvalues of the empirical correlation matrixC that lie outside the interval, then this means that the empirical eigenvalues lie outside the range of the RMT and contain part of the true information. In addition, if the empirical intercorrelation matrix C has the same properties as the random matrix R, it indicates that the matrix C contains randomly existing elements; if the properties of the empirical intercorrelation matrix C exhibit different properties from those of the random matrix R, then it means that the elements of the matrix C are nonrandomly existing and contain real information.The constituent elements of the characteristic vectoru obeyed the standard normal distribution N (0, 1) are defined as follows:(2)Pu=12πeu2/4.Complex network theory achieves the analysis of the nature of the market and the linkage behavior of the financial market by constructing a network of relationships between financial markets [14]. A network of financial markets consists of a combination of linkage coefficients between financial variables, where the individual variables within the market are referred to as vertices and the linkage relationships between variables form the edges of the network, with the weights of the edges being measured by the linkage coefficients between them. As the value of the number of interrelationships may be negative, to meet the measurement requirements of the construction algorithm, the number of interrelationships is usually converted into a distance measure so that the weights are all non-negative, as shown in Figure 1.Figure 1
Nonlinear random matrix model.Currently, two methods, phase adjustment processing and random rearrangement of the data are generally used to identify the causes of multifractals and to be able to analyze the magnitude of the impact of these two causes on multifractal features. The random rearrangement of the two identification methods focuses on the multifractal features caused by long-term memory features, which work by causing the long-term memory features in the original time series to be corrupted, while ensuring that the original probability distribution features remain unchanged. In this way, there is no memory, but there is the same probability distribution between the original sequence and the randomly rearranged sequence, and the time series is characterized by a single fractal state, which means that the multiple fractal features are caused by the long-term memory features it has after the time series has been rearranged. Green logistics is a scientific concept of logistics development based on the general principles of economics and founded on the theory of sustainable development, the theory of ecological economics, the theory of ecological ethics, and the theory of internalisation of external costs and the assessment of logistics performance. At the same time, green logistics is also a logistics activity that can inhibit the pollution of the environment from logistics activities, reduce resource consumption, and use advanced logistics technology to plan and implement operational processes such as transportation, warehousing, loading and unloading, distribution processing, packaging, and distribution.The phase adjustment process focuses on the multifractal features caused by the thick-tailed probability distribution, which is used to determine the cause of the multifractal features by removing the original distribution characteristics of the data. Alternatively, the phase adjustment process can be used for multiple fractal features caused by thick-tailed distributions of probability density functions, where the nonGaussian nature of the series is weakened, provided that the correlation of the series does not change, and the correlation coefficient index after the phase adjustment process will be independent of each other and theq value. If the multifractal characteristics are caused by both long-term memory features and thick-tailed distributions, then the data series after processing with phase adjustment and random rearrangement shows weakened multifractal characteristics.Coordination transport is one of the most important functional elements of coordination activities, and the exhaust emissions and fuel consumption generated during its delivery are the main causes of environmental pollution caused by coordination activities, so the key to implementing green coordination lies in improving transport issues. First, suitable transport routes and means of transport should be chosen to avoid emptying, roundabout, convection, or repeated transport and effectively increase the actual loading rate of transport vehicles. Second, the internal combustion engine technology of transport vehicles should be continuously improved, and the use of clean fuels should be encouraged to achieve the goal of energy saving and emission reduction. The operational characteristics as well as the shape between smart logistics and traditional logistics are different. The basic characteristics of wisdom logistics are expressed in the efficient development of logistics, networked logistics organisation, shared logistics information, intelligent logistics operation, green logistics development, intensive logistics services, integrated logistics operation, and regional logistics integration. Moreover, the social transaction cost of intelligent logistics is low, resource allocation efficiency is high, industrial value-added value is excellent, spatial layout flexibility is strong, and network construction has given rise to a new industrial ecology, development mode, and technological innovation. Finally, the leakage of goods during coordination transportation should be prevented, causing serious pollution to the environment [15]. The differential moving average autoregressive model is mainly used to fit time series with smooth properties or time series that can be transformed to have smooth properties and a time series fitting method is widely used by scholars at present. The central idea is to make the unstable original series smooth through the differential operator, where m is the total number of differential operations.(3)Fx1,x2,…,xm,t1,t2,…,tm,h1,h2,…,hm=Fx1,…xm−1−1,t1,…tm−1,h1,…hm−1.There are two methods for testing the smooth characteristics of a time series: one is to choose between the statistical properties of the autocorrelation graph and the time-series graph and the other is to test the hypothesis test following the test statistic. The former test is more intuitive and simpler but is susceptible to subjective consciousness and subjective experience, thus the latter hypothesis testing method is still required to assist.The graphical test of stability is based on the principle that a time series with a wide smoothness has a constant variance and a constant mean and is an artificial and subjective test for the smoothness of a series based on a time-series graph. A smooth time-series graph will show that the time series has been fluctuating up and down around a fixed value and that the fluctuation range has clear boundaries. A common test for smoothness is the unit root test, which states that if the series has the property of being smooth, then the characteristic roots of the series should all lie within the unit circle. Commonly used tests are the DF test, the ADF test, and the PP test. The ADF test is a modification of the DF test, that is, the augmented PDF test, referred to as the ADF test. Similarly, the DF test is a special case of the ADF test when the autocorrelation coefficient is 1, so the two can be combined into the ADF test.(4)pk=∑t=1nxt−xxt−k+x∑t=1nxt−x3.A model with good properties should be able to reasonably configure the fitting accuracy and the number of parameters. Guided by the basic idea of this criterion, the relative merits of a model fitting result can be considered from two aspects: on the one hand, from the unknown parameters of the fitted model, usually, the number of variables and the difficulty of parameter estimation are proportional; that is, the more variables in the model, the difficulty of parameter estimation will increase [16]. The greater the number of variables in the model, the greater the difficulty of parameter estimation and the greater the unknown risk, as shown in Figure 2. On the other hand, the likelihood function, which is used to measure the goodness of fit of the model, is proportional to the accuracy of the fit.Figure 2
Multiple fractal characteristics of the original sequence, random rearrangement, and phase adjustment.With the extent of exploitation of resources and the development of the economy and society, environmental economics has become a focal point of economic development in all countries. Due to the increasing pressure on the world's energy resources, especially the decreasing amount of nonrenewable energy sources, people's awareness of environmental protection is increasing and energy conservation and emission reduction are being given high priority. The importance of comparative trade policy uncertainty measurement is not only reflected in academic research but also has an important reference value for socio-economic actors to make decisions.


## 3.2. Analysis of the Link between International Trade Growth and Environmental Change

A complex network is a graph consisting of some nodes and the edges connecting them. A network can be classified as directed or undirected, considering whether the connected edges between the nodes have a direction. When considering whether the edges in the network are weighted or not, the network can be divided into weighted and unweighted networks. If both the direction and the weight of the edges are considered, then the network can be divided into directed and undirected, weighted and unweighted networks. n a directionless unweighted network, the edges between nodes have no direction, the edges only represent the relationship between the nodes, and the edges do not have weights; that is, the edges are of the same thickness [17]. In an undirected weighted network, the edges are not directional, but the edges are weighted, and the thickness of the line represents the weight of the edge. In a directional unweighted network, the edges are directional, but the edges do not have weights. Environmental protection generally refers to the general term for all kinds of actions taken by human beings to solve real or potential environmental problems, harmonise the relationship between human beings and the environment, protect the living environment of human beings, and guarantee the sustainable development of economy and society. The methods and means include engineering and technology, administration and management, as well as economics, publicity, and education.In a directed weighted network, the edges between nodes have both direction and weight, and the line between nodes shows the transferability between nodes, while the thickness of the line shows the strength of the relationship. From a statistical perspective, a network is a holistic system in which there are many interacting individuals. In this study, the study of the conventional energy trade relationship network takes into account both the direction of conventional energy flow, that is, the directionality of the edges and the trade volume of conventional energy, that is, the weight of the edges, so the conventional energy trade relationship network constructed in this study is a complex network with directional power, which better reflects the difference in energy demand of each country in the whole conventional energy trade market and more intuitively reflects the whole trade network’s structural characteristics.In a conventional energy trade network, if the point strength and intensity distribution of the nodes are greater, then the greater the trade volume of energy traded by that country with other countries. According to previous research, complex networks are widespread in real life, and most complex networks are distributed as power-law distributions, where a power-law distribution means that the influence on something is often a small number of factors. In energy international trade networks, there are fewer nodes with larger weights and more nodes with fewer weights. In the following study, the incoming intensity is used to analyze whether the incoming intensity conforms to the power-law distribution characteristics. First, the incoming strength of each network is ranked from the top to the bottom to obtain the ordinal numberR. The function of fitting the ordinal number R to the incoming strength of nodes in double logarithmic coordinates is shown in Figure 3. In the logistics process, the environmental damage caused by logistics is suppressed and the logistics environment is cleaned up so that the logistics resources are fully utilised. Green logistics makes the best use of logistics resources. From a management point of view, green logistics refers to the process of green economic management activities to achieve customer satisfaction, connect green demand subjects and green supply subjects, and overcome the space and time constraints of green goods and services effectively and quickly.Figure 3
Intensity distribution fitting function.In a complex network, the intermediary centrality of a node indicates how often the node appears on the shortest path throughout the network. In a conventional energy trade network, the greater the intermediary centrality of a node, the greater the country’s role in the transmission of energy through the network, that is, its ability to transit and control [18]. If the country is influenced by prices or other factors, the impact on the energy network is greater. To better analyze the degree, to which each trading country is positioned as a hub in the energy network, the intermediary centrality indicator is used for the study. The intermediary centrality of a node is defined as follows:(5)GBi=∑j,kgjj−1,k+1gkk−1,j+1.In a complex network, the distance between two nodes is the minimum number of edges that one of the nodes passes through to the other node, and the average path length is the average distance between two nodes in the whole network. The larger the average path length of the network, the less efficient the circulation of the network is; conversely, the more efficient the network is. In a conventional energy trade network, the more efficient the network is, the more efficient the energy flows in the trade market and the more efficient the exchange between countries. The average route length of the network is defined as follows:(6)L=1NN−1∑i=1N∑j=1N−1lij.The response to a standard deviation increases in the growth rate of international trade volume is 0.073. In the first period, the income growth rate of language service industry is significantly positive [19]. In turn, the impulse response in the upper right-hand corner of Figure 4 shows that a one standard deviation increase in the growth rate of language services revenue results in a significantly positive response to the growth rate of international trade of 0.032 in the first period, followed by an alternating decline and rebound, both of which are insignificant and decay to zero. This suggests that the relationship between international trade and the language services industry is mutually influential.Figure 4
Impulse response of the model.In terms of the level of economic development, among the three indicators, the added value of the coordination industry as a proportion of GDP has a relatively large weight of 0.0962, indicating that this indicator is more important to the development of the economy and green coordination, which can directly reflect the contribution of the coordination industry to the regional national economy [20]. In terms of the level of infrastructure, the intensity of investment in exhaust gas control equipment has a greater weight than the mileage density of the coordination industry network, indicating that the improvement of infrastructure equipment related to environmental control is more conducive to promoting the development of green coordination [21]. Trade frictions are those that arise in the balance of trade in international trade between countries in the course of trade transactions, generally a persistent surplus in one country and a deficit in another, or trade activities in one country that touch or harm the industries of another. Friction exists not only between developed and developing countries, between developing countries, but also between developed countries. In terms of operation and management, the entropy weight of the proportion of coordination employees is the largest, with a weight of 0.0854, reflecting the importance of human input to coordination operations and green coordination development. In terms of environment and energy consumption, the weight of the comprehensive recycling rate of waste materials is the largest, with a weight of 0.1434, indicating that the green transformation capacity of the region is more important for environmental protection.


## 3.3. Experimental Design

Figure5 presents the impulse response plots when measuring economic fluctuations in terms of the year-on-year GDP growth rate, subject only to the imposed sign constraint on structural shocks. Compared to the baseline identification results in the previous section, the corresponding set of impulse response functions does not contract significantly when the constraint is progressively applied, and it is still not possible to make a judgment on the causal relationship between trade policy uncertainty and economic volatility from the current impulse response function plots. In addition, in the benchmark identification results, the sign constraint on structural shocks can already identify the causal relationship between exchange rate and capital account policy uncertainty and economic volatility through the impulse response plots, but when economic volatility is measured by the year-on-year GDP growth rate. The sign constraint on shocks alone cannot lead to this conclusion; therefore, in the subsequent robustness tests, this study will continue to impose a significant shock, Therefore, in the subsequent robustness check, we will continue to impose significant shock constraints to test the robustness of the benchmark identification results in the previous section.Figure 5
Impulse with structural shock sign constraint.When imposing a more relaxed constraint, that is, assigning a value toθ using the 60% quantile, it can already be seen from the impulse response plots that a positive trade policy uncertainty shock leads to an increase in GDP y-o-y growth, while a positive GDP y-o-y growth shock leads to an increase in trade policy uncertainty in the short run, but the impact, overall, is uncertain, and with GDP, the effect of a year-on-year growth rate shock on trade policy uncertainty is not clear. When θ is assigned a value using the 75th percentile, the result that a positive trade policy uncertainty shock leads to a larger GDP like-for-like growth rate does not change significantly; moreover, a positive GDP like-for-like growth rate shock still leads to a rise in trade policy uncertainty in the short run, while it leads to a fall in trade policy uncertainty overall, as shown in Figure 6.Figure 6
Parameter estimation of volatility.While the use of recursive constraints in the shock identification process can help researchers efficiently identify structural shocks in SVAR models, the economics behind them cannot be applied to the full empirical analysis. All particles have a velocity, a position, and a corresponding adaptation value that determine the direction of movement; the global optimal solution to the problem and the corresponding adaptation are searched for until the global optimal solution to the problem is optimized and the corresponding value is found by group collaboration. From a theoretical point of view, the main trade strategies for developing countries are primary export strategies, export substitution strategies, import substitution strategies, and export-oriented strategies. The choice and implementation of the correct economic development strategy are major decisions for developing countries on how to use foreign trade to develop their national economies. In order to ensure that trade development strategies are in line with national conditions and the international environment, so as to better serve the overall development strategy of the national economy and promote the economic development of the nation, it is necessary to carefully study the principles of trade development strategies and carefully analyze the factors affecting the choice of trade strategies in order to formulate trade development strategies that are more in line with the national conditions and thus more effectively promote the development of the national economy. The greatest advantage of this algorithm over other biological evolutionary intelligence algorithms is that it is easy to design and converges quickly.


## 4. Analysis of Results

### 4.1. Model Performance

A total of 3,466 training data were split into series of fixed length 5, and the predicted values of each series were generated from the true values of historical trading moments with a data input dimension of 5. The PSO-LSTM model was constructed and trained, after which 240 test sets of length 5 were rolled up and predicted, and a total of 1200 trading day minimum price predictions were obtained.The loss function MSE = 0.195662 was calculated and the fitted results are shown in Figure7, where the horizontal coordinate is time, the vertical coordinate is the daily minimum price, red represents the true value, and yellow represents the predicted value. The model fits well overall, except for the first 200 days when the predicted value appears, as shown in Figure 7.Figure 7
Day forecast.The training data were split into a series of a fixed length of 20, and the predicted values of each series were generated from the true values of historical trading moments, with the data input dimension of 20, to construct and train the PSO-LSTM model. The loss function MSE = 0.571372 was calculated, which shows that the model is a poor fit, with generally low or high forecast values in stages, and relatively small fluctuations in forecast values in some regions, making it difficult to fit short-term trends, but with some improvement in the delay of the forecast effect relative to the LSTM model.In the previous section, the core parameters in the DSGE model were calculated based on microscopic data, while the remaining parameters were calibrated in conjunction with the research results of related scholars. Next, numerical simulations are carried out based on the basic facts during the current US-China trade friction. Considering that during this Sino-US trade friction, in addition to the mutual announcement of tariff increases on imports originating from each other, the bilateral trade negotiation process between the two countries has also been tumultuous. Trade policy is a country's foreign trade policy. It is a system of technology trade and service trade formulated and implemented by a government in order to achieve certain policy objectives in a certain period of time. It provides the overall guidelines and principles for the country's foreign trade activities. We refer to a country’s foreign trade policy as international trade policy in a narrow sense. International trade policy in the broad sense refers to the international trade policy formed in the process of international trade development, which is agreed and commonly observed by all countries. When developing foreign economic and trade, countries will reach bilateral or multilateral consensus through negotiation.This trade friction between China and the United States has not only raised the uncertainty of trade policies between the two countries but also caused a shock to the expectations of market players in both countries regarding tariffs on imported goods. Therefore, in conducting numerical simulations, this study first analyzes the overall impact of the US-China trade friction on macroeconomic performance and then separately examines the impact of rising trade policy uncertainty on macroeconomic performance. Specifically, it is assumed that in the first period of the numerical simulation, market participants are aware that bilateral trade negotiations between the two countries are underway and that the probability of success of these negotiations is 50%, with a simultaneous 2% increase in import tariff levels for both countries if the negotiations break down, and an unchanged import tariff level if the negotiations are successful. The future import tariff rate follows a Bernoulli distribution with a value of 0 or 0.02, as shown in Figure8.Figure 8
Baseline model impulse response results.
(a)(b)(c)(d)It is worth noting that trade policy uncertainty shocks lead to an increase in employment, the number of exporters, and total exports in the short run, as they cause retailers to increase their mark-up rates on products, which in turn leads to higher inflation, lower real wages, and a corresponding reduction in firms’ export sunk costs, as well as narrowing the gap in the capital stock between exporters and nonexporters, although their risk of exporting their products is high. Although the increased risk of exporting reduces their expected returns to the export market, the lower sunk cost of exporting and the narrower capital stock gap result in a greater reduction in their total cost of entry into the export market, resulting in an increase in the number of exporters in the country and an increase in total exports in the short term. While an increase in product prices reduces the demand for the product, which in turn leads to a reduction in the labor employed by producers of intermediate goods in the production process, the fall in real wages lowers the market entry barrier for potential entrants and increases the demand for labor to cover the sunk cost of entry, which, combined with the fact that exporters need to employ more labor than nonexporters, leads to a rise in employment in the short run.


### 4.2. Experimental Results

Figure9 shows the proportional change in the total outward intensity of coal, oil, and gas for the decade 2012–2021 for conventional energy sources. In the conventional energy trade network, the outward intensity is the volume of trade in energy exported by each country, and the total outward intensity is the sum of the trade-in energy exported by each country in the same year. As can be seen from Figure 9, oil is the main and stable fuel exported from conventional energy sources, and coal exports are also relatively stable, while natural gas exports are the most volatile. The total export trade of conventional energy sources shows a trend of growth followed by a decline, while the total export trade of coal and oil shows less fluctuation over the decade and remains the same, but the total export of natural gas fluctuates more significantly, indicating that the fluctuation of the total export trade of conventional energy sources is mainly due to the fluctuation of the total export of natural gas.Figure 9
Intensity ratios.In the period 8 forecast, 93.4% of the fluctuations in the growth rate of international trade volumes can be explained by its historical shocks, with the remaining 6.6% being explained by the growth rate of income from the language services industry. For the language services industry, 81.3% of the fluctuations in the period 8 forecast can be explained by historical shocks, while the remaining 18.7% is explained by the growth rate of international trade. International trade and the language services industry are mainly influenced by their development but can also contribute to each other, with international trade having a more significant contribution to the language services industry, as shown in Figure10.Figure 10
Experimental results of the component matrix.As can be seen from Figure10, the first public factor F1 has a large loading on the import and export value of goods X1, international market share X2, and foreign trade dependence X6, which mainly reflects the development scale and economic impact of international trade, so F1 is named the economic scale factor; the second public factor F2 has a large loading on the FDI dependence X4, the degree of industrial pollution per unit of export trade X8, and the energy consumption per unit of export product. The third public factor F3 has a large loading on the export value of high-tech products X3, the imbalance between import and export trade X5, and the efficiency of primary products X7, mainly reflecting the structure of international trade and the overall sustainable development, so it is named the structural balance factor. The three main factors extracted above can reasonably and comprehensively reflect the sustainable development of international trade in each region.The main reason is that these regions are generally more open to the outside world, have introduced more foreign investment, and are strategically located, consuming less energy per unit of export product, which is conducive to saving internal resources and promoting the sustainable development of regional international trade. Mainly because these regions are in remote areas and have inconvenient transportation and lack of resources, economic and technological development is more backward, the degree of openness to the outside world is lower, and export trade requires more energy consumption, which is not conducive to the protection of the local energy environment, greatly limiting its sustainable development of international trade.International trade and the green coordination industry complement each other and influence each other. In the process of development of both, green coordination provides an important guarantee for the development of international trade and has a significant role in promoting the sustainable development of international trade; however, the green coordination industry contains various detailed index elements and has different impacts on international trade. Therefore, this section will use grey correlation analysis to analyze the correlation between international trade and green coordination performance indicators in each region, determine the degree of influence of green coordination performance indicators on international trade in each region, and analyzes the key factors of the green coordination industry affecting the development of international trade.That is, consumers show no significant preference for domestic and foreign goods, but the degree of consumer preference for different types of goods will have an impact on the demand for intermediate goods in different countries, so the impact of trade friction shocks and trade policy uncertainty shocks on macroeconomic operations under different domestic product preferences is compared here by resetting the value of the preference coefficient to 0.7.


## 4.1. Model Performance

A total of 3,466 training data were split into series of fixed length 5, and the predicted values of each series were generated from the true values of historical trading moments with a data input dimension of 5. The PSO-LSTM model was constructed and trained, after which 240 test sets of length 5 were rolled up and predicted, and a total of 1200 trading day minimum price predictions were obtained.The loss function MSE = 0.195662 was calculated and the fitted results are shown in Figure7, where the horizontal coordinate is time, the vertical coordinate is the daily minimum price, red represents the true value, and yellow represents the predicted value. The model fits well overall, except for the first 200 days when the predicted value appears, as shown in Figure 7.Figure 7
Day forecast.The training data were split into a series of a fixed length of 20, and the predicted values of each series were generated from the true values of historical trading moments, with the data input dimension of 20, to construct and train the PSO-LSTM model. The loss function MSE = 0.571372 was calculated, which shows that the model is a poor fit, with generally low or high forecast values in stages, and relatively small fluctuations in forecast values in some regions, making it difficult to fit short-term trends, but with some improvement in the delay of the forecast effect relative to the LSTM model.In the previous section, the core parameters in the DSGE model were calculated based on microscopic data, while the remaining parameters were calibrated in conjunction with the research results of related scholars. Next, numerical simulations are carried out based on the basic facts during the current US-China trade friction. Considering that during this Sino-US trade friction, in addition to the mutual announcement of tariff increases on imports originating from each other, the bilateral trade negotiation process between the two countries has also been tumultuous. Trade policy is a country's foreign trade policy. It is a system of technology trade and service trade formulated and implemented by a government in order to achieve certain policy objectives in a certain period of time. It provides the overall guidelines and principles for the country's foreign trade activities. We refer to a country’s foreign trade policy as international trade policy in a narrow sense. International trade policy in the broad sense refers to the international trade policy formed in the process of international trade development, which is agreed and commonly observed by all countries. When developing foreign economic and trade, countries will reach bilateral or multilateral consensus through negotiation.This trade friction between China and the United States has not only raised the uncertainty of trade policies between the two countries but also caused a shock to the expectations of market players in both countries regarding tariffs on imported goods. Therefore, in conducting numerical simulations, this study first analyzes the overall impact of the US-China trade friction on macroeconomic performance and then separately examines the impact of rising trade policy uncertainty on macroeconomic performance. Specifically, it is assumed that in the first period of the numerical simulation, market participants are aware that bilateral trade negotiations between the two countries are underway and that the probability of success of these negotiations is 50%, with a simultaneous 2% increase in import tariff levels for both countries if the negotiations break down, and an unchanged import tariff level if the negotiations are successful. The future import tariff rate follows a Bernoulli distribution with a value of 0 or 0.02, as shown in Figure8.Figure 8
Baseline model impulse response results.
(a)(b)(c)(d)It is worth noting that trade policy uncertainty shocks lead to an increase in employment, the number of exporters, and total exports in the short run, as they cause retailers to increase their mark-up rates on products, which in turn leads to higher inflation, lower real wages, and a corresponding reduction in firms’ export sunk costs, as well as narrowing the gap in the capital stock between exporters and nonexporters, although their risk of exporting their products is high. Although the increased risk of exporting reduces their expected returns to the export market, the lower sunk cost of exporting and the narrower capital stock gap result in a greater reduction in their total cost of entry into the export market, resulting in an increase in the number of exporters in the country and an increase in total exports in the short term. While an increase in product prices reduces the demand for the product, which in turn leads to a reduction in the labor employed by producers of intermediate goods in the production process, the fall in real wages lowers the market entry barrier for potential entrants and increases the demand for labor to cover the sunk cost of entry, which, combined with the fact that exporters need to employ more labor than nonexporters, leads to a rise in employment in the short run.


## 4.2. Experimental Results

Figure9 shows the proportional change in the total outward intensity of coal, oil, and gas for the decade 2012–2021 for conventional energy sources. In the conventional energy trade network, the outward intensity is the volume of trade in energy exported by each country, and the total outward intensity is the sum of the trade-in energy exported by each country in the same year. As can be seen from Figure 9, oil is the main and stable fuel exported from conventional energy sources, and coal exports are also relatively stable, while natural gas exports are the most volatile. The total export trade of conventional energy sources shows a trend of growth followed by a decline, while the total export trade of coal and oil shows less fluctuation over the decade and remains the same, but the total export of natural gas fluctuates more significantly, indicating that the fluctuation of the total export trade of conventional energy sources is mainly due to the fluctuation of the total export of natural gas.Figure 9
Intensity ratios.In the period 8 forecast, 93.4% of the fluctuations in the growth rate of international trade volumes can be explained by its historical shocks, with the remaining 6.6% being explained by the growth rate of income from the language services industry. For the language services industry, 81.3% of the fluctuations in the period 8 forecast can be explained by historical shocks, while the remaining 18.7% is explained by the growth rate of international trade. International trade and the language services industry are mainly influenced by their development but can also contribute to each other, with international trade having a more significant contribution to the language services industry, as shown in Figure10.Figure 10
Experimental results of the component matrix.As can be seen from Figure10, the first public factor F1 has a large loading on the import and export value of goods X1, international market share X2, and foreign trade dependence X6, which mainly reflects the development scale and economic impact of international trade, so F1 is named the economic scale factor; the second public factor F2 has a large loading on the FDI dependence X4, the degree of industrial pollution per unit of export trade X8, and the energy consumption per unit of export product. The third public factor F3 has a large loading on the export value of high-tech products X3, the imbalance between import and export trade X5, and the efficiency of primary products X7, mainly reflecting the structure of international trade and the overall sustainable development, so it is named the structural balance factor. The three main factors extracted above can reasonably and comprehensively reflect the sustainable development of international trade in each region.The main reason is that these regions are generally more open to the outside world, have introduced more foreign investment, and are strategically located, consuming less energy per unit of export product, which is conducive to saving internal resources and promoting the sustainable development of regional international trade. Mainly because these regions are in remote areas and have inconvenient transportation and lack of resources, economic and technological development is more backward, the degree of openness to the outside world is lower, and export trade requires more energy consumption, which is not conducive to the protection of the local energy environment, greatly limiting its sustainable development of international trade.International trade and the green coordination industry complement each other and influence each other. In the process of development of both, green coordination provides an important guarantee for the development of international trade and has a significant role in promoting the sustainable development of international trade; however, the green coordination industry contains various detailed index elements and has different impacts on international trade. Therefore, this section will use grey correlation analysis to analyze the correlation between international trade and green coordination performance indicators in each region, determine the degree of influence of green coordination performance indicators on international trade in each region, and analyzes the key factors of the green coordination industry affecting the development of international trade.That is, consumers show no significant preference for domestic and foreign goods, but the degree of consumer preference for different types of goods will have an impact on the demand for intermediate goods in different countries, so the impact of trade friction shocks and trade policy uncertainty shocks on macroeconomic operations under different domestic product preferences is compared here by resetting the value of the preference coefficient to 0.7.


## 5. Conclusion

This study has investigated the stability and calming problems of stochastic systems with a single input nonlinear perturbation, and the robust stability and calming analysis of stochastic time-lag correlated systems with multiple input nonlinear perturbations can be investigated subsequently. Control problems can also be investigated accordingly. Factor analysis is then used to evaluate and analyze the level of sustainable development of international trade and compare and analyze the changes and differences in the level of sustainable development of regional international trade from both horizontal and vertical perspectives. Next, the impact of international trade indicators on green coordination performance is analyzed through multiple regression models, and the impact of international trade indicators on green coordination performance in each region is studied based on grey correlation models. Finally, the grey correlation analysis is used to calculate the correlation between green coordination performance indicators and the level of international trade development in each region, specifically analyze the impact of green coordination performance indicators on international trade in each region, and propose targeted suggestions to promote the development of international trade and green coordination accordingly. The endogenous identification of trade policy uncertainty reveals that trade policy uncertainty is a cause rather than a consequence of macroeconomic fluctuations in China, and the overall distribution of the impulse response function still supports the conclusion that trade policy uncertainty is a cause rather than a consequence of macroeconomic fluctuations when the lag order is reselected and the measure of economic fluctuations is changed.



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*Source: 9153383-2022-06-28.xml*