# Economic Growth Prediction Algorithm of Coastal Area Based on Impulse Response Function

Authors: Qiu Rong-Shan; Ding Ding; Han Li-Min
Journal: Security and Communication Networks
 (2021)

---

## Abstract

In order to solve the problems of low accuracy and long prediction time of traditional economic growth prediction algorithms in coastal areas, an algorithm based on impulse response function was designed to analyze economic growth prediction in coastal areas. Crawler technology is used to capture the economic data of coastal areas and normalize the captured data. Based on the processed data, the impulse response function is used to analyze the relationship between different economic variables, so as to build the PSO-LSTM model, which is used to predict the economic growth trend of coastal areas. The experimental results show that, compared with the experimental comparison algorithm, the prediction accuracy of the algorithm designed in this paper is always above 97%, and the prediction time is always below 1 s, which has certain practical significance.


---

## Body

## 1. Introduction

Occupying 70 percent of China’s total area, the ocean is a treasure house of human resources and a spatial support for human survival and development. Life originated in the ocean, and human development will depend on it. On the one hand, the resources on the land of the region can no longer support the continued development of the economy and society; on the other hand, the space on the land determines that human beings must also go to the ocean [1]. Therefore, the 21st century is the century of the ocean, and coastal countries have turned their eyes to the ocean to seek the fulcrum of future development. Countries around the world have begun to develop and utilize Marine resources and vigorously develop the ocean, and they are constantly strengthening the research, development, and utilization of the ocean and have achieved fruitful results. Nowadays, in order to maintain the economic vitality of coastal areas, scientific and technological innovation is closely combined with the economy of coastal areas to fully solve the problem of slow economic development in coastal areas, improve the independent innovation ability of coastal areas, promote the adjustment and transformation of economic structure, and effectively support the economic growth and sound and rapid development of coastal areas [2].At present, some progress has been made in the research on the prediction algorithm of regional economic growth. For example, [3] proposed a prediction algorithm of macroeconomic indicators based on correlation analysis. Firstly, a large number of macroeconomic indicators were preprocessed by interpolation and classification methods to obtain time series data with consistent frequency. Then, the correlation analysis was carried out for the pretreated indexes, and the set of associated indexes with the greatest comprehensive influence on the specified target indexes was automatically selected through the index selection mechanism. Finally, the prediction model such as multiple regression analysis and back propagation (BP) neural network is combined to predict the target index, and the contribution degree of each associated index to the target index is calculated. However, the prediction accuracy of this method is low. Reference [4] proposed a GMDH based macroeconomic short-term prediction algorithm. This method compares traditional macroeconomic short-term forecasting methods. It is usually based on quantitative or qualitative forecasting models. The quantitative features are both qualitative and GMDH algorithms. The hybrid regression mathematical model based on the GMDH forecasting model is used for macroeconomic short-term forecasting. The results are similar to traditional GMDH. The model is consistent. In order to verify the advantages of this algorithm, it is found in the practical application that this method has the problem of long prediction time and has a big gap with the ideal application effect. Reference [5] is put forward based on the optimization of macroeconomic forecasting algorithm of wavelet neural network; wavelet neural network model is adopted to improve the macroeconomic forecasting, used in the process of the intelligent algorithm of wolves to optimize the weights of wavelet neural network model, and adopts the normalization after some provinces economic data for the proposed model of the training. A good model can be used for macroeconomic forecasting to achieve relevant forecast results. However, the prediction accuracy of this method is low, and there is a big gap between it and the ideal application effect. Reference [6] uses data mining technology based on energy minimization technology to complete the logical mining task. These empirical results provide useful insights for decision-making and policy implementation, including the development of strategies to help the industry cope with ongoing price volatility, thus enabling the Malaysian palm oil industry to continue to dominate the international market. In recent years, machine learning algorithms have been successfully used to harness the potential of identifying hidden patterns in financial market behavior, and, as such, it has become a land of opportunity for financial applications such as algorithmic trading. Reference [7] proposed a statistical arbitrage trading strategy, which contained two key elements: a regression algorithm integration for asset return prediction and a dynamic asset selection.In order to solve the problems existing in the traditional methods, this paper proposes an algorithm for economic growth prediction in coastal areas based on impulse response function.Our contribution is threefold:(1)
In order to solve the problems of low accuracy and long prediction time of traditional economic growth prediction algorithms in coastal areas, an algorithm based on impulse response function was designed to analyze economic growth prediction in coastal areas.(2)
Crawler technology is used to capture the economic data of coastal areas and normalize the captured data. Based on the processed data, the impulse response function is used to analyze the relationship between different economic variables, so as to build the PSO-LSTM model, which is used to predict the economic growth trend of coastal areas.(3)
The experimental results show that, compared with the experimental comparison algorithm, the prediction accuracy of the algorithm designed in this paper is always above 97%, and the prediction time is always below 1 s, which has certain practical significance.The remainder of this paper is organized as follows. Section2 introduces the design of economic growth prediction algorithm in coastal areas. Section 3 discusses experiment and analysis. Section 4 presents the conclusions of the study.


## 2. Design of Economic Growth Prediction Algorithm in Coastal Areas

### 2.1. Analysis of Economic Variables Based on Impulse Response Function

Crawler technology is used to capture economic data of coastal areas and process the data. The specific process is shown in Figure1.Figure 1
Data processing process.Different features may use different dimensions, so the difference between different eigenvalues may be large. When algorithms such as distance calculation or gradient descent are involved, the prediction effect may be greatly affected if data processing is not performed on them. In order to eliminate the influence caused by different dimensions or different value ranges among features, data should be normalized in advance [8].By linear transformation of the original data, the deviation normalization maps the data to the interval [0,1]. The calculation formula is as follows:(1)xnorm=x−xminxmax−xmin.The impulse response function is used to measure the influence trajectory of the impact of a standard deviation of the random disturbance term on the current and future values of other variables, and it can describe the dynamic interaction and effect between variables more intuitively [9]. The impulse response function method based on VAR model is used to study the long-term relationship between economic variables in coastal areas. VAR function is needed to further analyze the impulse response of the system relationship among variables. Through this analysis, it tries to find out the long-term response of various economic variables such as the opening index of producer services trade in the process of economic growth prediction in coastal areas to the pulse disturbance of economic growth in coastal areas and then determine the long-term relationship between all variables [10].


#### 2.1.1. Vector Autoregression Model

The vector autoregression model (VAR) is used to analyze the relationship between economic variables in coastal areas. The general form of VAR(P) is as follows:(2)yt=A1yt−1+...+Apyt−p+Bxt+εt.In the above equation,yt is a k-dimensional endogenous variable, and xt is a d-dimensional exogenous variable. A1,A2,...,Ap and B are the coefficient matrices to be estimated, and εt is the disturbance vector, which can be correlated synchronously with each other but not with their own lag values nor with the variables on the right-hand side of the equation [11]. In this way, the OLS method can be used to estimate each equation, and the obtained parameter estimators are consistent.


#### 2.1.2. Impulse Response Function and Prediction Variance Decomposition

On the basis of the vector autoregression model, the model can be further analyzed by using impulse response function and prediction variance decomposition. The impulse response function describes the response of an endogenous variable to the impact of a unit change from another endogenous variable and provides the positive and negative directions, adjustment time delay, stability process, and other information of the response generated by the impact of the system. Cholesky decomposition method proposed by Sims (1980) is the most commonly used method [12]. From the point of view of the problem studied in this paper, the analysis results of impulse response function can describe the dynamic process of economic variable change in coastal areas. Take VAR(2) model as an example to illustrate the basic idea of impulse response function.(3)xt=a1xt−1+a2xt−2+b1yt−1+b2yt−2+ε1t,yt=c1xt−1+c2xt−2+d1yt−1+d2yt−2+ε2t..Assume that the above system is active fromt=0. Let x1=x2=y1=y2=0, and the disturbance terms ε10=0 and ε20=0 in phase 0, and all the others are 0. Then, the perturbation given at the initial stage will be transferred continuously in the system. By iterative calculation, x0,x1,x2,x3,...,xn can be obtained as the response function of y caused by the impulse of x, and y0,y1,y2,y3,...,yn can also be obtained as the response function of y caused by the impulse of x. When the pulse of phase 0 is ε10=0 and ε20=0, the response functions of x and y caused by the pulse of y can be obtained. The above impulse response process can clearly capture the effects of various factors on economic growth in coastal areas.


#### 2.1.3. Variance Decomposition Theory

Based on the representation form ofVMA∞, Sims proposed a variance decomposition method to quantitatively grasp the influence relationship among economic variables in coastal areas.(4)yit=∑j=1kcij0εjt+cij1εjt−1+cij2εjt−2+...+cijnεjt−n.The sum of the effects of thej-th perturbation εj on yt from infinity to the present is in each bracket. Calculate its variance [13], and assume that sequence εt is independent; then(5)Ecij0εjt+cij1εjt−1+cij2εjt−2+...+cijnεjt−n2=∑q=0∞cijq2δij.This is the result that the effect of thej-th disturbance term on the i-th variable from infinity to the present time point is evaluated by variance [14]. In addition, it is assumed that the covariance matrix of the disturbance term vector is a diagonal matrix, and then the variance of yi is the simple sum of k terms of the above variances:(6)VARyit=∑j=0k∑q=0∞cijq2δij.The variance ofyi can be decomposed into k uncorrelated influences. Therefore, in order to determine how much influence each disturbance term has on the variance of yi, the following scale is defined:(7)RVCj⟶i∞=∑q=0∞cijq2δijVARyit=∑q=0∞cijq2δij∑i=0k∑q=0∞cijq2δij,where RAC is the contribution of relative variance; that is, the influence of the j-th variable on the i-th variable is observed according to the relative contribution of the j-th variable based on the variance of impact to the variance of yi [15]. In fact, it is impossible to evaluate the cijq sum of s=∞. If the model meets the condition of stationary direction, cijq decreases geometrically with the increase of q. Therefore, only a limited number of s terms are needed to complete the analysis of the relationship between various economic variables in coastal areas.


### 2.2. Prediction Based on the PSO-LSTM Model

Based on the processed data, the relationship between different economic variables was analyzed through the above process, and then the PSO-LSTM model was built to predict the economic growth trend of coastal areas.Long short-term memory (LSTM) network is a variant of RNN. RNN can only have short-term memory because of the possibility of gradient disappearance. LSTM network solves the problem of gradient disappearance to a certain extent by combining short-term memory and long-term memory through gate control. You can learn to rely on information for a long time. The schematic diagram of LSTM circulation module is shown in Figure2.Figure 2
Schematic diagram of the LSTM circulation module.The key to LSTM is the addition of a memory cell inside the hidden layer for storing historical information. In addition, three gates, input gate, forget gate, and output gate are added to each neural unit of the hidden layer in order to update and maintain historical information. The structure of a single LSTM node is shown in Figure3.Figure 3
Schematic diagram of one LSTM cell node structure.The specific calculation formula for each layer of LSTM is as follows.The calculation formula of forgetting gate is as follows:(8)ft=σWf∗ht−1,xt.The calculation formula of the input gate is as follows:(9)it=σWi∗ht−1,xt+bi,C˜t=tanhWc∗ht−1,xt+bc.The calculation formula of update gate is as follows:(10)Ct=ft∗Ct−1+it∗C˜t.The calculation formula of the output gate is as follows:(11)Ot=σWo∗ht−1,xt+bo,ht=ot∗tanhCt.The performance of the experimental model is closely related to the construction of the training set and test set. Clean and tidy input data, reasonable feature selection, and the most suitable algorithm model ensure that the model can achieve the expected experimental results [16, 17]. The prediction task of the prediction algorithm designed in this paper is a process of supervised learning, so the data is divided into two parts, test set and training set, when using the LSTM model for the prediction experiment. The prediction model in this paper can be simply designed as the structure shown in Figure 4.Figure 4
Structure of the prediction model.Aiming at the problem that the LSTM network model cannot accurately obtain the initial connection weight and threshold, particle swarm optimization (PSO) is used to optimize the initial connection weight and threshold of the LSTM model, so as to better solve the problem of economic development prediction in coastal areas. The optimal initial weight and threshold obtained by particle swarm optimization algorithm are used to construct the PSO-LSTM model, and the specific model implementation process is shown as follows.PSO is a swarm intelligence optimization algorithm inspired by bird predation process. In PSO, the potential solution to each optimization problem is treated as a particle, like a bird in a flock of birds. Each particle has a speed that determines its direction and distance, as well as a fitness value, and then all the particles look for the optimal value in the solution space based on the current optimal particle.Suppose that, in aD-dimensional search space, the number of particles is N, and a particle Xi in the particle swarm can be expressed as(12)Xi=xi1,xi2,...,xiN,i=1,2,...,N.The velocity of a particleXi in the particle swarm can be expressed as(13)Vi=vi1,vi2,...,viN,i=1,2,...,N.The optimal position found by a single particle is called the individual extreme value, which is represented byPbest. The optimal position found by the entire particle swarm is called the global extreme value, which is represented by gbest. After that, the particle is updated according to the two following formulas:(14)Vi′=ωVi+c1∗rand0,1∗Pbest−Xi+c2∗rand0,1∗gbest−Xi,(15)Xi′=Xi+Vi′.Among them,c1 and c2 represent the learning factor, usually taking c1=c2=2; ω represents the inertia factor, larger ω means strong global search ability and weak local search ability, and smaller ω means strong local search ability and weak global search ability; rand0,1 represents a random number in the range [0, 1].PSO has fewer parameters to adjust, is easy to realize, and has strong universality by using real number solution. At present, PSO has been widely used in pattern recognition, image processing, neural network training, power system design and decision-making, and scheduling related industries.Therefore, this paper uses the algorithm to improve the LSTM model built above and then builds the PSO-LSTM model, which is used to forecast the economic development of coastal areas. The PSO-LSTM model’s building process is shown in Figure5.Figure 5
PSO-LSTM model’s building process.The steps of economic growth prediction algorithm in coastal areas are shown below.Step 1.
Initialize the LSTM model and determine the model parameters.Step 2.
Data processing. In this paper, the maximum-minimum method is used to normalize economic data in coastal areas, so that the range of processed data falls within [0, 1].Step 3.
Initialize PSO parameters.Step 4.
Initialize the velocity and position of the particle.Step 5.
Determine the particle fitness function:(16)fxi=1N∑j=1Jy^itrain−yitrain,where yitrain and y^itrain, respectively, represent the expected output and actual output of the training set.Step 6.
Calculate the fitnessfitXi corresponding to each particle Xi and compare fitXi with individual extreme value Pbest. If fitXi<Pbest, replace Pbest with fitXi to complete the update of Pbest.Step 7.
Compare the best fitness (individual extreme)Pbest of each particle with the global extreme value gbest. If Pbest<gbest, replace gbest with Pbest to complete the update of gbest.Step 8.
Update the velocity and position of the particle; calculate the fitness of the new particle, and find the individual extreme value and global extreme value of the new particle.Step 9.
After satisfying the termination condition of PSO algorithm (usually the maximum number of iterations or the minimum fitness value), the optimal particles are input into the LSTM model as its initial weight and threshold, and the PSO-LSTM model is trained.Step 10.
Use the trained model to forecast economic growth in coastal areas and get accurate prediction results.


## 2.1. Analysis of Economic Variables Based on Impulse Response Function

Crawler technology is used to capture economic data of coastal areas and process the data. The specific process is shown in Figure1.Figure 1
Data processing process.Different features may use different dimensions, so the difference between different eigenvalues may be large. When algorithms such as distance calculation or gradient descent are involved, the prediction effect may be greatly affected if data processing is not performed on them. In order to eliminate the influence caused by different dimensions or different value ranges among features, data should be normalized in advance [8].By linear transformation of the original data, the deviation normalization maps the data to the interval [0,1]. The calculation formula is as follows:(1)xnorm=x−xminxmax−xmin.The impulse response function is used to measure the influence trajectory of the impact of a standard deviation of the random disturbance term on the current and future values of other variables, and it can describe the dynamic interaction and effect between variables more intuitively [9]. The impulse response function method based on VAR model is used to study the long-term relationship between economic variables in coastal areas. VAR function is needed to further analyze the impulse response of the system relationship among variables. Through this analysis, it tries to find out the long-term response of various economic variables such as the opening index of producer services trade in the process of economic growth prediction in coastal areas to the pulse disturbance of economic growth in coastal areas and then determine the long-term relationship between all variables [10].


### 2.1.1. Vector Autoregression Model

The vector autoregression model (VAR) is used to analyze the relationship between economic variables in coastal areas. The general form of VAR(P) is as follows:(2)yt=A1yt−1+...+Apyt−p+Bxt+εt.In the above equation,yt is a k-dimensional endogenous variable, and xt is a d-dimensional exogenous variable. A1,A2,...,Ap and B are the coefficient matrices to be estimated, and εt is the disturbance vector, which can be correlated synchronously with each other but not with their own lag values nor with the variables on the right-hand side of the equation [11]. In this way, the OLS method can be used to estimate each equation, and the obtained parameter estimators are consistent.


### 2.1.2. Impulse Response Function and Prediction Variance Decomposition

On the basis of the vector autoregression model, the model can be further analyzed by using impulse response function and prediction variance decomposition. The impulse response function describes the response of an endogenous variable to the impact of a unit change from another endogenous variable and provides the positive and negative directions, adjustment time delay, stability process, and other information of the response generated by the impact of the system. Cholesky decomposition method proposed by Sims (1980) is the most commonly used method [12]. From the point of view of the problem studied in this paper, the analysis results of impulse response function can describe the dynamic process of economic variable change in coastal areas. Take VAR(2) model as an example to illustrate the basic idea of impulse response function.(3)xt=a1xt−1+a2xt−2+b1yt−1+b2yt−2+ε1t,yt=c1xt−1+c2xt−2+d1yt−1+d2yt−2+ε2t..Assume that the above system is active fromt=0. Let x1=x2=y1=y2=0, and the disturbance terms ε10=0 and ε20=0 in phase 0, and all the others are 0. Then, the perturbation given at the initial stage will be transferred continuously in the system. By iterative calculation, x0,x1,x2,x3,...,xn can be obtained as the response function of y caused by the impulse of x, and y0,y1,y2,y3,...,yn can also be obtained as the response function of y caused by the impulse of x. When the pulse of phase 0 is ε10=0 and ε20=0, the response functions of x and y caused by the pulse of y can be obtained. The above impulse response process can clearly capture the effects of various factors on economic growth in coastal areas.


### 2.1.3. Variance Decomposition Theory

Based on the representation form ofVMA∞, Sims proposed a variance decomposition method to quantitatively grasp the influence relationship among economic variables in coastal areas.(4)yit=∑j=1kcij0εjt+cij1εjt−1+cij2εjt−2+...+cijnεjt−n.The sum of the effects of thej-th perturbation εj on yt from infinity to the present is in each bracket. Calculate its variance [13], and assume that sequence εt is independent; then(5)Ecij0εjt+cij1εjt−1+cij2εjt−2+...+cijnεjt−n2=∑q=0∞cijq2δij.This is the result that the effect of thej-th disturbance term on the i-th variable from infinity to the present time point is evaluated by variance [14]. In addition, it is assumed that the covariance matrix of the disturbance term vector is a diagonal matrix, and then the variance of yi is the simple sum of k terms of the above variances:(6)VARyit=∑j=0k∑q=0∞cijq2δij.The variance ofyi can be decomposed into k uncorrelated influences. Therefore, in order to determine how much influence each disturbance term has on the variance of yi, the following scale is defined:(7)RVCj⟶i∞=∑q=0∞cijq2δijVARyit=∑q=0∞cijq2δij∑i=0k∑q=0∞cijq2δij,where RAC is the contribution of relative variance; that is, the influence of the j-th variable on the i-th variable is observed according to the relative contribution of the j-th variable based on the variance of impact to the variance of yi [15]. In fact, it is impossible to evaluate the cijq sum of s=∞. If the model meets the condition of stationary direction, cijq decreases geometrically with the increase of q. Therefore, only a limited number of s terms are needed to complete the analysis of the relationship between various economic variables in coastal areas.


## 2.1.1. Vector Autoregression Model

The vector autoregression model (VAR) is used to analyze the relationship between economic variables in coastal areas. The general form of VAR(P) is as follows:(2)yt=A1yt−1+...+Apyt−p+Bxt+εt.In the above equation,yt is a k-dimensional endogenous variable, and xt is a d-dimensional exogenous variable. A1,A2,...,Ap and B are the coefficient matrices to be estimated, and εt is the disturbance vector, which can be correlated synchronously with each other but not with their own lag values nor with the variables on the right-hand side of the equation [11]. In this way, the OLS method can be used to estimate each equation, and the obtained parameter estimators are consistent.


## 2.1.2. Impulse Response Function and Prediction Variance Decomposition

On the basis of the vector autoregression model, the model can be further analyzed by using impulse response function and prediction variance decomposition. The impulse response function describes the response of an endogenous variable to the impact of a unit change from another endogenous variable and provides the positive and negative directions, adjustment time delay, stability process, and other information of the response generated by the impact of the system. Cholesky decomposition method proposed by Sims (1980) is the most commonly used method [12]. From the point of view of the problem studied in this paper, the analysis results of impulse response function can describe the dynamic process of economic variable change in coastal areas. Take VAR(2) model as an example to illustrate the basic idea of impulse response function.(3)xt=a1xt−1+a2xt−2+b1yt−1+b2yt−2+ε1t,yt=c1xt−1+c2xt−2+d1yt−1+d2yt−2+ε2t..Assume that the above system is active fromt=0. Let x1=x2=y1=y2=0, and the disturbance terms ε10=0 and ε20=0 in phase 0, and all the others are 0. Then, the perturbation given at the initial stage will be transferred continuously in the system. By iterative calculation, x0,x1,x2,x3,...,xn can be obtained as the response function of y caused by the impulse of x, and y0,y1,y2,y3,...,yn can also be obtained as the response function of y caused by the impulse of x. When the pulse of phase 0 is ε10=0 and ε20=0, the response functions of x and y caused by the pulse of y can be obtained. The above impulse response process can clearly capture the effects of various factors on economic growth in coastal areas.


## 2.1.3. Variance Decomposition Theory

Based on the representation form ofVMA∞, Sims proposed a variance decomposition method to quantitatively grasp the influence relationship among economic variables in coastal areas.(4)yit=∑j=1kcij0εjt+cij1εjt−1+cij2εjt−2+...+cijnεjt−n.The sum of the effects of thej-th perturbation εj on yt from infinity to the present is in each bracket. Calculate its variance [13], and assume that sequence εt is independent; then(5)Ecij0εjt+cij1εjt−1+cij2εjt−2+...+cijnεjt−n2=∑q=0∞cijq2δij.This is the result that the effect of thej-th disturbance term on the i-th variable from infinity to the present time point is evaluated by variance [14]. In addition, it is assumed that the covariance matrix of the disturbance term vector is a diagonal matrix, and then the variance of yi is the simple sum of k terms of the above variances:(6)VARyit=∑j=0k∑q=0∞cijq2δij.The variance ofyi can be decomposed into k uncorrelated influences. Therefore, in order to determine how much influence each disturbance term has on the variance of yi, the following scale is defined:(7)RVCj⟶i∞=∑q=0∞cijq2δijVARyit=∑q=0∞cijq2δij∑i=0k∑q=0∞cijq2δij,where RAC is the contribution of relative variance; that is, the influence of the j-th variable on the i-th variable is observed according to the relative contribution of the j-th variable based on the variance of impact to the variance of yi [15]. In fact, it is impossible to evaluate the cijq sum of s=∞. If the model meets the condition of stationary direction, cijq decreases geometrically with the increase of q. Therefore, only a limited number of s terms are needed to complete the analysis of the relationship between various economic variables in coastal areas.


## 2.2. Prediction Based on the PSO-LSTM Model

Based on the processed data, the relationship between different economic variables was analyzed through the above process, and then the PSO-LSTM model was built to predict the economic growth trend of coastal areas.Long short-term memory (LSTM) network is a variant of RNN. RNN can only have short-term memory because of the possibility of gradient disappearance. LSTM network solves the problem of gradient disappearance to a certain extent by combining short-term memory and long-term memory through gate control. You can learn to rely on information for a long time. The schematic diagram of LSTM circulation module is shown in Figure2.Figure 2
Schematic diagram of the LSTM circulation module.The key to LSTM is the addition of a memory cell inside the hidden layer for storing historical information. In addition, three gates, input gate, forget gate, and output gate are added to each neural unit of the hidden layer in order to update and maintain historical information. The structure of a single LSTM node is shown in Figure3.Figure 3
Schematic diagram of one LSTM cell node structure.The specific calculation formula for each layer of LSTM is as follows.The calculation formula of forgetting gate is as follows:(8)ft=σWf∗ht−1,xt.The calculation formula of the input gate is as follows:(9)it=σWi∗ht−1,xt+bi,C˜t=tanhWc∗ht−1,xt+bc.The calculation formula of update gate is as follows:(10)Ct=ft∗Ct−1+it∗C˜t.The calculation formula of the output gate is as follows:(11)Ot=σWo∗ht−1,xt+bo,ht=ot∗tanhCt.The performance of the experimental model is closely related to the construction of the training set and test set. Clean and tidy input data, reasonable feature selection, and the most suitable algorithm model ensure that the model can achieve the expected experimental results [16, 17]. The prediction task of the prediction algorithm designed in this paper is a process of supervised learning, so the data is divided into two parts, test set and training set, when using the LSTM model for the prediction experiment. The prediction model in this paper can be simply designed as the structure shown in Figure 4.Figure 4
Structure of the prediction model.Aiming at the problem that the LSTM network model cannot accurately obtain the initial connection weight and threshold, particle swarm optimization (PSO) is used to optimize the initial connection weight and threshold of the LSTM model, so as to better solve the problem of economic development prediction in coastal areas. The optimal initial weight and threshold obtained by particle swarm optimization algorithm are used to construct the PSO-LSTM model, and the specific model implementation process is shown as follows.PSO is a swarm intelligence optimization algorithm inspired by bird predation process. In PSO, the potential solution to each optimization problem is treated as a particle, like a bird in a flock of birds. Each particle has a speed that determines its direction and distance, as well as a fitness value, and then all the particles look for the optimal value in the solution space based on the current optimal particle.Suppose that, in aD-dimensional search space, the number of particles is N, and a particle Xi in the particle swarm can be expressed as(12)Xi=xi1,xi2,...,xiN,i=1,2,...,N.The velocity of a particleXi in the particle swarm can be expressed as(13)Vi=vi1,vi2,...,viN,i=1,2,...,N.The optimal position found by a single particle is called the individual extreme value, which is represented byPbest. The optimal position found by the entire particle swarm is called the global extreme value, which is represented by gbest. After that, the particle is updated according to the two following formulas:(14)Vi′=ωVi+c1∗rand0,1∗Pbest−Xi+c2∗rand0,1∗gbest−Xi,(15)Xi′=Xi+Vi′.Among them,c1 and c2 represent the learning factor, usually taking c1=c2=2; ω represents the inertia factor, larger ω means strong global search ability and weak local search ability, and smaller ω means strong local search ability and weak global search ability; rand0,1 represents a random number in the range [0, 1].PSO has fewer parameters to adjust, is easy to realize, and has strong universality by using real number solution. At present, PSO has been widely used in pattern recognition, image processing, neural network training, power system design and decision-making, and scheduling related industries.Therefore, this paper uses the algorithm to improve the LSTM model built above and then builds the PSO-LSTM model, which is used to forecast the economic development of coastal areas. The PSO-LSTM model’s building process is shown in Figure5.Figure 5
PSO-LSTM model’s building process.The steps of economic growth prediction algorithm in coastal areas are shown below.Step 1.
Initialize the LSTM model and determine the model parameters.Step 2.
Data processing. In this paper, the maximum-minimum method is used to normalize economic data in coastal areas, so that the range of processed data falls within [0, 1].Step 3.
Initialize PSO parameters.Step 4.
Initialize the velocity and position of the particle.Step 5.
Determine the particle fitness function:(16)fxi=1N∑j=1Jy^itrain−yitrain,where yitrain and y^itrain, respectively, represent the expected output and actual output of the training set.Step 6.
Calculate the fitnessfitXi corresponding to each particle Xi and compare fitXi with individual extreme value Pbest. If fitXi<Pbest, replace Pbest with fitXi to complete the update of Pbest.Step 7.
Compare the best fitness (individual extreme)Pbest of each particle with the global extreme value gbest. If Pbest<gbest, replace gbest with Pbest to complete the update of gbest.Step 8.
Update the velocity and position of the particle; calculate the fitness of the new particle, and find the individual extreme value and global extreme value of the new particle.Step 9.
After satisfying the termination condition of PSO algorithm (usually the maximum number of iterations or the minimum fitness value), the optimal particles are input into the LSTM model as its initial weight and threshold, and the PSO-LSTM model is trained.Step 10.
Use the trained model to forecast economic growth in coastal areas and get accurate prediction results.


## 3. Experimental Design and Result Analysis

### 3.1. Experimental Scheme Design

In order to test the practical application effect of the prediction algorithm of economic growth in coastal areas based on impulse response function, the experimental design is carried out. The specific experimental environment is shown in Table1.Table 1
Experimental environment.
Operating systemWindows 10 64-bitDatabaseMySQL-5.6.25JDKJDK 1.8.0-71ServerTomcat-8.0.23Development of languageJavaBrowserGoogle ChromeSimulation softwareMATLAB 7.2The data used this time came from a coastal area, and the data set was from the data released on the official website of the National Bureau of Statistics. The collected data were cleaned and repaired, so as to improve the scientificity and accuracy of the simulation experiment results. The data included historical data on 39 economic indicators from January 2010 to October 2020. Among them, the time unit of indicators such as business climate index, entrepreneur confidence index, and national tax revenue is quarterly, while the time unit of other indicators is monthly. Introduction of economic forecast data set is shown in Table2.Table 2
Introduction of economic forecast data set.
Index nameThe dimensionNumber of training samplesNumber of test samplesGDP20111 + 19111 + 19CPI20111 + 19111 + 19


### 3.2. Analysis of Impulse Response Function

The impulse response function method based on VAR model is used to study the long-term relationship between variables, and the impact response path between the import and export of service trade and economic growth is obtained. Impulse response can reflect the process of how an endogenous variable influences other variables through the model when it changes and finally returns to itself. The impulse response is analyzed using Eviews 7.0, and the results are shown in Figure6.Figure 6
The influence of economic growth on information of one standard deviation.As can be seen from Figure6, GDP growth rate has a certain volatility to its own standard deviation disturbance, showing a weak negative effect in the third, sixth, seventh, and ninth periods, but the cumulative impact is 0.080346, showing a positive effect. The disturbance of GDP growth rate to the standard deviation of the growth rate of service trade export also has certain fluctuation, but the overall effect is positive. The cumulative effect is 0.051226, indicating that the growth rate of service trade export has a positive effect on economic growth in the long run. The response of GDP growth rate to the disturbance of standard deviation of the growth rate of service trade import fluctuates greatly, and the positive effect and negative effect appear alternately. The cumulative effect is 0.0207, indicating that the growth rate of service trade import has a weak negative effect on economic growth in the long run. In general, the impact of the growth rate of service trade import and export on economic growth showed a gradually decreasing trend. The response of service trade exports to one standard deviation’s information is shown in Figure 7.Figure 7
The response of service trade exports to one standard deviation’s information.As can be seen from Figure7, the impact of export growth rate of service trade on its own standard deviation shows a highly positive effect in the first period, and no significant effect is shown in the subsequent periods, but its cumulative effect is 0.090504, showing a highly positive effect. The impact response of service trade export growth rate on GDP growth rate is positive in the first period, and it becomes weakly negative in the subsequent periods. The cumulative effect is 0.029412, indicating that economic growth has a weak inhibition on the increase of service trade export growth rate. The impact response of service trade import growth rate to export growth rate is 0 in the initial stage, and it fluctuates below the horizontal axis in the second and eighth stages, which is a weakly negative effect, and its cumulative effect is 0.0854105, which is generally positive. Its economic meaning is that the growth rate of service trade import will promote the growth rate of export on the whole. Response results of service trade import standard information are shown in Figure 8.Figure 8
Response results of service trade import standard information.The impact response of the import growth rate of service trade to its own standard deviation has a certain volatility. In the first period, it shows a highly positive effect and then a little fluctuation, but the overall performance is a highly positive effect. The impact response of economic growth rate to the standard deviation of service trade import growth rate shows a highly positive effect in the first period and starts to decline in the second period and continues to be negative. Its economic meaning is the impact of the economic growth rate of service trade import growth rate; there is a lag in the initial phase which will promote the increase of the import growth rate; later, its inhibition effect will gradually appear, showing that the service trade export growth to the impact of the import growth rate also has a certain volatility, and the basic trend of positive and negative effects appears alternately. The cumulative effect is 0.089771, which is a positive effect.


### 3.3. Analysis of Experimental Comparison Results

The prediction algorithm based on correlation analysis, the prediction algorithm based on GMDH, and the prediction algorithm based on impulse response function designed in this paper are taken as the experimental comparison method. The prediction accuracies of different algorithms are compared to verify the prediction effect of this algorithm. The specific comparison results are shown in Figure9.Figure 9
Comparison results of prediction accuracy.Through the analysis of the results in Figure9, it can be seen that the prediction accuracy of the prediction algorithm based on correlation analysis varies between 55% and 84%, and that of the prediction algorithm based on GMDH varies between 62% and 87%. Compared with the two algorithms, the prediction accuracy of the prediction algorithm based on impulse response function designed in this paper is always above 97%. It shows that this method can be used to accurately predict the economic growth in coastal areas, and the practical application effect is better.The prediction algorithm based on correlation analysis, the prediction algorithm based on GMDH, and the prediction algorithm based on impulse response function designed in this paper are taken as the experimental comparison method. The prediction efficiency of the algorithm is verified by comparing the prediction times of different algorithms. The specific comparison results are shown in Figure10.Figure 10
Prediction time comparison results.From the analysis of the data in Figure10, it can be seen that the prediction time of the prediction algorithm based on correlation analysis varies between 1.7 s and 4.3 s, and that of the prediction algorithm based on GMDH varies between 1.6 s and 4.2 s. Compared with the two algorithms, the prediction time of the prediction algorithm based on impulse response function designed in this paper always stays below 1 s. It is shown that this method can realize the rapid forecast of economic growth in coastal areas, with higher prediction efficiency and better practical application effect.


## 3.1. Experimental Scheme Design

In order to test the practical application effect of the prediction algorithm of economic growth in coastal areas based on impulse response function, the experimental design is carried out. The specific experimental environment is shown in Table1.Table 1
Experimental environment.
Operating systemWindows 10 64-bitDatabaseMySQL-5.6.25JDKJDK 1.8.0-71ServerTomcat-8.0.23Development of languageJavaBrowserGoogle ChromeSimulation softwareMATLAB 7.2The data used this time came from a coastal area, and the data set was from the data released on the official website of the National Bureau of Statistics. The collected data were cleaned and repaired, so as to improve the scientificity and accuracy of the simulation experiment results. The data included historical data on 39 economic indicators from January 2010 to October 2020. Among them, the time unit of indicators such as business climate index, entrepreneur confidence index, and national tax revenue is quarterly, while the time unit of other indicators is monthly. Introduction of economic forecast data set is shown in Table2.Table 2
Introduction of economic forecast data set.
Index nameThe dimensionNumber of training samplesNumber of test samplesGDP20111 + 19111 + 19CPI20111 + 19111 + 19


## 3.2. Analysis of Impulse Response Function

The impulse response function method based on VAR model is used to study the long-term relationship between variables, and the impact response path between the import and export of service trade and economic growth is obtained. Impulse response can reflect the process of how an endogenous variable influences other variables through the model when it changes and finally returns to itself. The impulse response is analyzed using Eviews 7.0, and the results are shown in Figure6.Figure 6
The influence of economic growth on information of one standard deviation.As can be seen from Figure6, GDP growth rate has a certain volatility to its own standard deviation disturbance, showing a weak negative effect in the third, sixth, seventh, and ninth periods, but the cumulative impact is 0.080346, showing a positive effect. The disturbance of GDP growth rate to the standard deviation of the growth rate of service trade export also has certain fluctuation, but the overall effect is positive. The cumulative effect is 0.051226, indicating that the growth rate of service trade export has a positive effect on economic growth in the long run. The response of GDP growth rate to the disturbance of standard deviation of the growth rate of service trade import fluctuates greatly, and the positive effect and negative effect appear alternately. The cumulative effect is 0.0207, indicating that the growth rate of service trade import has a weak negative effect on economic growth in the long run. In general, the impact of the growth rate of service trade import and export on economic growth showed a gradually decreasing trend. The response of service trade exports to one standard deviation’s information is shown in Figure 7.Figure 7
The response of service trade exports to one standard deviation’s information.As can be seen from Figure7, the impact of export growth rate of service trade on its own standard deviation shows a highly positive effect in the first period, and no significant effect is shown in the subsequent periods, but its cumulative effect is 0.090504, showing a highly positive effect. The impact response of service trade export growth rate on GDP growth rate is positive in the first period, and it becomes weakly negative in the subsequent periods. The cumulative effect is 0.029412, indicating that economic growth has a weak inhibition on the increase of service trade export growth rate. The impact response of service trade import growth rate to export growth rate is 0 in the initial stage, and it fluctuates below the horizontal axis in the second and eighth stages, which is a weakly negative effect, and its cumulative effect is 0.0854105, which is generally positive. Its economic meaning is that the growth rate of service trade import will promote the growth rate of export on the whole. Response results of service trade import standard information are shown in Figure 8.Figure 8
Response results of service trade import standard information.The impact response of the import growth rate of service trade to its own standard deviation has a certain volatility. In the first period, it shows a highly positive effect and then a little fluctuation, but the overall performance is a highly positive effect. The impact response of economic growth rate to the standard deviation of service trade import growth rate shows a highly positive effect in the first period and starts to decline in the second period and continues to be negative. Its economic meaning is the impact of the economic growth rate of service trade import growth rate; there is a lag in the initial phase which will promote the increase of the import growth rate; later, its inhibition effect will gradually appear, showing that the service trade export growth to the impact of the import growth rate also has a certain volatility, and the basic trend of positive and negative effects appears alternately. The cumulative effect is 0.089771, which is a positive effect.


## 3.3. Analysis of Experimental Comparison Results

The prediction algorithm based on correlation analysis, the prediction algorithm based on GMDH, and the prediction algorithm based on impulse response function designed in this paper are taken as the experimental comparison method. The prediction accuracies of different algorithms are compared to verify the prediction effect of this algorithm. The specific comparison results are shown in Figure9.Figure 9
Comparison results of prediction accuracy.Through the analysis of the results in Figure9, it can be seen that the prediction accuracy of the prediction algorithm based on correlation analysis varies between 55% and 84%, and that of the prediction algorithm based on GMDH varies between 62% and 87%. Compared with the two algorithms, the prediction accuracy of the prediction algorithm based on impulse response function designed in this paper is always above 97%. It shows that this method can be used to accurately predict the economic growth in coastal areas, and the practical application effect is better.The prediction algorithm based on correlation analysis, the prediction algorithm based on GMDH, and the prediction algorithm based on impulse response function designed in this paper are taken as the experimental comparison method. The prediction efficiency of the algorithm is verified by comparing the prediction times of different algorithms. The specific comparison results are shown in Figure10.Figure 10
Prediction time comparison results.From the analysis of the data in Figure10, it can be seen that the prediction time of the prediction algorithm based on correlation analysis varies between 1.7 s and 4.3 s, and that of the prediction algorithm based on GMDH varies between 1.6 s and 4.2 s. Compared with the two algorithms, the prediction time of the prediction algorithm based on impulse response function designed in this paper always stays below 1 s. It is shown that this method can realize the rapid forecast of economic growth in coastal areas, with higher prediction efficiency and better practical application effect.


## 4. Conclusion

Technological progress and innovation are the key to promoting the rapid implementation of the coastal area economic development strategy. Therefore, effective implementation of the coastal area economic development strategy is conducive to the development of circular economy outside the region, creating new economic development strategic points and encouraging coastal areas to get rid of traditional development paths. Relying on this, we foster new industrial growth points for regional development It is of great practical significance to promote the coordinated development of regional economy, enhance the overall competitiveness, and then drive the structural adjustment and industrial upgrading for the comprehensive development of the economic society in coastal areas. Therefore, this paper puts forward a prediction algorithm of economic growth in coastal areas based on impulse response function. The experimental results show that the impact of the growth rate of import and export of service trade on economic growth shows a gradually decreasing trend, which will promote the growth rate of export on the whole, and the impact of economic growth on the growth of service trade imports shows an alternating trend of positive and negative effects, which is a positive effect. Moreover, compared with the experimental comparison algorithm, the prediction accuracy of the algorithm designed in this paper is always above 97%, and the prediction time is always below 1 s, which can fully solve the problems existing in the traditional method and has a certain practical significance.



---

*Source: 3864188-2021-11-10.xml*