A spatiotemporal vehicle activity analysis and marketing recommendation method

Abstract

The present invention belongs to the technical field of marketing recommendation, and relates to a spatiotemporal vehicle activity analysis and marketing recommendation method. By deeply analyzing the spatiotemporal data of vehicles, a graph convolutional network is adopted to capture the complex spatial and temporal relationships between vehicles, and a variational autoencoder is used to further extract deep behavioral features and enhance the generalization ability of prediction, so as to identify specific behavioral patterns in real time and automatically generate personalized marketing recommendations, thereby greatly improving the pertinence and effectiveness of marketing activities. It can not only provide a deeper understanding of vehicle activity analysis, but also predict and identify specific behavioral patterns in real time. In intelligent transportation systems and smart city management, it can help related enterprises and institutions formulate more effective marketing strategies through precise data analysis, thereby optimizing resource allocation and improving service quality and economic benefits.

Description

Technical Field

[0001] The present invention belongs to the field of marketing technology and relates to a spatiotemporal vehicle activity analysis and marketing recommendation method. Background Art

[0002] Vehicle activity analysis and marketing recommendation systems based on this technology have significant commercial value and social significance in the context of intelligent transportation and smart cities. By accurately analyzing the activity patterns of vehicles in a specific area, such systems can not only help companies understand consumer behavior habits, but also provide personalized marketing strategies based on these habits, thereby improving marketing efficiency and effectiveness. For example, by analyzing the vehicles that frequently enter and exit a business park at night, companies can promote late-night food delivery services or nighttime conveniences in a targeted manner and directly market to specific demand groups.

[0003] Existing vehicle activity analysis technologies usually rely on traditional data analysis methods and simple statistical models, such as frequency statistics and cluster analysis, to identify the activity patterns of vehicles within a specific time period. These analyses often rely on preset thresholds or simple pattern recognition and lack in-depth behavioral understanding. With the rise of deep learning technology, some methods have tried to combine deep neural networks to solve this problem, but these methods often have limitations when processing complex spatiotemporal data. Especially when it is necessary to analyze the dynamic behavior patterns of vehicles at a specific time and place, how to effectively extract and utilize this information from a large amount of spatiotemporal data has become a major challenge. In addition, existing methods often lack precision in predicting vehicle behavior patterns and are unable to effectively identify and predict vehicle behavior trends in specific environments. This is specifically manifested in the following aspects: (1) Inability to effectively address the challenges brought by the unstructured and complex nature of data: Vehicle activity data usually includes a large amount of spatiotemporal information. This data is highly unstructured in time and space. Traditional deep neural networks (such as fully connected networks or standard convolutional neural networks) usually require predefined, regular data structures and are difficult to directly process unstructured graph data or complex spatiotemporal data; (2) Insufficient capture of spatiotemporal relationships: The spatiotemporal relationships between vehicles are crucial for analyzing their behavior patterns and true activity. For example, the frequent appearance of multiple vehicles at the same place at a specific time may indicate a specific event or demand. Traditional neural network models are mainly designed to process independent and identically distributed data and are often unable to effectively capture and utilize such complex spatial relationships; (3) Difficulty in handling dynamic characteristics: The dynamic nature of vehicle behavior is another challenge in analysis. Vehicle activity patterns may change with time, location, external events, and other factors. Traditional deep learning models may find it difficult to make accurate long-term behavior predictions when dealing with such dynamic changes, especially without the support of sufficient time series data. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and to provide a spatiotemporal vehicle activity analysis and marketing recommendation method. By deeply analyzing the spatiotemporal data of vehicles, graph convolutional networks (GCNs) are used to capture the complex spatial and temporal relationships between vehicles. At the same time, variational autoencoders (VAEs) are used to further extract deep behavioral features and enhance the generalization ability of predictions, identify specific behavioral patterns in real time, and automatically generate personalized marketing recommendations, greatly improving the pertinence and effectiveness of marketing activities.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for spatiotemporal vehicle activity analysis and marketing recommendation, comprising the following steps:

[0007] S1. Vehicle data collection: Collect vehicle data collected by GPS trackers, traffic monitoring equipment, mobile applications or sensors, and perform data cleaning and data standardization on the vehicle data;

[0008] S2. Graph data modeling: Vehicles are represented as nodes in a graph, and the interactions or behavioral similarities between vehicles are represented as edges in the graph for graph data modeling;

[0009] S3. Graph model construction: Build a graph model based on the graph convolutional network. The graph convolutional network processes node features, learns the dependencies between nodes, and obtains vehicle behavior data.

[0010] S4, feature extraction: Use the variational autoencoder to process and refine the vehicle behavior data obtained in S3 to obtain a high-dimensional feature vector of the vehicle;

[0011] S5. Vehicle activity analysis: For the high-dimensional feature vector of the vehicle, a neural network-based regression model is trained to calculate the activity score, the K-means clustering algorithm is used to identify different behavior patterns, and the autoregressive integrated moving average model (ARIMA) is used to predict the time trend of vehicle activity;

[0012] S6. Marketing strategy generation: Based on the activity scores, behavior patterns, and trend forecasts obtained in step S5, identify the target customer groups with the greatest potential, design customized marketing strategies for different vehicle groups, conduct A / B tests on different marketing strategies to evaluate which strategies are most effective, and make adjustments and optimizations accordingly.

[0013] As a further technical solution of the present invention, the vehicle data in step S1 includes geographic location coordinates, timestamp, driving speed, frequent stop locations, and traffic condition data. Data cleaning includes removing noise and outliers and processing missing values. Data standardization includes time synchronization and spatial standardization.

[0014] As a further technical solution of the present invention, the node in step S2 is defined as: each node Represents a vehicle entity, the feature vector of the node It is composed of the vehicle data processed in step S1, which includes the vehicle's driving speed, current location, and historical location. The definition of edge is: Representative vehicle and The relationship between them is based on geographical distance, route intersection, time overlap, and edge weights. Determined based on the mutual proximity between vehicles, using a Gaussian kernel to measure: ,in It is a vehicle and The distance between is the standard deviation of the Gaussian kernel, which is used to control the decay rate of the weights.

[0015] As a further technical solution of the present invention, the graph convolutional network in step S3 updates the feature representation of the node through the features of the neighboring nodes. The new features after each convolution Calculated by the following formula: ,in, is the set of neighbor nodes of node i, and It is The weight matrix and bias vector of the layer, is a nonlinear activation function, is a normalization constant representing the number of neighbors, Neighbor node After the graph convolution operation, the maximum aggregation function is used to update the features of each node by summarizing the information of neighboring nodes, capturing the spatial relationship between nodes, and thus obtaining vehicle behavior data.

[0016] As a further technical solution of the present invention, the variational autoencoder in step S4 includes an encoder and a decoder. The encoder is composed of a neural network composed of multiple layers of fully connected layers. Convert to latent variables , output the mean of the latent variable and variance ,The structure of the decoder is symmetrical with that of the encoder. The decoder is based on latent variables Reconstructing input data , where the latent variable output by the encoder is The posterior distribution of is set to Gaussian distribution: ,in and The neural network is based on the input Calculate the mean and variance of the latent variable The prior distribution of is set to the standard normal distribution: ; The decoder is based on latent variables Reconstructing input data The distribution of ,in and is the mean and variance of the decoder output; the goal of the variational autoencoder (VAE) is to maximize the lower bound of evidence, and its loss function consists of two parts: , where the first term is the reconstruction error, which reflects the quality of the reconstructed data; the second term is the KL divergence, which measures the difference between the encoded latent variable distribution and its prior distribution. Through the above steps, the high-dimensional feature vector of the vehicle is obtained.

[0017] As a further technical solution of the present invention, the first step of the regression model based on the neural network in step S5 The hidden layer is expressed as: ,in , and They are The weight matrix and bias vector of the layer, is the ReLU activation function, and the regression model outputs the predicted activity score ,in is the number of hidden layers.

[0018] As a further technical solution of the present invention, the goal of the K-means clustering algorithm in step S5 is to minimize the intra-cluster variance: ,in is the number of clusters, It is The set of samples in the clusters, It is a cluster The center of the clustering process annotates and analyzes vehicle behavior patterns based on clustering results to identify groups of vehicles active at specific times or vehicles that frequently visit a certain location.

[0019] As a further technical solution of the present invention, when the autoregressive integrated moving average model (ARIMA) is used to predict the time trend of vehicle activity in step S5, the high-dimensional feature vectors of each vehicle node are first arranged in chronological order to construct a time series data set. The prediction result is: ,in is the order of the autoregressive term, is the difference order, is the order of the sliding average term, is the lag operator, It's time The observed value of is the error term, and future trend prediction is performed from high-dimensional time series data through the autoregressive integrated moving average model.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) By constructing a graphical model that reflects the spatial and temporal relationships between vehicles, GCNs are used to accurately capture the dynamic interactions of vehicles at a specific time and place, thereby effectively revealing the behavior patterns and trends of vehicle groups. At the same time, VAEs are used to deeply explore the potential characteristics of vehicle behavior and improve the model's processing capabilities and prediction accuracy for complex spatiotemporal data.

[0022] (2) Cluster analysis can be used to identify the behavior patterns of vehicles at specific times and locations. By continuously monitoring and analyzing the location and time data of vehicles, it is possible to predict future trends in vehicle behavior and update the dynamic changes in vehicle behavior in real time, which helps companies adjust their marketing strategies in a timely manner to adapt to changes in the market and customer behavior. It can not only provide a deeper understanding of vehicle activity analysis, but also predict and identify specific behavior patterns in real time, such as vehicles frequently entering and exiting specific areas. In the management of intelligent transportation systems and smart cities, it can help related companies and institutions develop more effective marketing strategies through precise data analysis, thereby optimizing resource allocation and improving service quality and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A flow chart of the spatiotemporal vehicle activity analysis and marketing recommendation method provided by the present invention. DETAILED DESCRIPTION

[0024] The present invention will be further described below by way of embodiments in conjunction with the accompanying drawings.

[0025] Example:

[0026] like Figure 1 As shown, this embodiment provides a spatiotemporal vehicle activity analysis and marketing recommendation method, which specifically includes the following steps:

[0027] S1. Vehicle data collection: Collect vehicle data collected by GPS trackers, traffic monitoring equipment, mobile applications or sensors, and perform data cleaning and data standardization on the vehicle data; vehicle data includes geographic location coordinates, timestamps, driving speed, frequent stop locations, and traffic conditions data. Data cleaning includes removing noise and outliers and processing missing values. Data standardization includes time synchronization and spatial standardization.

[0028] S2. Graph data modeling: Vehicles are represented as nodes in a graph, and the interactions or behavioral similarities between vehicles are represented as edges in the graph for graph data modeling; the node is defined as: each node Represents a vehicle entity, the feature vector of the node It is composed of the vehicle data processed in step S1, which includes the vehicle's driving speed, current location, and historical location. The definition of edge is: Representative vehicle and The relationship between them is based on geographical distance, route intersection, time overlap, and edge weights. Determined based on the mutual proximity between vehicles, using a Gaussian kernel to measure: ,in It is a vehicle and The distance between is the standard deviation of the Gaussian kernel, which is used to control the decay rate of the weights.

[0029] S3. Graph model construction: Build a graph model based on the graph convolutional network. The graph convolutional network processes node features, learns the dependencies between nodes, and obtains vehicle behavior data. The purpose of graph convolution is to update the feature representation of nodes through the features of neighboring nodes. The new features after each convolution Calculated by the following formula: ,in, is the set of neighbor nodes of node i, and It is The weight matrix and bias vector of the layer, is a nonlinear activation function, is a normalization constant representing the number of neighbors, Neighbor node After the graph convolution operation, the maximum aggregation function is used to update the features of each node by summarizing the information of neighboring nodes, capturing the spatial relationship between nodes, and thus obtaining vehicle behavior data.

[0030] S4, feature extraction: Use the variational autoencoder to process and refine the vehicle behavior data obtained in S3 to obtain a high-dimensional feature vector of the vehicle; the goal of feature extraction is to provide a richer and more useful feature representation for behavior pattern recognition and analysis by deeply learning and understanding the deep-level characteristics of vehicle behavior. The variational autoencoder consists of two parts: the encoder and the decoder. The encoder is composed of a neural network composed of multiple layers of fully connected layers. Convert to latent variables , output the mean of the latent variable and variance ,The structure of the decoder is symmetrical with that of the encoder. The decoder is based on latent variables Reconstructing input data , where the latent variable output by the encoder is The posterior distribution of is set to Gaussian distribution: ,in and The neural network is based on the input Calculate the mean and variance of the latent variable The prior distribution of is set to the standard normal distribution: ; The decoder is based on latent variables Reconstructing input data The distribution of ,in and is the mean and variance of the decoder output; the goal of the variational autoencoder (VAE) is to maximize the lower bound of evidence, and its loss function consists of two parts: , where the first item is the reconstruction error, which reflects the quality of the reconstructed data; the second item is the KL divergence, which measures the difference between the encoded latent variable distribution and its prior distribution. Through the above steps, not only can the complex characteristics of vehicle behavior be effectively extracted, but also the recognition and prediction of behavior patterns can be enhanced through the learned latent variables, providing an accurate analysis basis for the marketing recommendation system. S5. Vehicle activity analysis: For the high-dimensional feature vector of the vehicle, a neural network-based regression model is trained to calculate the activity score, the K-means clustering algorithm is used to identify different behavior patterns, and the autoregressive integrated moving average model (ARIMA) is used to predict the time trend of vehicle activity; specifically:

[0031] S51, activity index calculation: The input data is the high-dimensional feature vector of the vehicle obtained from step S4. These vectors contain information about the vehicle speed, route, dwell time, etc. For the high-dimensional feature vector, this embodiment trains a regression model based on a neural network to calculate the activity index. The first The hidden layer is expressed as: ,in , and They are The weight matrix and bias vector of the layer, is the ReLU activation function, and the regression model outputs the predicted activity score ,in is the number of hidden layers;

[0032] S52, Behavior pattern recognition: For the extracted high-dimensional feature vectors, the K-means clustering algorithm is applied to identify different behavior patterns. The goal of this clustering algorithm is to minimize the intra-cluster variance: ,in is the number of clusters, It is The set of samples in the clusters, It is a cluster The center can annotate and analyze vehicle behavior patterns based on clustering results, identify vehicle groups active at specific times or vehicles that frequently visit a certain location, and make targeted marketing recommendations for vehicles with different behavior patterns.

[0033] S53, Trend Analysis and Forecasting: Arrange the obtained high-dimensional feature vectors of each vehicle node in chronological order, construct a time series data set, and use the Autoregressive Integrated Moving Average Model (ARIMA) to predict the time trend of vehicle activity: ,in is the order of the autoregressive term, is the difference order, is the order of the sliding average term, is the lag operator, It's time The observed value of is the error term. Through the autoregressive integrated moving average model, future trend forecasts can be effectively made from high-dimensional time series data. These forecast results provide support for more accurate marketing strategy formulation.

[0034] S5. Vehicle activity analysis: For the high-dimensional feature vector of the vehicle, a neural network-based regression model is trained to calculate the activity score, the K-means clustering algorithm is used to identify different behavior patterns, and the autoregressive integrated moving average model (ARIMA) is used to predict the time trend of vehicle activity; specifically:

[0035] S51, activity index calculation: The input data is the high-dimensional feature vector of the vehicle obtained from step S4. These vectors contain information about the vehicle speed, route, dwell time, etc. For the high-dimensional feature vector, this embodiment trains a regression model based on a neural network to calculate the activity index. The first The hidden layer is expressed as: ,in , and They are The weight matrix and bias vector of the layer, is the ReLU activation function, and the regression model outputs the predicted activity score ,in is the number of hidden layers;

[0036] S52, Behavior pattern recognition: For the extracted high-dimensional feature vectors, the K-means clustering algorithm is applied to identify different behavior patterns. The goal of this clustering algorithm is to minimize the intra-cluster variance: ,in is the number of clusters, It is The set of samples in the clusters, It is a cluster The center can annotate and analyze vehicle behavior patterns based on clustering results, identify vehicle groups active at specific times or vehicles that frequently visit a certain location, and make targeted marketing recommendations for vehicles with different behavior patterns.

[0037] S53, Trend Analysis and Forecasting: Arrange the obtained high-dimensional feature vectors of each vehicle node in chronological order, construct a time series data set, and use the Autoregressive Integrated Moving Average Model (ARIMA) to predict the time trend of vehicle activity: ,in is the order of the autoregressive term, is the difference order, is the order of the sliding average term, is the lag operator, It's time The observed value of is the error term. Through the autoregressive integrated moving average model, future trend predictions can be effectively made from high-dimensional time series data. These prediction results provide support for more accurate marketing strategy formulation. S5. Vehicle activity analysis: For the high-dimensional feature vector of the vehicle, a neural network-based regression model is trained to calculate the activity score, the K-means clustering algorithm is used to identify different behavior patterns, and the autoregressive integrated moving average model (ARIMA) is used to predict the time trend of vehicle activity; specifically:

[0038] S51, activity index calculation: The input data is the high-dimensional feature vector of the vehicle obtained from step S4. These vectors contain information about the vehicle speed, route, dwell time, etc. For the high-dimensional feature vector, this embodiment trains a regression model based on a neural network to calculate the activity index. The first The hidden layer is expressed as: ,in , and They are The weight matrix and bias vector of the layer, is the ReLU activation function, and the regression model outputs the predicted activity score ,in is the number of hidden layers;

[0039] S52, Behavior pattern recognition: For the extracted high-dimensional feature vectors, the K-means clustering algorithm is applied to identify different behavior patterns. The goal of this clustering algorithm is to minimize the intra-cluster variance: ,in is the number of clusters, It is The set of samples in the clusters, It is a cluster The center can annotate and analyze vehicle behavior patterns based on clustering results, identify vehicle groups active at specific times or vehicles that frequently visit a certain location, and make targeted marketing recommendations for vehicles with different behavior patterns.

[0040] S53, Trend Analysis and Forecasting: Arrange the obtained high-dimensional feature vectors of each vehicle node in chronological order, construct a time series data set, and use the Autoregressive Integrated Moving Average Model (ARIMA) to predict the time trend of vehicle activity: ,in is the order of the autoregressive term, is the difference order, is the order of the sliding average term, is the lag operator, It's time The observed value of is the error term. Through the autoregressive integrated moving average model, future trend forecasts can be effectively made from high-dimensional time series data. These forecast results provide support for more accurate marketing strategy formulation.

[0041] S6. Marketing strategy generation: Based on the activity scores, behavior patterns and trend predictions obtained in step S5, identify the target customer groups with the greatest potential, and design customized marketing strategies for different vehicle groups. For example, loyalty rewards or discount promotions can be offered to vehicle groups with high activity and high visit frequency; time-specific discounts can be provided to vehicle groups that are mainly active during specific time periods; discounts for specific service areas can be provided to drivers who frequently visit specific service areas; relevant marketing advertisements and user services can be pushed to users in advance based on predictions of future trends and behavior patterns of vehicles; finally, A / B tests can be conducted on different marketing strategies to evaluate which strategies are most effective, and adjustments and optimizations can be made accordingly.

[0042] The algorithms, network structures, and expressions not described or explained in detail in this document are general technologies or meanings in the art.

[0043] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0044] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A spatiotemporal vehicle activity analysis and marketing recommendation method, characterized in that: The specific steps include: S1. Vehicle data collection: Collect vehicle data collected by GPS trackers, traffic monitoring equipment, mobile applications or sensors, and perform data cleaning and data standardization on the vehicle data; S2. Graph data modeling: Vehicles are represented as nodes in a graph, and the interactions or behavioral similarities between vehicles are represented as edges in the graph for graph data modeling; S3. Graph model construction: Build a graph model based on the graph convolutional network. The graph convolutional network processes node features, learns the dependencies between nodes, and obtains vehicle behavior data. S4, feature extraction: Use the variational autoencoder to process and refine the vehicle behavior data obtained in S3 to obtain a high-dimensional feature vector of the vehicle; specifically, the variational autoencoder includes an encoder and a decoder. The encoder is composed of a neural network composed of multiple layers of fully connected layers. Convert to latent variables , output the mean of the latent variable and variance ,The structure of the decoder is symmetrical with that of the encoder. The decoder is based on latent variables Reconstructing input data , where the latent variable output by the encoder is The posterior distribution of is set to Gaussian distribution: ,in and The neural network is based on the input Calculate the mean and variance of the latent variable The prior distribution of is set to the standard normal distribution: ; The decoder is based on latent variables Reconstructing input data The distribution of ,in and are the mean and variance of the decoder output; The goal of the variational autoencoder is to maximize the lower bound of evidence, and its loss function consists of two parts: , where the first term is the reconstruction error, reflecting the quality of the reconstructed data; The second term is the KL divergence, which measures the difference between the encoded latent variable distribution and its prior distribution, thereby obtaining a high-dimensional feature vector for the vehicle; S5. Vehicle activity analysis: For the high-dimensional feature vector of the vehicle, a neural network-based regression model is trained to calculate the activity score, the K-means clustering algorithm is used to identify different behavior patterns, and the autoregressive integral moving average model is used to predict the time trend of vehicle activity; S6. Marketing strategy generation: Based on the activity scores, behavior patterns, and trend forecasts obtained in step S5, identify the target customer groups with the greatest potential, design customized marketing strategies for different vehicle groups, conduct A / B tests on different marketing strategies to evaluate which strategies are most effective, and make adjustments and optimizations accordingly.

2. The method for spatiotemporal vehicle activity analysis and marketing recommendation according to claim 1, characterized in that: The vehicle data in step S1 includes geographic location coordinates, timestamps, driving speed, frequent stop locations, and traffic condition data. Data cleaning includes removing noise and outliers and processing missing values. Data standardization includes time synchronization and space standardization.

3. The method for analyzing spatiotemporal vehicle activity and marketing recommendation according to claim 2, characterized in that: The node definition in step S2 is: each node Represents a vehicle entity, the feature vector of the node It is composed of the vehicle data processed in step S1, which includes the vehicle's driving speed, current location, and historical location. The definition of edge is: Representative vehicle and The relationship between them is based on geographical distance, route intersection, time overlap, and edge weights. Determined based on the mutual proximity between vehicles, using a Gaussian kernel to measure: ,in It is a vehicle and The distance between is the standard deviation of the Gaussian kernel, which is used to control the decay rate of the weights.

4. The method for analyzing spatiotemporal vehicle activity and marketing recommendation according to claim 3 is characterized in that: Step S3: The graph convolutional network updates the feature representation of the node through the features of the neighboring nodes. The new features after each convolution Calculated by the following formula: ,in, is the set of neighbor nodes of node i, and It is The weight matrix and bias vector of the layer, is a nonlinear activation function, is a normalization constant representing the number of neighbors, Neighbor node After the graph convolution operation, the maximum aggregation function is used to update the features of each node by summarizing the information of neighboring nodes, capturing the spatial relationship between nodes, and thus obtaining vehicle behavior data.

5. The method for spatiotemporal vehicle activity analysis and marketing recommendation according to claim 4, characterized in that: Step S5: the first step of the neural network-based regression model The hidden layer is expressed as: ,in , and They are The weight matrix and bias vector of the layer, is the ReLU activation function, and the regression model outputs the predicted activity score ,in is the number of hidden layers.

6. The method for spatiotemporal vehicle activity analysis and marketing recommendation according to claim 5, characterized in that: The goal of the K-means clustering algorithm in step S5 is to minimize the intra-cluster variance: ,in is the number of clusters, It is The set of samples in the clusters, It is a cluster The center of the clustering process annotates and analyzes vehicle behavior patterns based on clustering results to identify groups of vehicles active at specific times or vehicles that frequently visit a certain location.

7. The method for spatiotemporal vehicle activity analysis and marketing recommendation according to claim 6, characterized in that: When the autoregressive integrated moving average model is used to predict the time trend of vehicle activity in step S5, the high-dimensional feature vectors of each vehicle node are first arranged in chronological order to construct a time series data set. The prediction result is: ,in is the order of the autoregressive term, is the difference order, is the order of the sliding average term, is the lag operator, It's time The observed value of is the error term, and future trend prediction is performed from high-dimensional time series data through the autoregressive integrated moving average model.

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