CN113781777A - Traffic accident number prediction method and system based on multivariate time series model - Google Patents

Traffic accident number prediction method and system based on multivariate time series model Download PDF

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CN113781777A
CN113781777A CN202111009422.1A CN202111009422A CN113781777A CN 113781777 A CN113781777 A CN 113781777A CN 202111009422 A CN202111009422 A CN 202111009422A CN 113781777 A CN113781777 A CN 113781777A
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丰明洁
王雪松
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Tongji University
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    • GPHYSICS
    • G08SIGNALLING
    • G08GTRAFFIC CONTROL SYSTEMS
    • G08G1/00Traffic control systems for road vehicles
    • G08G1/01Detecting movement of traffic to be counted or controlled
    • G08G1/0104Measuring and analyzing of parameters relative to traffic conditions
    • GPHYSICS
    • G08SIGNALLING
    • G08GTRAFFIC CONTROL SYSTEMS
    • G08G1/00Traffic control systems for road vehicles
    • G08G1/01Detecting movement of traffic to be counted or controlled
    • G08G1/0104Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125Traffic data processing
    • GPHYSICS
    • G08SIGNALLING
    • G08GTRAFFIC CONTROL SYSTEMS
    • G08G1/00Traffic control systems for road vehicles
    • G08G1/01Detecting movement of traffic to be counted or controlled
    • G08G1/0104Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125Traffic data processing
    • G08G1/0129Traffic data processing for creating historical data or processing based on historical data
    • GPHYSICS
    • G08SIGNALLING
    • G08GTRAFFIC CONTROL SYSTEMS
    • G08G1/00Traffic control systems for road vehicles
    • G08G1/01Detecting movement of traffic to be counted or controlled
    • G08G1/0104Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0137Measuring and analyzing of parameters relative to traffic conditions for specific applications

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Abstract

The invention relates to a traffic accident number prediction method and a traffic accident number prediction system based on a multivariate time series model, wherein the accident prediction method comprises the following steps: step 1: acquiring road traffic accident data, traffic violation data, traffic enforcement data, holiday data and weather data; step 2: constructing a sample data set; and step 3: establishing an accident prediction model based on a vector autoregressive model; and 4, step 4: inputting holiday conditions and weather conditions of a plurality of days needing to predict the number of traffic accidents into an accident prediction model, and predicting the number of traffic accidents each day of the plurality of days. Compared with the prior art, the method has the advantages of more accurate and reliable prediction result, contribution to improving the effective utilization rate of traffic law enforcement resources and the like.

Description

Traffic accident number prediction method and system based on multivariate time series model
Technical Field
The invention relates to the technical field of traffic management, in particular to a traffic accident number prediction method and system based on a multivariate time series model.
Background
According to the world health organization statistics, the rank of 2016 road traffic casualties among global causes of human death has risen to the eighth, demonstrating the importance and urgency of strengthening road traffic safety management. Traffic enforcement activities are important means for managing road traffic safety of related departments, and manual enforcement is an important measure for traffic enforcement activities for a long time. With the progress of traffic enforcement tools, electronic traffic enforcement equipment such as electronic police is gradually put into use, and road traffic safety management steps into a stage of both manual law enforcement and electronic police law enforcement. Accurate prediction of the future road traffic safety level is a precondition for reasonable deployment of traffic law enforcement resources, and is beneficial to realizing efficient management of road traffic safety. Therefore, road traffic accident prediction is one of important contents in the fields of traffic safety management and road safety assessment.
At present, traffic enforcement measures are organized by relevant government departments, are oriented to vehicle drivers, are developed on roads, and have important influence on driver behaviors and road traffic safety. Research shows that traffic police law enforcement, vehicle driver's law violation and traffic accidents are endogenous and mutually influenced. For example, the following steps are carried out: the traffic accident and the traffic violation of one street are simultaneously highly issued, on one hand, the traffic accident is highly issued due to the fact that the illegal behaviors of drivers are increased, on the other hand, the traffic policeman strengthens the law enforcement force on the region due to the fact that the traffic accident is highly issued, and therefore the traffic violation amount is increased. Therefore, the influence of traffic law violation and traffic law enforcement cannot be ignored when the number of traffic accidents needs to be accurately predicted. And the traditional traffic accident prediction model based on the time sequence is usually only based on historical accident data, and the accuracy is not high.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a traffic accident number prediction method and system based on a multivariate time series model, which have more accurate and reliable prediction results and are beneficial to improving the effective utilization rate of traffic law enforcement resources.
The purpose of the invention can be realized by the following technical scheme:
a traffic accident number prediction method based on a multivariate time series model comprises the following steps:
step 1: acquiring road traffic accident data, traffic violation data, traffic enforcement data, holiday data and weather data;
step 2: constructing a sample data set;
and step 3: establishing an accident prediction model based on a vector autoregressive model;
and 4, step 4: inputting holiday conditions and weather conditions of a plurality of days needing to predict the number of traffic accidents into an accident prediction model, and predicting the number of traffic accidents each day of the plurality of days.
Preferably, the data acquisition method in step 1 is as follows:
road traffic accident data, traffic violation data and traffic law enforcement data are obtained by a traffic management department, the traffic violation data are divided into field traffic violation data and non-field traffic violation data, the former is obtained by a traffic police, and the latter is obtained by an electronic police; acquiring holiday data through a calendar, and acquiring weather data through a weather recording website.
Preferably, the step 2 specifically comprises:
gathering the data acquired in the step 1 to a day level to obtain the number of traffic accidents, the number of field traffic violations, the number of off-field traffic violations, the law enforcement duration of traffic policemen, holidays and weather of each day;
setting the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices as endogenous variables; setting the holiday conditions and the weather conditions as exogenous variables, and constructing a sample data set.
Preferably, the step 3 specifically comprises:
step 3-1: performing structural decomposition on the time sequence of the endogenous variable;
step 3-2: selecting an optimal order of the vector autoregressive model;
step 3-3: and establishing a vector autoregressive model, namely an accident prediction model, based on the optimal order.
More preferably, the step 3-1 specifically comprises:
and carrying out structural decomposition on the time sequence of the number of the traffic accidents, the number of the field traffic violations, the number of the off-site traffic violations and the law enforcement duration of the traffic police to obtain the structural composition of each endogenous variable.
More preferably, the step 3-2 is specifically:
the number of traffic accidents, the number of field traffic violations, the number of non-field traffic violations and the law enforcement duration of traffic polices are used as endogenous variables, holiday conditions and weather conditions are used as exogenous variables, a vector autoregressive model with the order from 1 to 14 is established, and the order which enables the red pond information criterion of the model to be the lowest is selected as the optimal order.
More preferably, the step 3-3 is specifically:
assuming that the optimal order is p, the total days of the sample data set is T, the number of traffic accidents, the number of field traffic violations, the number of off-field traffic violations and the traffic police law enforcement duration are endogenous variables, holidays and weather are exogenous variables, and constructing a vector autoregressive model as follows:
yt=Aθt+B1yt-1+…+Bpyt-p+Cxtt t=1,2,…,T
wherein, ytThe traffic accident number, the onsite traffic violation number, the offsite traffic violation number and the traffic police law enforcement duration on the t day form a vector; y ist-pIs ytP-order lag of (1); thetatThe time sequence composition structure of the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices; a is a coefficient corresponding to the composition structure; b ispIs a coefficient corresponding to an endogenous variable p-order lag; x is the number oftIs the vector of the holiday and weather components of the exogenous variable, C is the coefficient of the exogenous variable, εtAre residual terms.
A traffic accident number prediction system based on a multivariate time series model for use in the traffic accident prediction method, wherein the accident prediction system comprises a processor; the processor is provided with:
the data acquisition module is used for acquiring holiday conditions and weather conditions of a plurality of days for which the number of traffic accidents needs to be predicted;
and the accident prediction module is provided with an accident prediction model and used for predicting the number of traffic accidents per day according to the data acquired by the data acquisition module.
Preferably, the construction method of the accident prediction model comprises the following steps:
firstly, carrying out structural decomposition on a time sequence of an endogenous variable;
secondly, selecting an optimal order of the vector autoregressive model;
and finally, establishing a vector autoregressive model, namely an accident prediction model, based on the optimal order.
More preferably, the method for establishing the vector autoregressive model based on the optimal order comprises the following steps:
assuming that the optimal order is p, the total days of the sample data set is T, the number of traffic accidents, the number of field traffic violations, the number of off-field traffic violations and the traffic police law enforcement duration are endogenous variables, holidays and weather are exogenous variables, and constructing a vector autoregressive model as follows:
yt=Aθt+B1yt-1+…+Bpyt-p+Cxtt t=1,2,…,T
wherein, ytThe traffic accident number, the onsite traffic violation number, the offsite traffic violation number and the traffic police law enforcement duration on the t day form a vector; y ist-pIs ytP-order lag of (1); thetatThe time sequence composition structure of the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices; a is a coefficient corresponding to the composition structure; b ispIs a coefficient corresponding to an endogenous variable p-order lag; x is the number oftIs the vector of the holiday and weather components of the exogenous variable, C is the coefficient of the exogenous variable, εtAre residual terms.
Compared with the prior art, the invention has the following beneficial effects:
firstly, the prediction result is more accurate and reliable: when the traffic accident number prediction method and the system are used for predicting the traffic accident number, the influence of traffic violation, traffic enforcement, holidays and weather on accidents is brought into the prediction model, and compared with the traffic accident prediction model based on historical accident data only, the prediction result is more accurate and reliable.
Secondly, the effective utilization rate of traffic law enforcement resources is improved: the traffic accident number prediction method and the system thereof in the invention carry out the prediction of the traffic accident number on the day level, and the prediction result is beneficial to supporting the relevant traffic safety management departments to customize the road traffic safety management strategy so as to efficiently utilize the limited traffic law enforcement resources.
Drawings
FIG. 1 is a schematic flow chart illustrating a traffic accident number prediction method according to the present invention;
FIG. 2 is a diagram illustrating a fitting condition of an autoregressive model to a traffic accident number in a sample data set according to an embodiment of the present invention;
fig. 3 is a schematic diagram of traffic accident prediction obtained from holiday conditions and weather conditions 8 days after the sample data set is input in the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of the present invention.
A traffic accident number prediction method based on a multivariate time series model is disclosed, the flow of which is shown in figure 1, and the method comprises the following steps:
step 1: acquiring road traffic accident data, traffic violation data, traffic enforcement data, holiday data and weather data; the traffic accident data, the traffic violation data and the traffic police law enforcement data are obtained by a traffic management department, wherein the traffic violation data are divided into field traffic violation data and non-field traffic violation data, the former is obtained by a traffic police, and the latter is obtained by an electronic police. Acquiring holiday data through a calendar, and acquiring weather data through a weather recording website;
step 2: constructing a sample data set;
gathering the data acquired in the step 1 to a day level to obtain the number of traffic accidents, the number of field traffic violations, the number of off-field traffic violations, the law enforcement duration of traffic policemen, holidays and weather of each day;
setting the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices as endogenous variables; setting holiday conditions and weather conditions as exogenous variables, and constructing a sample data set;
and step 3: establishing an accident prediction model based on a vector autoregressive model;
step 3-1: performing structural decomposition on the time sequence of the endogenous variable;
the time sequence data generally comprises long-term trend, seasonal variation, cyclic fluctuation and irregular fluctuation, and the time sequence of the number of traffic accidents, the number of field traffic violations, the number of non-field traffic violations and the time length of the law enforcement of the traffic police is subjected to structural decomposition to obtain the structural composition of each endogenous variable;
step 3-2: selecting an optimal order of the vector autoregressive model;
taking the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices as endogenous variables, taking holiday conditions and weather conditions as exogenous variables, establishing a vector autoregressive model with the order from 1 to 14, and selecting the order which enables the lowest order of a model red pond Information Criterion (AIC) as an optimal order;
step 3-3: establishing a vector autoregressive model, namely an accident prediction model, based on the optimal order;
assuming that the optimal order is p, the total days of the sample data set is T, the number of traffic accidents, the number of field traffic violations, the number of off-field traffic violations and the traffic police law enforcement duration are endogenous variables, holidays and weather are exogenous variables, and constructing a vector autoregressive model as follows:
Figure BDA0003238345040000051
t=1,2,…,T
wherein y iscrash,t、yTecVio,t、yPolVio,tAnd yenfor,tThe number of traffic accidents, the number of onsite traffic violations, the number of offsite traffic violations and the length of time for enforcement of the traffic police on the t day; y iscrash,t-p、yTecVio,t-p、yPolVio,t-pAnd yenfor,t-pRespectively the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the p-order lag of the time length of law enforcement of traffic polices;θcrash,t、θTecVio,t、θPolVio,tand thetaenfor,tThe time sequence composition structure of the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices; a is a coefficient corresponding to the composition structure; b ispIs a coefficient corresponding to a p-order lag; x is the number ofholiday,tAnd xwhether,tThe holiday and weather conditions on day t, respectively, C is the coefficient of the exogenous variable, εtAre residual terms.
The above equation can be simplified as:
yt=Aθt+B1yt-1+…+Bpyt-p+Cxtt t=1,2,…,T
wherein, ytThe traffic accident number, the onsite traffic violation number, the offsite traffic violation number and the traffic police law enforcement duration on the t day form a vector; y ist-pIs ytP-order lag of (1); thetatThe time sequence composition structure of the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices; a is a coefficient corresponding to the composition structure; b ispIs a coefficient corresponding to an endogenous variable p-order lag; x is the number oftIs the vector of the holiday and weather components of the exogenous variable, C is the coefficient of the exogenous variable, εtAre residual terms.
And 4, step 4: inputting holiday conditions and weather conditions of a plurality of days needing to predict the number of traffic accidents into an accident prediction model, and predicting the number of traffic accidents each day of the plurality of days.
The embodiment also relates to a traffic accident number prediction system for the traffic accident number prediction method, which comprises a processor.
The processor is provided with:
the data acquisition module is used for acquiring holiday conditions and weather conditions of a plurality of days for which the number of traffic accidents needs to be predicted;
and the accident prediction module is provided with an accident prediction model and used for predicting the number of traffic accidents per day according to the data acquired by the data acquisition module.
Therefore, the construction method of the prediction model comprises the following steps:
firstly, carrying out structural decomposition on a time sequence of an endogenous variable;
secondly, selecting an optimal order of the vector autoregressive model;
and finally, establishing a vector autoregressive model, namely an accident prediction model, based on the optimal order.
The method for establishing the vector autoregressive model based on the optimal order comprises the following steps:
assuming that the optimal order is p, the total days of the sample data set is T, the number of traffic accidents, the number of field traffic violations, the number of off-field traffic violations and the traffic police law enforcement duration are endogenous variables, holidays and weather are exogenous variables, and constructing a vector autoregressive model as follows:
yt=Aθt+B1yt-1+…+Bpyt-p+Cxtt t=1,2,…,T
wherein, ytThe traffic accident number, the onsite traffic violation number, the offsite traffic violation number and the traffic police law enforcement duration on the t day form a vector; y ist-pIs ytP-order lag of (1); thetatThe time sequence composition structure of the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices; a is a coefficient corresponding to the composition structure; b ispIs a coefficient corresponding to an endogenous variable p-order lag; x is the number oftIs the vector of the holiday and weather components of the exogenous variable, C is the coefficient of the exogenous variable, εtAre residual terms.
The following provides a specific application case:
aiming at a highway network in a certain city, the invention is tested by utilizing traffic accident data, traffic violation data, traffic police law enforcement duration data recorded by a traffic management department, and holiday data and weather data recorded by the network.
According to the steps 1 and 2 of the invention, traffic accident data, traffic violation data, traffic police law enforcement duration data, holiday data and weather data of a highway network in a certain city are collected. The traffic violation data is divided into on-site traffic violation data and off-site traffic violation data, wherein the on-site traffic violation data is obtained by a traffic police, and the off-site traffic violation data is obtained by an electronic police. And (3) aggregating the data to a day level to obtain the number of traffic accidents, the number of field violations, the number of non-field violations, the length of time for traffic police to enforce law, the conditions of holidays and weather conditions of each day, thereby forming a sample data set, wherein the total number of 365 days. The number of traffic accidents, the number of field violations, the number of off-site violations and the time length of law enforcement of traffic police are time series data and are set as endogenous variables; holidays and weather are not affected by other variables and are exogenous variables.
Based on the sample data set, according to the step 3-1 of the invention, the time series of the number of traffic accidents, the number of field violations, the number of non-field violations and the time length of the law enforcement of the traffic police are subjected to structural decomposition, and the composition structures of the four variables are found to include long-term trends and week cycle fluctuations. According to the step 3-2 of the invention, the number of traffic accidents, the number of field traffic violations, the number of non-field traffic violations and the law enforcement duration of traffic policemen are used as endogenous variables, holidays and weather are used as exogenous variables, a vector autoregressive model with the order from 1 to 14 is established, the red pool information criterion of the model is found to be the lowest when the order is 3, and the order 3 is selected as the optimal order. According to step 3-3 of the present invention, a vector autoregressive model with order 3 is built, as shown in Table 1. Based on the model, the number of traffic accidents can be predicted, and the fitting condition of the model to the number of traffic accidents in the sample data set is shown in fig. 2, wherein a black thin straight line is the actual number of traffic accidents, and a black thick dotted line is a traffic accident number fitting value generated by a vector autoregressive model. According to fig. 2, the traffic accident prediction method based on the vector self-regression model exhibits very high fitting accuracy to the number of traffic accidents.
TABLE 1 autoregressive model
Figure BDA0003238345040000071
According to step 4 of the present invention, the holiday conditions and weather conditions 8 days after the sample data set is input, and the number of traffic accidents in the 8 days is predicted, as shown in fig. 3, wherein the black thick dotted line is the predicted value of the number of traffic accidents, and the black thin dotted line is the upper and lower bounds of the predicted value. Fig. 3 illustrates the feasibility of the traffic accident number prediction method based on the vector autoregressive model.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. A traffic accident number prediction method based on a multivariate time series model is characterized by comprising the following steps:
step 1: acquiring road traffic accident data, traffic violation data, traffic enforcement data, holiday data and weather data;
step 2: constructing a sample data set;
and step 3: establishing an accident prediction model based on a vector autoregressive model;
and 4, step 4: inputting holiday conditions and weather conditions of a plurality of days needing to predict the number of traffic accidents into an accident prediction model, and predicting the number of traffic accidents each day of the plurality of days.
2. The method for predicting the number of traffic accidents based on the multivariate time series model as claimed in claim 1, wherein the data acquisition method in the step 1 comprises the following steps:
the road traffic accident data, the traffic violation data and the traffic law enforcement data are obtained by a traffic management department, the traffic violation data are divided into field traffic violation data and non-field traffic violation data, the former is obtained by a traffic police, and the latter is obtained by an electronic police; acquiring holiday data through a calendar, and acquiring weather data through a weather recording website.
3. The method for predicting the number of traffic accidents based on the multivariate time series model as set forth in claim 1, wherein the step 2 specifically comprises:
gathering the data acquired in the step 1 to a day level to obtain the number of traffic accidents, the number of field traffic violations, the number of off-field traffic violations, the law enforcement duration of traffic policemen, holidays and weather of each day;
setting the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices as endogenous variables; setting the holiday conditions and the weather conditions as exogenous variables, and constructing a sample data set.
4. The method for predicting the number of traffic accidents based on the multivariate time series model as set forth in claim 1, wherein the step 3 specifically comprises:
step 3-1: performing structural decomposition on the time sequence of the endogenous variable;
step 3-2: selecting an optimal order of the vector autoregressive model;
step 3-3: and establishing a vector autoregressive model, namely an accident prediction model, based on the optimal order.
5. The method for predicting the number of traffic accidents based on the multivariate time series model as claimed in claim 4, wherein the step 3-1 comprises:
and carrying out structural decomposition on the time sequence of the number of the traffic accidents, the number of the onsite traffic violations, the number of the offsite traffic violations and the law enforcement duration of the traffic police to obtain the structural composition of each endogenous variable.
6. The method for predicting the number of traffic accidents based on the multivariate time series model as claimed in claim 4, wherein the step 3-2 comprises:
the number of traffic accidents, the number of field traffic violations, the number of non-field traffic violations and the law enforcement duration of traffic polices are used as endogenous variables, holiday conditions and weather conditions are used as exogenous variables, a vector autoregressive model with the order from 1 to 14 is established, and the order which enables the red pond information criterion of the model to be the lowest is selected as the optimal order.
7. The method for predicting the number of traffic accidents based on the multivariate time series model as claimed in claim 4, wherein the steps 3-3 are specifically as follows:
assuming that the optimal order is p, the total days of the sample data set is T, the number of traffic accidents, the number of field traffic violations, the number of off-field traffic violations and the traffic police law enforcement duration are endogenous variables, holidays and weather are exogenous variables, and constructing a vector autoregressive model as follows:
yt=Aθt+B1yt-1+…+Bpyt-p+Cxtt t=1,2,…,T
wherein, ytThe traffic accident number, the field traffic violation number, the off-site traffic violation number and the traffic police law enforcement duration on the t day form a vector; y ist-pIs ytP-order lag of (1); thetatThe time sequence composition structure of the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices; a is a coefficient corresponding to the composition structure; b ispIs a coefficient corresponding to an endogenous variable p-order lag; x is the number oftIs a vector consisting of the birth date and weather of the exogenous variable, C is the coefficient of the exogenous variable, εtAre residual terms.
8. A traffic accident number prediction system based on a multivariate time series model for use in the traffic accident prediction method according to any one of claims 1-7, wherein the accident prediction system comprises a processor; the processor is provided with:
the data acquisition module is used for acquiring holiday conditions and weather conditions of a plurality of days for which the number of traffic accidents needs to be predicted;
and the accident prediction module is provided with an accident prediction model and used for predicting the number of daily traffic accidents according to the data acquired by the data acquisition module.
9. The traffic accident number prediction system based on the multivariate time series model as claimed in claim 8, wherein the construction method of the accident prediction model comprises the following steps:
firstly, carrying out structural decomposition on a time sequence of an endogenous variable;
secondly, selecting an optimal order of the vector autoregressive model;
and finally, establishing a vector autoregressive model, namely an accident prediction model, based on the optimal order.
10. The system of claim 9, wherein the method for establishing the vector autoregressive model based on the optimal order comprises:
assuming that the optimal order is p, the total days of the sample data set is T, the number of traffic accidents, the number of field traffic violations, the number of off-field traffic violations and the traffic police law enforcement duration are endogenous variables, holidays and weather are exogenous variables, and constructing a vector autoregressive model as follows:
yt=Aθt+B1yt-1+…+Bpyt-p+Cxtt t=1,2,…,T
wherein, ytThe traffic accident number, the field traffic violation number, the off-site traffic violation number and the traffic police law enforcement duration on the t day form a vector; y ist-pIs ytP-order lag of (1); thetatThe time sequence composition structure of the number of traffic accidents, the number of field traffic violations, the number of off-site traffic violations and the law enforcement duration of traffic polices; a is a coefficient corresponding to the composition structure; b ispIs a coefficient corresponding to an endogenous variable p-order lag; x is the number oftIs a vector consisting of the birth date and weather of the exogenous variable, C is the coefficient of the exogenous variable, εtAre residual terms.
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