Time Series Forecasting Algorithm And Application Based On Visibility Graph And Evidence Theory

In recent years,with the improvement of internet technology and the performance of storage devices,a large amount of data has been derived from various complex systems.A large part of the data is measured on a time scale,and an orderly sequence of the observed values recorded in the order of time is called a time series.Analyze the sequence with times as the variable,obtain the data characteristics it contains,construct a mathematical model according to the data characteristics and change rules between historical data,and extrapolate it to the next moment to predict future moments or observations in a period value.In the existing research,time series prediction has been successfully applied in different fields,such as: communication engineering,stock price,medicine,etc.Since the structure of time series is similar to that of network,which describes the relationship between nodes and edge properties,time series can be studied through network topology.Lacasa proposed a visibility graph algorithm,which mapped the time series nodes and edges to the complex network one by one through visual rules,and the obtained network still retained the dynamic information of the original sequence.The time series expressed through the network is not just a set of linear data,but a geometric model that describes the relationship between nodes.In complex network,the link strength is used to predict the possibility of creating an edge between nodes.Inspired by the link prediction idea,the link strength between the historical node and the predicted node is explored in the complex network transformed by viewable algorithm,and the time series is predicted by the network structure.In real life,due to the difference of equipment and measurement methods,the observed values of time series appear data anomalies and fuzziness.Uncertainty is the main factor that affects the accuracy of time series prediction.The purpose of time series research is to model historical data and predict the development trend of time by using the constructed model.Time series prediction based on the analysis and modeling of uncertain data will increase the prediction error,and it will cause different degrees of loss when applied to the actual system.D-S evidence theory weakens the conditions required by traditional probability theory,expands the basic event space to its power set,and has a stronger ability to express and process uncertain information.So in the time series,the basic assignment probability is used to describe the uncertainty of the observed values,and the uncertainty of the time series is effectively dealt with by evidence theory.Therefore,this paper takes time series prediction as the research object,discusses the modeling and uncertainty processing of time series in visibility graph model,and puts forward two new time series prediction models,which mainly work in the following three aspects:1.Time series prediction model based on visibility graph and evidence theory: convert the time series into a network through a visibility graph algorithm,and use the link prediction method of node similarity in the network,that is,to calculate the similarity between the historical node and the last node in the time series Degree,the training data set obtains the first k maximum similarity related nodes,and uses the related node information and the last known node to calculate the preliminary prediction result.Calculate the degree of influence of the first k related nodes on the final prediction result through the evidence difference and time distance between the nodes,and revise the preliminary prediction value.2.Improved weighted viewable time series prediction: the network transformed by the viewable algorithm is the unauthorized network,and the uncertainty is not processed from the original data due to the interaction between nodes that are not evaluated.In view of the existing problems,a time series prediction method based on weighted viewable is proposed,which represents the weight of the edge by the reliability of evidence and the degree of nodes,and measures the interaction between time nodes,thus effectively dealing with the uncertainty.Then,according to the characteristics of time series,the farther the node is,the less indirect influence it will have on the final prediction result.The weight coefficients of the direct influence and indirect influence that cause the error of the prediction result are assigned by time distance to obtain more accurate prediction value.3.Experiment and analysis of the model: The model proposed in this paper was applied to the prediction of the number of people diagnosed with the COVID-19 in China and the United States respectively,and the experimental error comparison with other time series models showed that the model proposed in this paper could predict the development trend of the number of people diagnosed with the epidemic well.Because this model is based on the evidence theory to discuss the uncertainty,so it can be cured through to the basic probability assignment forecast Numbers and the development trend of the death toll,with other time series models to predict the experimental results of healing and deaths compared with the cure in the framework of model in this paper based on the identification and prediction is more close to the true value of the death toll.In order to verify the prediction performance of the model when the amount of data is large,we applied the model to the data set of the number of people diagnosed with COVID-19 in the United States,and compared and analyzed the error indexes of the proposed model and other prediction models used for COVID-19 prediction in the United States.The experimental results show that the proposed model has good prediction performance.