The Study Of Forecasting Time Series Based On Visibility Graph

As one of the data form,time series is a sequence of data ordered chronologically.By analyzing the inner attributes of time series,we are not only able to obtain valuable information,but also forecast the possible development of time series in the future.Both in scientific and engineering fields that use temporal measurements,time series is wildly applied,such as astronomy,control engineering,communication engineering and so on.Since time series records data at different time points,the first and primary part of time series study is to analyze data.Data analysis is aimed at extracting the structural features of time series in order to explain the essential properties of time series and its generation process.On the base of correct data analysis,the goal for time series study is the establishment of a proper model to forecast time series.Afterwards,according to distinctive data sources,the model is applied to corresponding areas,such as production forecast,budget analysis,process control and quality evaluation.With the development of Internet,time series is closely linked with networks.In particular,Lacasa proposed visibility algorithm which is able to convert time series into a graph efficiently.To be specific,time series in the visibility graph is no more simple data,instead,it becomes a network with edges and nodes.In this way,the related theories and techniques of complex networks are able to play a role in the study of time series,which makes study of time series based on visibility graph a new research topic.On the other hand,problems about how to make predictions in networks have been solved appropriately.One solution proposed by Linyuan Lv utilized network architecture and nodes to define node similarity so as to represent the possibility that a new edge will be generated between two nodes.This kind of strategy provides great convenience for make predictions in visibility graph.Nevertheless,due to the existence of uncertainty,inaccurate estimations happen inevitably,which leads to various loss.When handling uncertainty,not only data itself should be taken into consideration,but factors such as model selection and parameter estimation should also be referred.Inspired by fuzzy logic,uncertainty can be described by memberships of fuzzy variables and fuzzy sets,and processed by making fuzzy rules in different situations.Hence,people can flexibly deal with uncertainty in different data under different models.In this case,if fuzzy logic is applied to time series,it is potential to improve the performance of forecasting model.To address the issues above,this paper is a study of analyzing and forecasting time series,and discusses time series modeling in visibility graph as well as uncertainty processing.The main results are detailed in the following three aspects.1.Fuzzy forecasting model of time series based on visibility graph.In visibility graph,the last known node is chosen to calculate the similarity between other nodes.Then,the node with highest similarity,together with the last known node,is used to determine the time series at next time point,which is considered as an initial result.Furthermore,fuzzy sets and fuzzy rules are designed based on the level of visibility of the node with highest similarity,so that the weights of revision part can be determined.Finally,the initial result is revised.2.Experiments and analysis of fuzzy forecasting model.The proposed fuzzy forecasting model is applied to predict three different data sets,including cost index,stock price and enrollment numbers,in the way of both one-step-ahead and multi-step-ahead forecasting.According to the analysis and comparisons of results,the validity and efficiency are demonstrated.3.Random forecasting model of time series based on visibility graph.Aimed at handling the shortcomings in fuzzy forecasting model,a random forecasting model with the framework of Bayesian MCMC is proposed.This model uses MCMC sampling method to avoid the subjective factors when designing fuzzy logic,and also utilizes Bayesian inference to present the uncertainties.Then,the model is applied to forecast CCI as a simple testing case in order to illustrate the predictability.Besides,the follow-up optimization and improvement of this model is discussed.