Research On Time Series Prediction Algorithm Based On Graph Model And Vector Autoregressive

The prediction of time series is a key problem in signal processing,which has been widely applied in various actual scenarios,such as the prediction of disease transmission,traffic flow,air quality,and temperature.Classical signal processing theory has played an important role in the processing and analysis of regular data,but the majority of the data collected from the real world are high-dimensional,irregular,and non-stationary.Classical signal processing methods cannot fully depict the internal temporal-spatial correlation of the high-dimensional and irregular data.Thus,how to characterize the intrinsic correlation of time series and then predict the irregular time-varying data has become a meaningful topic.In recent years,graph signal processing has emerged as a powerful tool to analyze irregular domain data by characterizing the relationship between data using nodes and edges on a graph model,and models the time series data to be predicted as time-varying graph signals on graph nodes,so as to make better use of the spatial and temporal correlation between time series data.Currently,scholars have proposed graph-based time series prediction models to fuse the temporal and spatial correlation characteristics of time series,but the mining of the correlation between data at different times and nonlinear temporal-spatial correlations between signals is still insufficient.Therefore,it is a key problem to further characterize the linear and nonlinear correlation between signals at different times and more accurately describe the evolution characteristics of data.This thesis mainly studies the prediction of time series based on the graph model and vector autoregressive model.The summary of the particular work is as follows:(1)In view of the problem that existing models and methods for predicting the time series,which do not fully consider the inherent relevance of the data,this thesis proposes a graph polynomial vector autoregression model based on least squares optimization to predict time series,which can more accurately depict the evolution characteristics of data,so as to achieve good prediction results.In this method,an irregular structure of data is modeled as a graph and the time-varying data is modeled as time-varying graph signals,to depict correlations between data.Then,the graph polynomial vector autoregressive model is used to predict the evolution process of the time series on the graph.To estimate the model parameters,a new least squares optimization problem is given that takes into account the correlation between each time before the predicted time and all prior time signals.Experimental results show that the proposed method has universality and better prediction effect compared with the existing prediction methods.(2)To address the issue that the existing prediction methods do not take into account the nonlinear temporal-spatial correlation of high-dimensional time series data that is irregular and non-stationary,this thesis introduces a graph-based vector autoregression model that employs a nonlinear expansion function to predict the time series(time-varying graph signal).Firstly,a graph and time-varying graph signals ar e modeled for the data.Secondly,two forms of nonlinear expansion functions are introduced into the time series model on a graph to characterize the nonlinear temporal-spatial correlations,which enhances the nonlinear expression ability of the prediction model for the time series.Then,by utilizing the minimum mean square error criterion,an optimization problem for estimating the parameters of nonlinear prediction model is proposed.In addition,this thesis combines the proposed nonlinear prediction model with the empirical mode decomposition algorithm,which is used to process the non-stationary time series data,to further capture the nonlinear correlation of time series in the prediction.The simulation results demonstrate that the proposed methods can more effectively describe the nonlinear temporal-spatial correlations of data,and more accurately represent the evolution characteristics of time series,so as to obtain better prediction results compared with the existing methods.