The Network Approach For Time Series Analysis And Its Applications

Nonlinear time series analysis has been an important branch in the field of non-linear dynamics,which is of great theoretical and application significance in science,engineering,finance and economics,as well as life and medical science,etc.In re-cent years,complex network theory has flourished in the field of nonlinear time series analysis.The main idea of this method is to map the time series into the complex networks and then use the topological structure of complex networks to analyze the properties of the nonlinear time series.Nowadays,although several algorithms which mapping time series to complex networks have successfully made many applications,the research areas are still in the early stage,where there are many issues about fun-damental theories waiting to be solved.Therefore,in this thesis,we propose several new algorithms to map time series into complex networks and carry out systematic research from three aspects of theory,simulation and application.The organization of this thesis is as follows.In Chapter 1 we introduce the penetrable parameter p and present exact result-s on the topological properties of the limited penetrable horizontal visibility graph[LPHVG(p)]associated with independent and identically distributed(i.i.d)random series.We show that the i.i.d.random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution,independent of the probability distribution from which the series was generated.We deduce the exact expression-s of mean degree and clustering coefficient,demonstrate the long distance visibility property of the graph and perform numerical simulations to test the accuracy of our theoretical results.We then use the algorithm in several deterministic chaotic series,such as the logistic map,Henon map,Lorenz system,energy price chaotic system and the real crude oil price.Our results show that the limited penetrable horizontal visi-bility algorithm is efficient to discriminate chaos from uncorrelated randomness and is able to measure the global evolution characteristics of the real time series.In Chapter 2 we introduce the concept of sequential LPHVG(?)motifs and present a theoretical way of computing the exact motif profiles associated with dif-ferent types of real-value series.We perform several numerical simulations to further check the accuracy of our theoretical results.Finally we use the analytical results of LPHVG(p)motif profiles to distinguish among random,periodic,and chaotic signals and find that the frequency of the type-I motif captures sufficient information to easily distinguish among different processes.In Chapter 3 we define the algorithm and provide theoretical results on the topological properties of the directed limited penetrable horizontal visibility graph[DLPHVG(p)].We perform several numerical simulations to further check the ac-curacy of our theoretical results.Finally,we present an application for measuring real-value time series irreversibility.In Chapter 4 we extend LPHVG(p)and create an image limited penetrable hori-zontal visibility graph[ILPHVG(p)].We define the algorithm and provide theoretical results on the topological properties of this graph.And then we present an applica-tion to discriminate noise from chaos.We also propose a new method to measure the systematic risk using the image limited penetrable horizontal visibility graph.The empirical results show the effectiveness of our proposed algorithms.In Chapter 5 we present a simple and fast computational method,the phase space coarse graining algorithm that converts a time series into a directed and weighted complex network.The constructed directed and weighted complex network inherits several properties of the series in its structure.Thereby,periodic series convert into regular networks,and random series do so into random networks.Moreover,chaotic series convert into scale-free networks.It is shown that the phase space coarse grain-ing algorithm allows us to distinguish,identify and describe in detail various time series.Finally,we apply the phase space coarse graining algorithm to the practical observations series,international gasoline regular spot price series and identify its dynamic characteristics.In Chapter 6 we propose a novel hybrid method that uses an integrated data fluctuation network(DFN)and several artificial intelligence(AI)algorithms,named DFN-AI model.In the proposed DFN-AI model,a complex network time series anal-ysis technique is performed as a preprocessor for the original data to extract the fluc-tuation features and reconstruct the original data,and then an artificial intelligence tool,e.g.,BPNN,RBFNN or ELM,is employed to model the reconstructed data and predict the future data.To verify these results we examine the daily,weekly,and monthly price data from the crude oil trading hub in Cushing,Oklahoma.Empirical results demonstrate that the proposed DFN-AI models(i.e.,DFN-BP,DFN-RBF,and DFN-ELM)perform significantly better than their corresponding single AI models in both the direction and level of prediction.This confirms the effectiveness of our proposed modeling of the nonlinear patterns hidden in crude oil prices.In addition,our proposed DFN-AI methods are robust and reliable and are unaffected by random sample selection,sample frequency,or breaks in sample structure.