Complex Network Analysis Of Time Series And Its Applications

The time series can be used to study the interactions between system elements,which re-flect the dynamic evolution of complex systems from the microscopic perspective.The time series analysis based on complex network transforms the characteristics of time series to the topological structures of the corresponding network,which provides a new method and per-spective for the study of nonlinear time series.Based on the complex network theory,we study the dynamic characteristics and correlation structure of time series from the perspective of hor-izontal visibility graph,investor information network,and random matrix theory.In Chapter 1,we briefly introduce the background of time series analysis and complex network theory,summarize the methods for mapping the time series to complex networks,conduct the relevant literature review,and outline the research contents and innovations.In Chapter 2,the algorithm of horizontal visibility graph(HVG)maps time series into graphs and retains temporal characteristics of the original time series.We derive the degree distributions of HVGs through an iterative construction process for certain time series.The de-gree distributions of the HVG and the directed HVG for random series are indeed exponential,which confirms the analytical results from other methods in the literature.We also obtained the analytical degree distributions of HVGs and in-degree and out-degree distributions of D-HVGs transformed from multifractal binomial measures.Results from numerical simulations confirmed the analytical results.In Chapter 3,we study the profiles of tetradic motifs in horizontal visibility graphs con-verted from different types of time series.For multifractal binomial measures,the occur-rence frequencies of the tetradic motifs are determined,which converge to a constant vector(2/3.0.8/99.8/33.1/99.0).For fractional Gaussian noises,the motif occurrence frequencies are found to depend nonlinearly on the Hurst exponent and the length of time series.These find-ings suggest the potential ability of tetradic motif profiles in distinguishing fractional Gaussian noises with different correlation structures.We apply the tetradic motif analysis to heartbeat rates of healthy subjects,congestive heart failure subjects,and atrial fibrillation subjects.Dif-ferent subjects can be distinguished from the occurrence frequencies of tetradic motifsIn Chapter 4,we propose a new concept of time series motifs for time series analysis.The concept of time series motifs is different because it considers not only the spatial informa-tion(visibility)but also the temporal information(relative magnitude)between the data points under consideration.The occurrence frequencies of the six triadic time series motifs are de-rived for uncorrelated time series,which increase approximately linearly with the length of the time series.When t is sufficiently large,the motif profile converges to a constant vector f=(0.2.0.2.0.1.0.2.0.1.0.2).For fractional Gaussian noises,numerical simulations unveil the dependence of motif occurrence frequencies on the Hurst exponent.The triadic motif anal-ysis is utilized to investigate the dynamical characteristics of the individual physiological time series and financial time series.The certain motif occurrence frequency distributions are able to capture heart rate oscillations during the meditation and the fluctuations of the market index returns.We perform triadic time series motif analysis numerically for different time series gen-erated from the logistic map,the chaotic logistic map,the chaotic Henon map,the chaotic Ikeda map,the hyperchaotic generalized Henon map,and the hyperchaotic folded-tower map.The motif occurrence profile can quantify the time series characteristics in different dynamical sys-tems and show comparative classification power as the DTW method.To test the effectiveness on the similarity measure of time series,we apply the triadic motif analysis to the classification of the time series in 128 data sets from UCR Time Series Classification Archive.In Chapter 5,we construct the empirical information network of traders using the order flow data of the constituent stocks of SZSE 100 Index in 2013.A statistical validation method is applied to the edges of the network to filter out noises and construct the corresponding Bon-ferroni network.We investigate the correlation between topological structures and statistical properties for their largest connected components.Comparing these two networks,we find that the Bonferroni network shows an assortative mixing pattern and provides a better proxy for the underlying information network,while the original network exhibits a disassortative mixing pattern.We consider two definitions of edge weight for comparison but there is no significant difference in a same network.We also analyze the mutual relationships among node degree,edge weight and node strength.We utilize Infomap algorithm to investigate the community structure in the networks.In Chapter 6,we perform a comparative analysis of the Chinese stock market around the occurrence of the 2008 crisis based on the random matrix analysis of high-frequency stock returns of 1228 Chinese stocks.Both raw correlation matrix and partial correlation matrix with respect to the market index for these two periods are investigated.We find that the Chinese stocks have stronger average correlation and partial correlation in 2008 than in 2007,implying that the systemic risk is higher in the bearish period than in the bullish period.After removing the influence of SSCI,the eigenvalue distribution becomes much closer to the RMT prediction.Moreover,each largest eigenvalue and its eigenvector reflect an evident market effect,while other deviating eigenvalues do not contain industrial sectorial information.Surprisingly,the eigenvectors of the second largest eigenvalues in 2007 and of the third largest eigenvalues in 2008 are able to distinguish the stocks from the two exchanges.We also find that the component magnitudes of the some largest eigenvectors are proportional to the stocks' capitalizations.