Some Studies On Time Series From Complex System

There are many complex systems around us, including traffic system and financial system which are more closely to us. These systems with statistical properties always change under time translation. A lot of physical and human factors may lead to extreme traffic events. Those time series which are generated by complex systems often show non-stationary properties. This paper two typical time series as the main research object:The traffic time series and the financial time series. By using three time series analysis methods, we study some statistical properties of the two kind time series. On the one hand, we propose two methods used to traffic time series:The first one is the entropic segmentation method. This method uses Jensen-Shannon divergence measure to quantify the differences of symbolic sequence probability distribution. The second one is recursive analysis. First of all, we use the recurrence plot to analyze the reclusiveness of traffic time series on the phase space. Then, we use the recurrence quantification analysis to quantitative analyze the local structure of recurrence plot, researching on time series similarity in the phase space trajectory. On the other hand, we proposed a multifractal analysis to study financial time series. This method aims at characterizing the heterogeneity of a roughness exponent of a signal via a multifractal theory. In this paper, we use the oscillation to define the roughness exponent, using the large deviations spectrum to describe the heterogeneity of the roughness exponent at each scale.This article is divided into five chapters, which is organized as follow:In Chapter 1, we briefly introduce the research background, research object, research significance and main work of the paper.In Chapter 2, we propose the entropic segmentation method. This method uses Jensen-Shannon divergence measure to detecting the "change points". In order to decide when to halt the segmentation, the hypothetical test should be used in the paper. By proposing this method on traffic congestion index sequence, the data is form 1 January 2010 to 31 January 2012, we find some universal law of Beijing traffic system:first, traffic congestion index perform more variability during morning rush time; second, the distribution of weekday morning rush time has a strong similarity (often from 7:30 to 9:00), the distribution of weekend morning rush time is far from weekday (often from 9:30 to 12:00); third, the complex of the traffic congestion index on Monday to Friday is higher than Saturday and Sunday, which suggest that it is easier to travel on Saturday and Sunday.In Chapter 3, we analysis a tool to describe the reclusiveness of traffic time series on the phase space, which is called recurrence plot (RP). In this chapter, we describe the traffic time series on a high dimensional space, using the phase space construction. The recurrence is defined as the closeness of two states. In this paper we applied the usual Euclidean norm. Then we look closely at the RP, by qualitative interpreting the structure of RP, we find the traffic time series present a variety of features periodicity, the non-stationary, the inherent relevant and so on.In Chapter 4, the recurrence quantification analysis (RQA) is used to quantitative analyze the local structure of recurrence plot. First of all, we introduce some indicators to represent quantitative interpretations of a recurrence plot. These indicators are based on the measures of recurrence density, diagonal lines and vertical lines. Then, we divide the recurrence plot into 49(7×7) windows. By computing the recurrence rate (RR), the determinism (DET), the divergence (DIV) and the entropy (ENTR) on each window, we find that the weekday traffic time series in phase space track similarities. At last, we combine the entropy segmentation method with the RQA. We compute the RQA measures on a moving window. In this way, we obtain a time dependent profile of RQA measures, which we call it, RQA time series. Then, we apply the entropy segmentation method both on RQA time series and traffic congestion index series. By comparing the segmentation result, we find that the segment positions are almost the same, especially DET and ENTR are more similarity. The result shows that recurrence techniques are able to identify various transitions in traffic time series.In Chapter 5, we use the large deviations estimates to analysis the financial time series from Shanghai stock composite index, Shenzhen component index and Hang Seng Index. First we propose a fully adaptive algorithm to estimate the large deviations spectrum at each scale. Then we verify that large deviations principles reveal significant information that otherwise remains hidden with classical approaches, and which can be reminiscent of some characteristics of the stock market that affect the stocks market. At last, we quantify the presence/absence of financial time series.In Chapter 6, we summarized the full paper.