Are Investors Reluctant to Realize Their Losses

Complex network approaches to nonlinear time series analysis

The complexity, nonlinearity, and nonstationarity of biological time series typically defy quantitative description. Living systems are governed by numerous, continuously changing, interacting variables in the presence of noise. Such conditions often challenge traditional methods such as Fourier transforms. An approach for assessing such nondeterministic complexity is recurrence quantification analysis (RQA). Strategies implementing quantification of recurrences have often been successful in diagnosing changes in nonstationary signals not easily detected by traditional methods.


Keywords:

recurrence;
time series analysis;
signal analysis

Recurrence Quantification Analysis

The Foundations of Econometric Analysis: On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers ( Philosophical Transactions of the Royal Society of London , A, vol. 226, 1927, pp. 267–73)

Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the method has still been missing so far. Here, we interpret an $\ensuremath{\varepsilon}$-recurrence network as a discrete subnetwork of a ``continuous'' graph with uncountably many vertices and edges corresponding to the system's attractor. This step allows us to show that various statistical measures commonly used in complex network analysis can be seen as discrete estimators of newly defined continuous measures of certain complex geometric properties of the attractor on the scale given by $\ensuremath{\varepsilon}$. In particular, we introduce local measures such as the $\ensuremath{\varepsilon}$-clustering coefficient, mesoscopic measures such as $\ensuremath{\varepsilon}$-motif density, path-based measures such as $\ensuremath{\varepsilon}$-betweennesses, and global measures such as $\ensuremath{\varepsilon}$-efficiency. This new analytical basis for the so far heuristically motivated network measures also provides an objective criterion for the choice of $\ensuremath{\varepsilon}$ via a percolation threshold, and it shows that estimation can be improved by so-called node splitting invariant versions of the measures. We finally illustrate the framework for a number of archetypical chaotic attractors such as those of the Bernoulli and logistic maps, periodic and two-dimensional quasiperiodic motions, and for hyperballs and hypercubes by deriving analytical expressions for the novel measures and comparing them with data from numerical experiments. More generally, the theoretical framework put forward in this work describes random geometric graphs and other networks with spatial constraints, which appear frequently in disciplines ranging from biology to climate science.

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Analytical framework for recurrence network analysis of time series.

Complex networks in stock market and stock price volatility pattern prediction are the important issues in stock price research. Previous studies have used historical information regarding a single stock to predict the future trend of the stock’s price, seldom considering comovement among stocks in the same market. In this study, in order to extract the information about relation stocks for prediction, we try to combine the complex network method with machine learning to predict stock price patterns. Firstly, we propose a new pattern network construction method for multivariate stock time series. The price volatility combination patterns of the Standard & Poor’s 500 Index (S&P 500), the NASDAQ Composite Index (NASDAQ), and the Dow Jones Industrial Average (DJIA) are transformed into directed weighted networks. It is found that network topology characteristics, such as average degree centrality, average strength, average shortest path length, and closeness centrality, can identify periods of sharp fluctuations in the stock market. Next, the topology characteristic variables for each combination symbolic pattern are used as the input variables for K-nearest neighbors (KNN) and support vector machine (SVM) algorithms to predict the next-day volatility patterns of a single stock. The results show that the optimal models corresponding to the two algorithms can be found through cross-validation and search methods, respectively. The prediction accuracy rates for the three indexes in relation to the testing data set are greater than 70%. In general, the prediction ability of SVM algorithms is better than that of KNN algorithms.

/pdf/stock-price-pattern-prediction-based-on-complex-network-and-1a4frph1hz.pdf

Stock Price Pattern Prediction Based on Complex Network and Machine Learning

This study investigates a new opinion formation model of heterogeneous agents, a network stubborn individuals and orators (NSO) model based on game theory and complex social networks Game theory s

Simulation study on opinion formation models of heterogeneous agents based on game theory and complex networks

In this article, we propose a novel method for transforming a time series into a complex network graph. The proposed algorithm is based on the spatial distribution of a time series. The characteristics of geometric parameters of a network represent the dynamic characteristics of a time series. Our algorithm transforms, respectively, a constant series into a fully connected graph, periodic time series into a regular graph, linear divergent time series into a tree, and chaotic time series into an approximately power law distribution network graph. We find that when the dimension of reconstructed phase space increases, the corresponding graph for a random time series quickly turns into a completely unconnected graph, while that for a chaotic time series maintains a certain level of connectivity. The characteristics of the generated network, including the total edges, the degree distribution, and the clustering coefficient, reflect the characteristics of the time series, including diverging speed, level of certainty, and level of randomness. This observation allows a chaotic time series to be easily identified from a random time series. The method may be useful for analysis of complex nonlinear systems such as chaos and random systems, by perceiving the differences in the outcomes of the systems—the time series—in the identification of the systemic levels of certainty or randomness. © 2011 Wiley Periodicals, Inc. Complexity, 2011 © 2011 Wiley Periodicals, Inc.

Novel method of identifying time series based on network graphs

We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel–Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.

Unraveling chaotic attractors by complex networks and measurements of stock market complexity.

In this paper, we compare two methods of mapping time series data to complex networks based on correlation coefficient and distance, respectively. These methods make use of two different physical aspects of large-scale data. We find that the method based on correlation coefficient cannot distinguish the randomness of a chaotic series from a purely random series, and it cannot express the certainty of chaos. The method based on distance can express the certainty of a chaotic series and can distinguish a chaotic series from a random series easily. Therefore, the distance method can be helpful in analyzing chaotic systems and random systems. We have also discussed the effectiveness of the distance method with noisy data.

Ying Li

Papers

Stock Price Pattern Prediction Based on Complex Network and Machine Learning

Simulation study on opinion formation models of heterogeneous agents based on game theory and complex networks

Novel method of identifying time series based on network graphs

Unraveling chaotic attractors by complex networks and measurements of stock market complexity.

A comparison of two methods for modeling large-scale data from time series as complex networksa)