Identifying States of a Financial Market

Münnix, Michael C.; Shimada, Takashi; Schäfer, Rudi; Leyvraz, F.; Seligman, T. H.; Guhr, Thomas; Stanley, H. Eugene

doi:10.1038/srep00644

Cited by 204 publications

(244 citation statements)

References 33 publications

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“…We find that there is indeed a genuine evolution of the correlation matrix of stocks returns for different markets in the U.S, in Europe and in Japan, a result that confirms recent studies (see e.g. [10,11,12]). We also give a partial description of this temporal evolution.…”

Section: Introductionsupporting

confidence: 90%

Eigenvector dynamics: General theory and some applications

Allez

Bouchaud

2012

Phys. Rev. E

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Abstract. We propose a general framework to study the stability of the subspace spanned by P consecutive eigenvectors of a generic symmetric matrix H0, when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation (H0 is then the Hamiltonian) and financial risk control (in which case H0 is the assets return covariance matrix). We argue that the problem can be formulated in terms of the singular values of an overlap matrix, that allows one to define an overlap distance. We specialize our results for the case of a Gaussian Orthogonal H0, for which the full spectrum of singular values can be explicitly computed. We also consider the case when H0 is a covariance matrix and illustrate the usefulness of our results using financial data. The special case where the top eigenvalue is much larger than all the other ones can be investigated in full detail. In particular, the dynamics of the angle made by the top eigenvector and its true direction defines an interesting new class of random processes.

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Section: Introductionsupporting

confidence: 90%

Eigenvector dynamics: General theory and some applications

Allez

Bouchaud

2012

Phys. Rev. E

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“…The largest eigenvalue is known as a spectral radius, representing the principal component of the system. Recently, the largest eigenvalue has been successfully used as a predicting index for sudden changes in complex systems, such as the financial crisis 21,53 and the housing market. 22 Previous studies have suggested that characterizing the largest eigenvalue of an adjacency matrix of complex networks is useful for better understanding the network behavior.…”

Section: Discussionmentioning

confidence: 99%

Spectral properties of the temporal evolution of brain network structure

Wang

Zhang

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The temporal evolution properties of the brain network are crucial for complex brain processes. In this paper, we investigate the differences in the dynamic brain network during resting and visual stimulation states in a task-positive subnetwork, task-negative subnetwork, and whole-brain network. The dynamic brain network is first constructed from human functional magnetic resonance imaging data based on the sliding window method, and then the eigenvalues corresponding to the network are calculated. We use eigenvalue analysis to analyze the global properties of eigenvalues and the random matrix theory (RMT) method to measure the local properties. For global properties, the shifting of the eigenvalue distribution and the decrease in the largest eigenvalue are linked to visual stimulation in all networks. For local properties, the short-range correlation in eigenvalues as measured by the nearest neighbor spacing distribution is not always sensitive to visual stimulation. However, the long-range correlation in eigenvalues as evaluated by spectral rigidity and number variance not only predicts the universal behavior of the dynamic brain network but also suggests non-consistent changes in different networks. These results demonstrate that the dynamic brain network is more random for the task-positive subnetwork and whole-brain network under visual stimulation but is more regular for the task-negative subnetwork. Our findings provide deeper insight into the importance of spectral properties in the functional brain network, especially the incomparable role of RMT in revealing the intrinsic properties of complex systems. The temporal evolution of brain network structure is crucial to revealing brain functions at different brain states, such as learning, memory, and visual stimulation. The sliding window method is effective for the construction of a dynamic brain network, and complex network analysis has been widely used to characterize these networks. Recently, the spectral property analysis of complex networks has attracted increasing attention based on its ability to measure more intrinsic properties of networks than complex network analysis. In particular, the dynamic brain network constructed from human electroencephalogram (EEG) data has been successfully studied by applying random matrix theory (RMT), which aims to identify the spectral fluctuation properties of networks. However, little is known about the spectral properties of the dynamic brain network based on human functional magnetic resonance imaging (fMRI) data at different brain states, and how spectral properties reflect changes in the dynamic brain network must be explained in greater detail. Here, we addressed these issues and investigated the spectral properties of a dynamic brain network constructed from human fMRI data. We show that the global and local properties of the eigenvalue of the brain network are effective for evaluating the changes in the dynamic brain network caused by visual stimulation. However, the differences between global properties...

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“…Also models that assume a first-order auto-regressive process have been suggested, see [6]. Our approach to identify different states of a stock market consists in an analysis of a covariance matrix, similar to [22], and of the transaction volumes, like in [24]. The properties of the covariance matrix of asset returns depend on the time horizon T in which they are determined.…”

Section: Introductionmentioning

confidence: 99%

Transitions in the stock markets of the US, UK and Germany

Raddant

Wagner

2016

Quantitative Finance

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In an analysis of the US, the UK, and the German stock market we find a change in the behavior based on the stock's beta values. Before 2006 risky trades were concentrated on stocks in the IT and technology sector. Afterwards risky trading takes place for stocks from the financial sector. We show that an agent-based model can reproduce these changes. We further show that the initial impulse for the transition might stem from the increase of high frequency trading at that time.

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Identifying States of a Financial Market

Cited by 204 publications

References 33 publications

Eigenvector dynamics: General theory and some applications

Eigenvector dynamics: General theory and some applications

Spectral properties of the temporal evolution of brain network structure

Transitions in the stock markets of the US, UK and Germany

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