Model for correlations in stock markets

Noh, Jae Dong

doi:10.1103/physreve.61.5981

Cited by 94 publications

(91 citation statements)

References 10 publications

(26 reference statements)

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“…Matrix elements of the off-diagonal blocks are 0. Such examples qualitatively correspond to the 'factor model' in quantitative finance [35,36,48], where the off-diagonal blocks have small entries. In a second example, ξ has smooth band structure, e.g., ξ jk = c |j−k| .…”

Section: Emerging Spectra Of Cwoementioning

confidence: 90%

Emerging spectra of singular correlation matrices under small power-map deformations

2013

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Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used this implies an analysis of highly singular correlation matrices. We attack this problem by using the so called power map which was introduced to reduce noise. Its non-linearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

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Section: Emerging Spectra Of Cwoementioning

confidence: 90%

Emerging spectra of singular correlation matrices under small power-map deformations

2013

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“…This 'noise' could be reduced through the use of longer simulated time series or through averaging over a large number of time series. In order to compare the eigenvectors from each of the Model Correlation matrices and that constructed from the equity returns time series, we use the Inverse Participation Ratio (IPR) [4,22]. The IPR allows quantification of the number of components that participate significantly in each eigenvector and tells us more about the level and nature of deviation from RMT.…”

Section: Market Plus Sectors Modelmentioning

confidence: 99%

“…Here, we show how a simple one-factor model, Section 2.2, of the correlation structure reproduces much of this behaviour. Furthermore, we show how additional features can be captured by including perturbations in this model, essentially a "market plus sectors" model, Section 2.3, [13,22,23].…”

Section: Model Correlation Matrixmentioning

confidence: 99%

Cross-Correlation Dynamics in Financial Time Series

2013

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The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. This behaviour is shown to be independent of the size of the time window and the number of stocks examined. A basic one-factor model is proposed, which captures the main dynamical features of the eigenvalue spectrum of the empirical data. Through the addition of perturbations to the one-factor model, (leading to a market plus sectors model), additional sectoral features are added, resulting in an Inverse Participation Ratio comparable to that found for empirical data.

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“…In a comprehensive study of the U.S. stock market, Plerou et al (2000) found that the deviating non-random eigenvalues were stable in time and that the largest eigenvalue corresponded to a common inuence on all stocks (in line with the market portfolio of the Capital Asset Pricing Model ). Various studies have proposed methods for identication of the non-random elements of the correlation matrix (Laloux et al, 1999;Noh, 2000;Gallucio et al, 1998). It can easily be imagined that ecient frontiers from the original correlation matrix might dier strongly from those generated from a correlation matrix that has been cleaned by eliminating the eigenvalues within the noise band.…”

Section: Analysis Of Correlation Matricesmentioning

confidence: 99%

Applications of Statistical Physics in Finance and Economics

Lux

2009

Handbook of Research on Complexity

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Applications of Statistical Physics in Finance and Economics Thomas LuxAbstract: This chapter reviews recent research adopting methods from statistical physics in theoretical or empirical work in economics and finance. The bulk of what has recently become known as 'econophysics' in broader circles draws its motivation from observed scaling laws in financial markets and the abundance of data available from the economy's financial sphere. Sec. 2 of this review presents the robust power laws encountered in financial economics and discusses potential explanations for scaling in finance derived from models of stochastic interactions of traders. Sec. 3 provides an overview over other applications of statistical physics methodology in finance and attempts to evaluate the impact they have had so far on financial economics. With the following section, the review turns to recent work on the emergence of wealth and income heterogeneity and the recent inception of new strands of research on this topic, both within econophysics and the neoclassical economics tradition. Sec. 5 reviews the new stylized facts that have been identified in cross-sectional data of firm characteristics and agent-based approaches to industrial organization and macroeconomic dynamics that have been motivated by these findings. We conclude with an assessment of the major methodological contributions of this new strand of research.Keywords: stylized facts, power laws, agent-based models, econophysics JEL classification: C10, C51, G12 Abstract: This chapter reviews recent research adopting methods from statistical physics in theoretical or empirical work in economics and nance. The bulk of what has recently become known as`econophysics' in broader circles draws its motivation from observed scaling laws in nancial markets and the abundance of data available from the economy's nancial sphere. Sec. 2 of this review presents the robust power laws encountered in nancial economics and discusses potential explanations for scaling in nance derived from models of stochastic interactions of traders. Sec. 3 provides an overview over other applications of statistical physics methodology in nance and attempts to evaluate the impact they have had so far on nancial economics. With the following section, the review turns to recent work on the emergence of wealth and income heterogeneity and the recent inception of new strands of research on this topic, both within econophysics and the...

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Model for correlations in stock markets

Cited by 94 publications

References 10 publications

Emerging spectra of singular correlation matrices under small power-map deformations

Emerging spectra of singular correlation matrices under small power-map deformations

Cross-Correlation Dynamics in Financial Time Series

Applications of Statistical Physics in Finance and Economics

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