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

Vinayak,; Schäfer, Rudi; Seligman, T. H.

doi:10.1103/physreve.88.032115

Cited by 20 publications

(41 citation statements)

References 59 publications

(122 reference statements)

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“…A higher value of ò lowers the mean of the cross-correlation coefficients, μ (see supplementary figure S1) and the maximum eigenvalue λ max of the crosscorrelation matrix. Figure 2 shows the effect of noise-suppression using power mapping method [10,16,19,26] on the short time cross-correlation matrix . Figure 2(a) shows a correlation matrix computed for the short epoch M=20 d for USA with N=194 stocks of S&P 500 ending on 30/11/2001 (arbitrarily chosen date).…”

Section: Noise-suppression In a Short Time Cross-correlation Matrixmentioning

confidence: 99%

“…To tackle the first factor of non-stationarity, we work with short time series so that the number of time steps over which we compute the correlations can be considered as reasonably stationary. However, with short time series the correlation matrices become highly singular [16][17][18]. To tackle the second factor of noise reduction, various techniques [19,20] are available.…”

Section: Introductionmentioning

confidence: 99%

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Identifying long-term precursors of financial market crashes using correlation patterns

et al. 2018

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The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial markets as an example of a complex system, and do comparative analyses of two stock markets-the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of crosscorrelation structure patterns of short-time epochs for a 32 year period . We identify 'market states' as clusters of similar correlation structures, which occur more frequently than by pure chance (randomness). The dynamical transitions between the correlation structures reflect the evolution of the market states. Power mapping method from the random matrix theory is used to suppress the noise on correlation patterns, and an adaptation of the intra-cluster distance method is used to obtain the 'optimum' number of market states. We find that the S&P 500 is characterized by four market states and Nikkei 225 by five. We further analyze the co-occurrence of paired market states; the probability of remaining in the same state is much higher than the transition to a different state. The transitions to other states mainly occur among the immediately adjacent states, with a few rare intermittent transitions to the remote states. The state adjacent to the critical state (market crash) may serve as an indicator or a 'precursor' for the critical state and this novel method of identifying the long-term precursors may be helpful for constructing the early warning system in financial markets, as well as in other complex systems.

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Section: Noise-suppression In a Short Time Cross-correlation Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Identifying long-term precursors of financial market crashes using correlation patterns

et al. 2018

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“…It has been shown in Ref. [27] that the so emerging spectrum is very sensitive to correlations and we believe that the study of the emerging spectra corresponding nc-CWE is very important.…”

Section: Summary and Discussionmentioning

confidence: 88%

“…Note that g W (z) can be obtained by calculating g X (u) using the relation (27) and then using the relation (11).…”

Section: Preliminariesmentioning

confidence: 99%

“…Ensemble of such Wishart matrices are known the correlated Wishart ensemble (CWE). Similarly, some other generalizations like using fixed-trace Wishart matrices while modeling the density matrices in quantum entanglement problems [26], or power-map deformation of Wishart matrices [27,28] in the context of short time series analysis of multivariate systems, have also been useful.…”

Section: Introductionmentioning

confidence: 99%

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Spectral density of the noncentral correlated Wishart ensembles

Vinayak

2014

Phys. Rev. E

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Wishart ensembles of random matrix theory have been useful in modeling positive definite matrices encountered in classical and quantum chaotic systems. We consider nonzero means for the entries of the constituting matrix A which defines the correlated Wishart matrix as W = AA † , and refer to the ensemble of such Wishart matrices as the non-central correlated Wishart ensemble (nc-CWE). We derive the Pastur self-consistent equation which describes the spectral density of nc-CWE at large matrix dimension.

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Complex Market Dynamics in the Light of Random Matrix Theory

Pharasi

Sharma

Chakraborti

et al. 2019

New Economic Windows

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We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the choice of an appropriate epoch over which the empirical cross-correlation return matrix is computed. A long epoch would smoothen the fluctuations in the return time series and suffers from non-stationarity, whereas a short epoch results in noisy fluctuations in the return time series and the correlation matrices turn out to be highly singular. An effective method to tackle this issue is the use of the power mapping, where a non-linear distortion is applied to a short epoch correlation matrix. The value of distortion parameter controls the noise-suppression. The distortion also removes the degeneracy of zero eigenvalues. Depending on the correlation structures, interesting properties of the eigenvalue spectra are found. We simulate different correlated Wishart matrices to compare the results with empirical return matrices computed using the S&P 500 (USA) market data for the period 1985-2016. We also briefly review two recent applications of RMT in financial stock markets:

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

Cited by 20 publications

References 59 publications

Identifying long-term precursors of financial market crashes using correlation patterns

Identifying long-term precursors of financial market crashes using correlation patterns

Spectral density of the noncentral correlated Wishart ensembles

Complex Market Dynamics in the Light of Random Matrix Theory

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