Random Matrix Theory Analysis of Cross Correlations in Financial Markets

We confirm universal behaviors such as eigenvalue distribution and spacings predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present. Some deviations in the small eigenvalue statistics outside the bounds of the universality class of RMT are not completely explained with the deterministic correlations as proposed in previous studies. We study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of ``level repulsion'' in RMT and explains some deviations from the previous studies observed in the market data. We also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on RMT. Some characteristic differences between properties of Tokyo Stock Exchange and New York Stock Exchange are found.Comment: RevTex, 17 pages, 8 figure

Uncovering the Internal Structure of the Indian Financial Market: Cross-correlation behavior in the NSE

The cross-correlations between price fluctuations of 201 frequently traded stocks in the National Stock Exchange (NSE) of India are analyzed in this paper. We use daily closing prices for the period 1996-2006, which coincides with the period of rapid transformation of the market following liberalization. The eigenvalue distribution of the cross-correlation matrix, $\mathbf{C}$, of NSE is found to be similar to that of developed markets, such as the New York Stock Exchange (NYSE): the majority of eigenvalues fall within the bounds expected for a random matrix constructed from mutually uncorrelated time series. Of the few largest eigenvalues that deviate from the bulk, the largest is identified with market-wide movements. The intermediate eigenvalues that occur between the largest and the bulk have been associated in NYSE with specific business sectors with strong intra-group interactions. However, in the Indian market, these deviating eigenvalues are comparatively very few and lie much closer to the bulk. We propose that this is because of the relative lack of distinct sector identity in the market, with the movement of stocks dominantly influenced by the overall market trend. This is shown by explicit construction of the interaction network in the market, first by generating the minimum spanning tree from the unfiltered correlation matrix, and later, using an improved method of generating the graph after filtering out the market mode and random effects from the data. Both methods show, compared to developed markets, the relative absence of clusters of co-moving stocks that belong to the same business sector. This is consistent with the general belief that emerging markets tend to be more correlated than developed markets.Comment: 15 pages, 8 figures, to appear in Proceedings of International Workshop on "Econophysics & Sociophysics of Markets & Networks" (Econophys-Kolkata III), Mar 12-15, 200

Detection of Multi-TeV Gamma Rays from Markarian 501 during an Unforeseen Flaring State in 1997 with the Tibet Air Shower Array

In 1997, the BL Lac Object Mrk 501 entered a very active phase and was the brightest source in the sky at TeV energies, showing strong and frequent flaring. Using the data obtained with a high density air shower array that has been operating successfully at Yangbajing in Tibet since 1996, we searched for gamma-ray signals from this source during the period from February through August in 1997. Our observation detected multi-TeV $\gamma$-ray signals at the 3.7-Sigma level during this period. The most rapid increase of the excess counts was observed between April 7 and June 16 and the statistical significance of the excess counts in this period was 4.7-Sigma. Among several observations of flaring TeV gamma-rays from Mrk 501 in 1997, this is the only observation using a conventional air shower array. We present the energy spectrum of gamma-rays which will be worthy to compare with those obtained by imaging atmospheric Cerenkov telescopes.Comment: 9 pages, 7 figures, To appear in Ap

Large-Scale Sidereal Anisotropy of Galactic Cosmic-Ray Intensity Observed by the Tibet Air Shower Array

We present the large-scale sidereal anisotropy ofgalactic cosmic-ray intensity in the multi-TeV region observed with the Tibet-IIIair shower array during the period from 1999 through 2003. The sidereal daily variation of cosmic rays observed in this experiment shows an excess of relative intensity around $4\sim7$ hours local sidereal time, as well as a deficit around 12 hours local sidereal time. While the amplitude of the excess is not significant when averaged over all declinations, the excess in individual declinaton bands becomes larger and clearer as the viewing direction moves toward the south. The maximum phase of the excess intensity changes from $\sim$7 at the northern hemisphere to $\sim$4 hours at the equatorial region. We also show that both the amplitude and the phase of the first harmonic vector of the daily variation are remarkably independent of primary energy in the multi-TeV region. This is the first result determining the energy and declination dependences of the full 24-hour profiles of the sidereal daily variation in the multi-TeV region with a single air shower experiment.Comment: 13 pages, 3 figures, 1 table. Accepted for publication in ApJ

Observation by an Air-Shower Array in Tibet of the Multi-TeV Cosmic-Ray Anisotropy due to Terrestrial Orbital Motion Around the Sun

We report on the solar diurnal variation of the galactic cosmic-ray intensity observed by the Tibet III air shower array during the period from 1999 to 2003. In the higher-energy event samples (12 TeV and 6.2 TeV), the variations are fairly consistent with the Compton-Getting anisotropy due to the terrestrial orbital motion around the sun, while the variation in the lower-energy event sample (4.0 TeV) is inconsistent with this anisotropy. This suggests an additional anisotropy superposed at the multi-TeV energies, e.g. the solar modulation effect. This is the highest-precision measurement of the Compton-Getting anisotropy ever made.Comment: 4 pages, 2 figures, includes .bbl fil

Observation of Multi-Tev Gamma Rays from the Crab Nebula Using the Tibet Air Shower Array

The Tibet experiment, operating at Yangbajing (4,300 m above sea level), is the lowest energy air shower array and the new high density array constructed in 1996 has sensitivity to $\gamma$-ray air showers at energies as low as 3 TeV. With this new array, the Crab Nebula was observed in multi-TeV $\gamma$-rays and a signal was detected at the 5.5 $\sigma$ level. We also obtained the energy spectrum of $\gamma$-rays in the energy region above 3 TeV which partially overlaps those observed with imaging atmospheric Cherenkov telescopes. This is the first observation of $\gamma$-ray signals from point sources with a conventional air shower array using scintillation detectors.Comment: 9 pages, 4 figures, Accepted for publication in ApJ Letter

Observation of Multi-Tev Diffuse Gamma Rays from the Galactic Plane with the Tibet Air Shower Array

Data from the Tibet-III air shower array (with energies around 3 TeV) and from the Tibet-II array (with energies around 10 TeV) have been searched for diffuse gamma rays from the Galactic plane. These arrays have an angular resolution of about 0.9 degrees. The sky regions searched are the inner Galaxy, 20 degrees <= l <= 55 degrees, and outer Galaxy, 140 degrees <= l <= 225 degrees, and |b| <= 2 degrees or <= 5 degrees. No significant Galactic plane gamma-ray excess was observed. The 99% confidence level upper limits for gamma-ray intensity obtained are (for |b| <= 2 degrees) 1.1 times 10^{-15} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 3 TeV and 4.1 times 10^{-17} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 10 TeV for the inner Galaxy, and 3.6 times 10^{-16} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 3 TeV and 1.3 times 10^{-17} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 10 TeV for the outer Galaxy, assuming a differential spectral index of 2.4. The upper limits are significant in the multi-TeV region when compared to those from Cherenkov telescopes in the lower energy region and other air shower arrays in the higher energy region; however, the results are not sufficient to rule out the inverse Compton model with a source electron spectral index of 2.0.Comment: 22 pages, 8 figures, Accepted for publication in Ap

Statistical Properties of Cross-Correlation in the Korean Stock Market

We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $\beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(\sigma)$ with the portfolio risk $\sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(\sigma) \sim \sigma^{-\gamma}$, with the exponent $\gamma \sim 2.92$ and those for Asian currency crisis decreases significantly

Primary proton spectrum between 200 TeV and 1000 TeV observed with the Tibet burst detector and air shower array

Since 1996, a hybrid experiment consisting of the emulsion chamber and burst detector array and the Tibet-II air-shower array has been operated at Yangbajing (4300 m above sea level, 606 g/cm^2) in Tibet. This experiment can detect air-shower cores, called as burst events, accompanied by air showers in excess of about 100 TeV. We observed about 4300 burst events accompanied by air showers during 690 days of operation and selected 820 proton-induced events with its primary energy above 200 TeV using a neural network method. Using this data set, we obtained the energy spectrum of primary protons in the energy range from 200 to 1000 TeV. The differential energy spectrum obtained in this energy region can be fitted by a power law with the index of -2.97 $\pm$ 0.06, which is steeper than that obtained by direct measurements at lower energies. We also obtained the energy spectrum of helium nuclei at particle energies around 1000 TeV.Comment: 25 pages, 22 figures, Accepted for publication in Phys. Rev.

Mice with cleavage-resistant N-cadherin exhibit synapse anomaly in the hippocampus and outperformance in spatial learning tasks

N-cadherin is a homophilic cell adhesion molecule that stabilizes excitatory synapses, by connecting pre- and post-synaptic termini. Upon NMDA receptor (NMDAR) activation by glutamate, membrane-proximal domains of N-cadherin are cleaved serially by a-disintegrin-and-metalloprotease 10 (ADAM10) and then presenilin 1(PS1, catalytic subunit of the γ-secretase complex). To assess the physiological significance of the initial N-cadherin cleavage, we engineer the mouse genome to create a knock-in allele with tandem missense mutations in the mouse N-cadherin/Cadherin-2 gene (Cdh2 R714G, I715D, or GD) that confers resistance on proteolysis by ADAM10 (GD mice). GD mice showed a better performance in the radial maze test, with significantly less revisiting errors after intervals of 30 and 300 s than WT, and a tendency for enhanced freezing in fear conditioning. Interestingly, GD mice reveal higher complexity in the tufts of thorny excrescence in the CA3 region of the hippocampus. Fine morphometry with serial section transmission electron microscopy (ssTEM) and three-dimensional (3D) reconstruction reveals significantly higher synaptic density, significantly smaller PSD area, and normal dendritic spine volume in GD mice. This knock-in mouse has provided in vivo evidence that ADAM10-mediated cleavage is a critical step in N-cadherin shedding and degradation and involved in the structure and function of glutamatergic synapses, which affect the memory function