Abstract:
Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. The correlation matrix formalism and concept of multifractality are used to study temporal aspects of the Ukraine Stock Market evolution. Random matrix theory (RMT) is carried out using daily returns of 431 stocks extracted from database time series of prices the First Stock Trade System index (www.kinto.com) for the ten-year period 1997-2006. We find that a majority of the eigenvalues of C fall within the RMT bounds for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices—implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Comparison with the Mantegna minimum spanning trees method gives a satisfactory consent. The found out the pseudoeffects related to the artificial unchanging areas of price series come into question We used two possible procedures of analyzing multifractal properties of a time series. The first one uses the continuous wavelet transform and extracts scaling exponents from the wavelet transform amplitudes over all scales. The second method is the multifractal version of the detrended fluctuation analysis method (MF-DFA). The multifractality of a time series we analysed by means of the difference of values singularity stregth (or Holder exponent) ®max and ®min as a suitable way to characterise multifractality. Singularity spectrum calculated from daily returns using a sliding 250 day time window in discrete steps of 1. . . 10 days. We discovered that changes in the multifractal spectrum display distinctive pattern around significant “drawdowns”. Finally, we discuss applications to the construction of crushes precursors at the financial markets.
