Complex correlation approach for high frequency financial data

We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.

[1]  Katarzyna J. Blinowska,et al.  A new method of the description of the information flow in the brain structures , 1991, Biological Cybernetics.

[2]  Giuseppe Buccheri,et al.  Evolution of Correlation Structure of Industrial Indices of US Equity Markets , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  F. Lillo,et al.  High-frequency cross-correlation in a set of stocks , 2000 .

[4]  H. Iyetomi,et al.  Interdependencies and Causalities in Coupled Financial Networks , 2014, PloS one.

[5]  János Kertész,et al.  Increasing market efficiency: Evolution of cross-correlations of stock returns , 2006 .

[6]  R N Mantegna,et al.  Spectral density of the correlation matrix of factor models: a random matrix theory approach. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  M. Nielsen,et al.  Finite sample accuracy and choice of sampling frequency in integrated volatility estimation , 2008 .

[8]  J. Horel.  Complex Principal Component Analysis: Theory and Examples , 1984 .

[9]  G. Iori,et al.  Weighted network analysis of high-frequency cross-correlation measures. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  S. Snyder,et al.  Proceedings of the National Academy of Sciences , 1999 .

[11]  Maria Elvira Mancino,et al.  Fourier series method for measurement of multivariate volatilities , 2002, Finance Stochastics.

[12]  Paweł Fiedor,et al.  Networks in financial markets based on the mutual information rate. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[14]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[15]  K Kaski,et al.  Time-dependent cross-correlations between different stock returns: a directed network of influence. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  J. Bouchaud,et al.  Noise Dressing of Financial Correlation Matrices , 1998, cond-mat/9810255.

[17]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[18]  R. Mantegna.  Hierarchical structure in financial markets , 1998, cond-mat/9802256.

[19]  Herbert F. Weisberg,et al.  Interpreting the First Eigenvalue of a Correlation Matrix , 1981 .

[20]  M. Oshikawa,et al.  Random matrix theory analysis of cross correlations in financial markets. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Zbigniew R. Struzik,et al.  Structural and topological phase transitions on the German Stock Exchange , 2013, 1301.2530.

[22]  M Tumminello,et al.  A tool for filtering information in complex systems. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Hiroshi Iyetomi,et al.  Dynamic Stock Correlation Network , 2015, KES.

[24]  E. Ben-Jacob,et al.  Dominating Clasp of the Financial Sector Revealed by Partial Correlation Analysis of the Stock Market , 2010, PloS one.

[25]  Michele Tumminello,et al.  Emergence of statistically validated financial intraday lead-lag relationships , 2014, 1401.0462.

[26]  K. Kaski,et al.  Dynamics of market correlations: taxonomy and portfolio analysis. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  F. Abergel,et al.  High Frequency Lead/lag Relationships Empirical facts , 2011, 1111.7103.

[28]  M. E. Mancino,et al.  Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise , 2008, Comput. Stat. Data Anal..