Modified generalized sample entropy and surrogate data analysis for stock markets

Abstract In this paper a modified method of generalized sample entropy and surrogate data analysis is proposed as a new measure to assess the complexity of a complex dynamical system such as stock market. The method based on Hausdorff distance presents a different way of time series patterns match showing distinct behaviors of complexity. Simulations are conducted over synthetic and real-world data for providing the comparative study. Results show that the modified method is more sensitive to the change of dynamics and has richer information. In addition, exponential functions can be used to successfully fit the curves obtained from the modified method and quantify the changes of complexity for stock market data.

[1]  Panos M. Pardalos,et al.  Statistical analysis of financial networks , 2005, Comput. Stat. Data Anal..

[2]  Jeffrey M. Hausdorff,et al.  Multiscale entropy analysis of human gait dynamics. , 2003, Physica A.

[3]  Chun-Chieh Wang,et al.  Time Series Analysis Using Composite Multiscale Entropy , 2013, Entropy.

[4]  Semi-analytic valuation of stock loans with finite maturity , 2015, Commun. Nonlinear Sci. Numer. Simul..

[5]  V. Plerou,et al.  A theory of power-law distributions in financial market fluctuations , 2003, Nature.

[6]  Alejandra Figliola,et al.  A multifractal approach for stock market inefficiency , 2008 .

[7]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[8]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[9]  Shang-Hong Lai,et al.  Hybrid image matching combining Hausdorff distance with normalized gradient matching , 2007, Pattern Recognit..

[10]  Qin Wei,et al.  Adaptive Computation of Multiscale Entropy and Its Application in EEG Signals for Monitoring Depth of Anesthesia During Surgery , 2012, Entropy.

[11]  H. Kantz,et al.  Analysing the information flow between financial time series , 2002 .

[12]  T. D. Matteo,et al.  Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development , 2004, cond-mat/0403681.

[13]  C. Granger,et al.  Nonstationarities in Stock Returns , 2005, Review of Economics and Statistics.

[14]  Madalena Costa,et al.  Multiscale entropy analysis of biological signals. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  V. Plerou,et al.  Scaling of the distribution of price fluctuations of individual companies. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Huachun Tan,et al.  A novel weighted Hausdorff distance for face localization , 2006, Image Vis. Comput..

[17]  Pengjian Shang,et al.  Generalized permutation entropy analysis based on the two-index entropic form Sq,δ. , 2015, Chaos.

[18]  R. Rigobón,et al.  No Contagion, Only Interdependence: Measuring Stock Market Comovements , 2002 .

[19]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[20]  Pengjian Shang,et al.  Weighted multifractal cross-correlation analysis based on Shannon entropy , 2015, Communications in Nonlinear Science and Numerical Simulation.

[21]  Pengjian Shang,et al.  POWER LAW AND STRETCHED EXPONENTIAL EFFECTS OF EXTREME EVENTS IN CHINESE STOCK MARKETS , 2010 .

[22]  Ron Shonkwiler.  Computing the Hausdorff Set Distance in Linear Time for Any L_p Point Distance , 1991, Inf. Process. Lett..

[23]  K. Kaski,et al.  Clustering and information in correlation based financial networks , 2003, cond-mat/0312682.

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

[25]  N. Sudha,et al.  Robust Hausdorff distance measure for face recognition , 2007, Pattern Recognit..

[26]  Pengjian Shang,et al.  The cross-correlations of stock markets based on DCCA and time-delay DCCA , 2012 .

[27]  Pengjian Shang,et al.  Cross-sample entropy statistic as a measure of synchronism and cross-correlation of stock markets , 2013 .

[28]  Giovani L. Vasconcelos,et al.  Long-range correlations and nonstationarity in the Brazilian stock market , 2003 .

[29]  Ron Shonkwiler,et al.  An Image Algorithm for Computing the Hausdorff Distance Efficiently in Linear Time , 1989, Inf. Process. Lett..

[30]  Luiz Otavio Murta,et al.  Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis , 2012 .

[31]  H. Eugene Stanley,et al.  Econophysics: Two-phase behaviour of financial markets , 2003, Nature.

[32]  José Roberto Castilho Piqueira,et al.  Brazilian exchange rate complexity: Financial crisis effects , 2012 .

[33]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[34]  Chengyu Liu,et al.  Comparison of different threshold values r for approximate entropy: application to investigate the heart rate variability between heart failure and healthy control groups , 2011, Physiological measurement.

[35]  Daniel P. Huttenlocher,et al.  Comparing Images Using the Hausdorff Distance , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[36]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.

[37]  Davide Faranda,et al.  Early warnings indicators of financial crises via auto regressive moving average models , 2015, Commun. Nonlinear Sci. Numer. Simul..

[38]  Pengjian Shang,et al.  Traffic signals analysis using qSDiff and qHDiff with surrogate data , 2015, Commun. Nonlinear Sci. Numer. Simul..

[39]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[40]  C. Tsallis.  Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World , 2009 .

[41]  Seong-Min Yoon,et al.  Multifractal features of financial markets , 2004 .

[42]  Ruey S. Tsay,et al.  Analysis of Financial Time Series , 2005 .

[43]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[44]  M. Marchesi,et al.  VOLATILITY CLUSTERING IN FINANCIAL MARKETS: A MICROSIMULATION OF INTERACTING AGENTS , 2000 .

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

[46]  Rosario N. Mantegna,et al.  Evolution of Worldwide Stock Markets, Correlation Structure and Correlation Based Graphs , 2011 .

[47]  J. A. Tenreiro Machado,et al.  Analysis of stock market indices through multidimensional scaling , 2011 .