Table of Contents
ISRN Signal Processing
Volume 2013, Article ID 434832, 14 pages
http://dx.doi.org/10.1155/2013/434832
Research Article

Dynamically Measuring Statistical Dependencies in Multivariate Financial Time Series Using Independent Component Analysis

Machine Learning Research Group, Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK

Received 30 March 2013; Accepted 4 May 2013

Academic Editors: A. Krzyzak, C.-M. Kuo, S. Kwong, W. Liu, and F. Perez-Cruz

Copyright © 2013 Nauman Shah and Stephen J. Roberts. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Berg and K. Aas, “Models for construction of multivariate dependence—a comparison study,” The European Journal of Finance, vol. 15, no. 7-8, pp. 639–659, 2009. View at Publisher · View at Google Scholar · View at Scopus
  2. M. M. Dacorogna, An Introduction to High-Frequency Finance, Academic Press, New York, NY, USA, 2001.
  3. J. Hlinka, M. Paluš, M. Vejmelka, D. Mantini, and M. Corbetta, “Functional connectivity in resting-state fMRI: is linear correlation sufficient?” NeuroImage, vol. 54, no. 3, pp. 2218–2225, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. S. J. Devlin, R. Gnanadesikan, and J. R. Kettenring, “Robust estimation and outlier detection with correlation coefficients,” Biometrika, vol. 62, no. 3, pp. 531–545, 1975. View at Google Scholar · View at Scopus
  5. A. R. Cowan, “Nonparametric event study tests,” Review of Quantitative Finance and Accounting, vol. 2, no. 4, pp. 343–358, 1992. View at Publisher · View at Google Scholar · View at Scopus
  6. G. J. Glasser and R. F. Winter, “Critical values of the coefficient of rank correlation for testing the hypothesis of independence,” Biometrika, vol. 48, no. 3-4, pp. 444–448, 1961. View at Google Scholar
  7. P. Embrechts, F. Lindskog, and A. McNeil, “Modelling dependence with copulas and applications to risk management,” in Handbook of Heavy Tailed Distributions in Finance, vol. 1, chapter 8, pp. 329–384, 2003. View at Google Scholar
  8. E. Jondeau, S. H. Poon, and M. Rockinger, Financial Modeling Under Non-Gaussian Distributions, Springer, New York, NY, USA, 2007.
  9. J. D. Fermanian and O. Scaillet, “Some statistical pitfalls in copula modeling for financial applications,” in Capital Formation, Governance and Banking, p. 59, 2005. View at Google Scholar
  10. T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley-Interscience, New York, NY, USA, 2006.
  11. A. Kraskov, H. Stögbauer, and P. Grassberger, “Estimating mutual information,” Physical Review E, vol. 69, no. 6, Article ID 066138, 16 pages, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Khan, S. Bandyopadhyay, and A. R. Ganguly, “Computing mutual information based nonlinear dependence among noisy and finite geophysical time series,” in Proceedings of the American Geophysical Union, Fall Meeting, 2005, abstract no. NG22A-03.
  13. M. M. V. Hulle, “Edgeworth approximation of multivariate differential entropy,” Neural Computation, vol. 17, no. 9, pp. 1903–1910, 2005. View at Publisher · View at Google Scholar
  14. L. B. Almeida, “Linear and nonlinear ICA based on mutual information,” in Proceedings of the IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium (AS-SPCC '00), pp. 117–122, IEEE, 2000.
  15. A. D. Back and A. S. Weigend, “A first application of independent component analysis to extracting structure from stock returns,” International Journal of Neural Systems, vol. 8, no. 4, pp. 473–484, 1997. View at Google Scholar · View at Scopus
  16. E. Oja, K. Kiviluoto, and S. Malaroiu, “Independent component analysis for financial time series,” in Proceedings of the IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium (AS-SPCC '00), pp. 111–116, IEEE, 2000.
  17. A. Hyvärinen, “Survey on independent component analysis,” Neural Computing Surveys, vol. 2, no. 4, pp. 94–128, 1999. View at Google Scholar
  18. C. J. Lu, T. S. Lee, and C. C. Chiu, “Financial time series forecasting using independent component analysis and support vector regression,” Decision Support Systems, vol. 47, no. 2, pp. 115–125, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Joe, “Relative entropy measures of multivariate dependence,” Journal of the American Statistical Association, vol. 84, no. 405, pp. 157–164, 1989. View at Publisher · View at Google Scholar
  20. M. Novey and T. Adali, “Complex ICA by negentropy maximization,” IEEE Transactions on Neural Networks, vol. 19, no. 4, pp. 596–609, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. S. Roberts and R. Everson, Independent Component Analysis: Principles and Practice, Cambridge University Press, New York, NY, USA, 2001.
  22. J. Palmer, K. Kreutz-Delgado, and S. Makeig, “Super-Gaussian mixture source model for ICA,” in Independent Component Analysis and Blind Signal Separation, pp. 854–861, 2006. View at Google Scholar
  23. R. A. Choudrey and S. J. Roberts, “Variational mixture of Bayesian independent component analyzers,” Neural Computation, vol. 15, no. 1, pp. 213–252, 2003. View at Publisher · View at Google Scholar · View at Scopus
  24. R. Everson and S. Roberts, “Independent component analysis: a flexible nonlinearity and decorrelating manifold approach,” Neural Computation, vol. 11, no. 8, pp. 1957–1983, 1999. View at Google Scholar · View at Scopus
  25. R. E. Kass, L. Tierney, and J. B. Kadane, “Laplace's method in Bayesian analysis,” in Statistical Multiple Integration: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference [on Statistical Multiple Integration] Held at Humboldt University, June 17–23, 1989, vol. 115, p. 89, American Mathematical Society, 1991. View at Google Scholar
  26. W. Addison and S. Roberts, “Blind source separation with non-stationary mixing using wavelets,” in Proceedings of the ICA Research Network Workshop, The University of Liverpool, 2006.
  27. N. J. Higham, “Matrix nearness problems and applications,” in Applications of Matrix Theory, 1989. View at Google Scholar
  28. K. B. Datta, Matrix and Linear Algebra, PHI Learning, 2004.
  29. K. Boudt, J. Cornelissen, and C. Croux, “The Gaussian rank correlation estimator: robustness properties,” Statistics and Computing, vol. 22, no. 2, pp. 471–483, 2012. View at Publisher · View at Google Scholar
  30. D. Evans, “A computationally efficient estimator for mutual information,” Proceedings of the Royal Society A, vol. 464, no. 2093, pp. 1203–1215, 2008. View at Publisher · View at Google Scholar · View at Scopus
  31. K. Torkkola, “On feature extraction by mutual information maximization,” in Proceedings of the IEEE International Conference on Acustics, Speech, and Signal Processing (ICASSP '02), vol. 1, pp. I/821–I/824, IEEE, May 2002. View at Scopus
  32. K. Nagarajan, B. Holland, C. Slatton, and A. D. George, “Scalable and portable architecture for probability density function estimation on FPGAs,” in Proceedings of the 16th IEEE Symposium on Field-Programmable Custom Computing Machines (FCCM '08), pp. 302–303, IEEE Computer Society, April 2008. View at Publisher · View at Google Scholar · View at Scopus
  33. C. G. Bowsher, “Modelling security market events in continuous time: intensity based, multivariate point process models,” Journal of Econometrics, vol. 141, no. 2, pp. 876–912, 2007. View at Publisher · View at Google Scholar · View at Scopus
  34. B. Peiers, “Informed traders, intervention, and price leadership: a deeper view of the microstructure of the foreign exchange market,” Journal of Finance, vol. 52, no. 4, pp. 1589–1614, 1997. View at Google Scholar · View at Scopus
  35. A. Dionisio, R. Menezes, and D. A. Mendes, “Mutual information: a measure of dependency for nonlinear time series,” Physica A, vol. 344, no. 1-2, pp. 326–329, 2004. View at Publisher · View at Google Scholar · View at Scopus
  36. J. Y. Campbell, A. W. Lo, A. C. MacKinlay, and R. F. Whitelaw, “The econometrics of financial markets,” Macroeconomic Dynamics, vol. 2, no. 4, pp. 559–562, 1998. View at Google Scholar
  37. G. Koutmos, C. Negakis, and P. Theodossiou, “Stochastic behaviour of the Athens stock exchange,” Applied Financial Economics, vol. 3, no. 2, pp. 119–126, 1993. View at Publisher · View at Google Scholar
  38. D. M. Guillaume, M. M. Dacorogna, R. R. Davé, U. A. Müller, R. B. Olsen, and O. V. Pictet, “From the bird's eye to the microscope: a survey of new stylized facts of the intra-daily foreign exchange markets,” Finance and Stochastics, vol. 1, no. 2, pp. 95–129, 1997. View at Publisher · View at Google Scholar
  39. R. Cheng, “Using pearson type IV and other Cinderella distributions in simulation,” in Proceedings of the Winter Simulation Conference (WSC '11), pp. 457–468, IEEE, 2011.
  40. Y. Nagahara, “The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters,” Statistics and Probability Letters, vol. 43, no. 3, pp. 251–264, 1999. View at Google Scholar · View at Scopus
  41. A. Shephard, Pearson IV, Institute for Fiscal Studies, University College London, 2008.
  42. S. Stavroyiannis, I. Makris, V. Nikolaidis, and L. Zarangas, “Econometric modeling and value-at-risk using the Pearson type IV distribution,” International Review of Financial Analysis, vol. 22, pp. 10–17, 2012. View at Publisher · View at Google Scholar
  43. M. Kendall, A. Stuart, and J. K. Ord, Kendall's Advanced Theory of Statistics, Charles Griffin, 1987.
  44. R. Willink, “A closed-form expression for the pearson type IV distribution function,” Australian and New Zealand Journal of Statistics, vol. 50, no. 2, pp. 199–205, 2008. View at Publisher · View at Google Scholar · View at Scopus
  45. A. Venelli, “Efficient entropy estimation for mutual information analysis using B-splines,” in Information Security Theory and Practices. Security and Privacy of Pervasive Systems and Smart Devices, pp. 17–30, 2010. View at Google Scholar
  46. C. G. Park and D. W. Shin, “An algorithm for generating correlated random variables in a class of infinitely divisible distributions,” Journal of Statistical Computation and Simulation, vol. 61, no. 1-2, pp. 127–139, 1998. View at Google Scholar · View at Scopus
  47. R. L. Iman and W. J. Conover, “A distribution-free approach to inducing rank correlation among input variables,” Communications in Statistics-Simulation and Computation, vol. 11, no. 3, pp. 311–334, 1982. View at Publisher · View at Google Scholar
  48. N. Shah and S. Roberts, “Hidden Markov independent component analysis as a measure of coupling in multivariate financial time series,” in Proceedings of the ICA Research Network International Workshop, Liverpool, UK, 2008.
  49. A. Rossi and G. M. Gallo, “Volatility estimation via hidden Markov models,” Journal of Empirical Finance, vol. 13, no. 2, pp. 203–230, 2006. View at Publisher · View at Google Scholar · View at Scopus
  50. J. Crotty, “Structural causes of the global financial crisis: a critical assessment of the ‘new financial architecture’,” Cambridge Journal of Economics, vol. 33, no. 4, pp. 563–580, 2009. View at Publisher · View at Google Scholar · View at Scopus
  51. J. A. Murphy, “An analysis of the financial crisis of 2008: causes and solutions,” Social Science Research Network, 2008.
  52. M. Pojarliev and R. M. Levich, “Detecting crowded trades in currency funds,” Financial Analysts Journal, vol. 67, no. 1, pp. 26–39, 2011. View at Publisher · View at Google Scholar · View at Scopus
  53. L. Sandoval and I. D. P. Franca, “Correlation of financial markets in times of crisis,” Physica A, vol. 391, no. 1, pp. 187–208, 2012. View at Google Scholar