- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

General simulation algorithm for autocorrelated binary processes

Francesco Serinaldi1,2,* and Federico Lombardo3,†

  • 1School of Civil Engineering and Geosciences, Newcastle University, Newcastle Upon Tyne, NE1 7RU, United Kingdom
  • 2Willis Research Network, 51 Lime St., London EC3M 7DQ, United Kingdom
  • 3Dipartimento di Ingegneria, Università degli Studi Roma Tre, Via Vito Volterra 62, 00146 Rome, Italy

  • *francesco.serinaldi@ncl.ac.uk
  • †federico.lombardo@uniroma3.it
PDF

Phys. Rev. E 95, 023312 – Published 23 February, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.023312

Abstract

The apparent ubiquity of binary random processes in physics and many other fields has attracted considerable attention from the modeling community. However, generation of binary sequences with prescribed autocorrelation is a challenging task owing to the discrete nature of the marginal distributions, which makes the application of classical spectral techniques problematic. We show that such methods can effectively be used if we focus on the parent continuous process of beta distributed transition probabilities rather than on the target binary process. This change of paradigm results in a simulation procedure effectively embedding a spectrum-based iterative amplitude-adjusted Fourier transform method devised for continuous processes. The proposed algorithm is fully general, requires minimal assumptions, and can easily simulate binary signals with power-law and exponentially decaying autocorrelation functions corresponding, for instance, to Hurst-Kolmogorov and Markov processes. An application to rainfall intermittency shows that the proposed algorithm can also simulate surrogate data preserving the empirical autocorrelation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (35)

  1. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw Hill, New York, 1991).
  2. D. P. Kroese, T. Brereton, T. Taimre, and Z. I. Botev, Wiley Interdisc. Rev. Comput. Stat. 6, 386 (2014).
  3. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University Press, Cambridge, 2007).
  4. N. J. Kasdin, Proc. IEEE 83, 802 (1995).
  5. G. E. P. Box, G. M. Jenkins, G. C. Reinsel, and G. M. Ljung, Time Series Analysis: Forecasting and Control, 5th ed. (John Wiley & Sons, Hoboken, NJ, 2015).
  6. S. R. Dey and A. V. Oppenheim, in Proceedings of the 2007 IEEE International Conference on Acoustics, Speech and Signal Processing–ICASSP '07 (IEEE, Piscataway, NJ, 2007), Vol. 3, pp. 1493–1496.
  7. D. Koutsoyiannis, Water Resour. Res. 42, W01401 (2006).
  8. P.-S. Koutsourelakis and G. Deodatis, J. Eng. Mech.-ASCE 131, 397 (2005).
  9. F. M. Izrailev, A. A. Krokhin, N. M. Makarov, and O. V. Usatenko, Phys. Rev. E 76, 027701 (2007).
  10. P. Boufounos, in Proceedings of the 2007 IEEE International Conference on Acoustics, Speech and Signal Processing–ICASSP '07 (IEEE, Piscataway, NJ, 2007), Vol. 3, pp. 981–984.
  11. C. R. Rojas, J. S. Welsh, and G. C. Goodwin, in Proceedings of the 2007 American Control Conference (IEEE, Piscataway, NJ, 2007), pp. 122–127.
  12. O. V. Usatenko, S. S. Melnik, S. S. Apostolov, N. M. Makarov, and A. A. Krokhin, Phys. Rev. E 90, 053305 (2014).
  13. T. Schreiber and A. Schmitz, Phys. Rev. Lett. 77, 635 (1996).
  14. D. Kugiumtzis, Phys. Rev. E 60, 2808 (1999).
  15. T. Schreiber and A. Schmitz, Physica D 142, 346 (2000).
  16. D. Koutsoyiannis, Water Resour. Res. 36, 1519 (2000).
  17. A. Gupta and S. Nadarajah, Handbook of Beta Distribution and Its Applications (Taylor & Francis, Philadelphia, 2004).
  18. M. Zhu and A. Y. Lu, J. Stat. Educ. 12, 2 (2004).
  19. M. C. Cario and B. L. Nelson, Oper. Res. Lett. 19, 51 (1996).
  20. D. Kugiumtzis, Phys. Rev. E 66, 025201 (2002).
  21. A. Bunde, J. F. Eichner, J. W. Kantelhardt, and S. Havlin, Phys. Rev. Lett. 94, 048701 (2005).
  22. J. F. Eichner, J. W. Kantelhardt, A. Bunde, and S. Havlin, Phys. Rev. E 73, 016130 (2006).
  23. M. I. Bogachev, J. F. Eichner, and A. Bunde, Phys. Rev. Lett. 99, 240601 (2007).
  24. J. F. Eichner, J. W. Kantelhardt, A. Bunde, and S. Havlin, Phys. Rev. E 75, 011128 (2007).
  25. M. I. Bogachev, J. F. Eichner, and A. Bunde, Eur. Phys. J.-Spec. Top. 161, 181 (2008).
  26. J. F. Eichner, J. W. Kantelhardt, A. Bunde, and S. Havlin, in In Extremis, edited by J. Kropp and H.-J. Schellnhuber (Springer, Berlin, 2011), pp. 2–43.
  27. M. I. Bogachev and A. Bunde, Europhys. Lett. 97, 48011 (2012).
  28. E. Volpi, A. Fiori, S. Grimaldi, F. Lombardo, and D. Koutsoyiannis, Water Resour. Res. 51, 8570 (2015).
  29. F. Serinaldi and C. G. Kilsby, Water 8, 152 (2016).
  30. D. Koutsoyiannis, Hydrolog. Sci. J. 48, 3 (2003).
  31. D. Koutsoyiannis and A. Montanari, Water Resour. Res. 43, W05429 (2007).
  32. F. Serinaldi, Stoch. Env. Res. Risk A 22, 671 (2008).
  33. F. Serinaldi, Stoch. Env. Res. Risk A 23, 677 (2009).
  34. S.-M. Papalexiou, D. Koutsoyiannis, and A. Montanari, J. Hydrol. 411, 279 (2011).
  35. H. Tyralis and D. Koutsoyiannis, Stoch. Env. Res. Risk A. 25, 21 (2011).

Outline

Information

Phys. Rev. E 95, 023312– Published 23 February, 2017
  • Received 25 June 2016
  • Revised 16 January 2017

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation