ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Smirnov D. A., Bezruchko B. P. Effect of rare sampling on estimation of directional couplings from time series. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 2, pp. 61-73. DOI: 10.18500/0869-6632-2013-21-2-61-73

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Russian
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Article
UDC: 
530.18

Effect of rare sampling on estimation of directional couplings from time series

Autors: 
Smirnov Dmitrij Alekseevich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Bezruchko Boris Petrovich, Saratov State University
Abstract: 

The problem of detection and quantitative estimation of directional couplings (mutual influences) between systems from discrete records of their oscillations (time series) arises in different fields of research. This work shows that results of the traditional «Granger causality» approach depend essentially on a sampling interval (a time step). We have revealed the causes and character of the influence of a sampling interval on numerical values of coupling estimates. As well, we have explained why one can get erroneous conclusions about bidirectional coupling for unidirectionally coupled systems in the case of a large sampling interval (rare sampling). The rare sampling effect is demonstrated both for linear and nonlinear systems in different dynamical regimes.

Reference: 
  1. Blechman AI. Synchronize dynamic systems. Moscow: Nauka; 1971. 894 p.
  2. Pikovsky NPP, Rosenblum MG, Kurts Yu. Synchronization. A fundamental nonlinear phenomenon. Moscow: Tehnosphera; 2003. 496 p.
  3. Anishchenko VS, Astakhov VV, Vadivasova ТЕ, Neiman AB, Strelkova GI, Schimansky-Geier L. Nonlinear effects of chaotic and stochastic systems. Moscow-Izhevsk: ICR; 2003. 544p.
  4. Kuznetsov AP, Emelyanova JP, Sataev IR, Tyuryukina LV. Synchronization in tasks. Saratov: Nauka; 2010. 256 p.
  5. Rosenblum MG, Pikovsky AS, Kurths J, Schafer C, Tass PA. Phase synchronization: from theory to data analysis. Editors: Moss F, Gielen S. Neuro-informatics. Handbook of Biological Physics (V. 4). New-York: Elsevier Science. 2001;279–321.
  6. Vadivasova TE, Anishchenko VS. Relationship between frequency and phase characteristics of chaos: Two criteria of synchronization. Journal of Communications Technology and Electronics. 2004;49(1):69-75.
  7. Hramov AYe, Koronovskii AA. An approach to chaotic synchronization. Chaos. 2004;14(3):603–610. DOI:10.1063/1.1775991
  8. Hramov AE, Koronovskii AA, Ponomarenko VI, Prokhorov MD. Detection of synchronization from univariate data using wavelet transform. Phys. Rev. E. 2007;75(5):056207. DOI:10.1103/PHYSREVE.75.056207
  9. Pavlov AN, Sosnovtseva OV, Pavlova ON, Mosekilde E, Holstein-Rathlou N-H. Characterizing multimode interaction in renal autoregulation. Physiological Measurement. 2008;29:945–958.
  10. Kralemann B, Cimponeriu L, Rosenblum M, Pikovsky A, Mrowka R. Uncovering interaction of coupled oscillators from data. Phys. Rev. E. 2007;76(5):055201(R). DOI: 10.1103/PhysRevE.76.055201
  11. Bezruchko B, Ponomarenko V, Rosenblum MG, Pikovsky AS. Characterizing direction of coupling from experimental observations. Chaos. 2003;13(1):179–184. DOI: 10.1063/1.1518425
  12. Hung Y-C, Hu C-K. Chaotic communication via temporal transfer entropy. Phys. Rev. Lett. 2008;101(24):244102. DOI:10.1103/PhysRevLett.101.244102
  13. Palus M, Novotna D. Quasi-biennial oscillations extracted from the monthly NAO index and temperature records are phase-synchronized. Nonlinear Processes in Geophysics. 2006;13(3):287–296. DOI:10.5194/npg-13-287-2006
  14. Mokhov II, Smirnov DA. Study of the mutual influence of the El Niño-Southern Oscillation processes and the North Atlantic and Arctic Oscillations. Izvestiya. Atmospheric and Oceanic Physics. 2006;42(5):598-614. DOI: 10.1134/S0001433806050069.
  15. Mokhov II, Smirnov DA, Karpenko AA. Estimates of the association of changes in global near-surface temperature with different natural and anthropogenic factors based on observational data. Doklady Akademii Nauk. 2012;443(2):225–231.
  16. Pereda E, Quian Quiroga R, Bhattacharya J. Nonlinear multivariate analysis of neurophysiological signals. Progr. in Neurobiology. 2005;77(1-2):1–37. DOI: 10.1016/j.pneurobio.2005.10.003
  17. Brea J, Russell DF, Neiman AB. Measuring direction in the coupling of biological oscillators: A case study for electroreceptors of paddlefish. Chaos. 2006;16(2):026111. DOI: 10.1063/1.2201466
  18. Bezruchko BP, Ponomarenko VI, Prokhorov MD, Smirnov DA, Tass PA. Modeling nonlinear oscillatory systems and diagnostics of coupling between them using chaotic time series analysis: applications in neurophysiology. Phys. Usp. 2008;51(3):304–310. DOI: 10.3367/UFNr.0178.200803h.0323.
  19. Smirnov D, Barnikol T, Barnikol U, Bezruchko BP, Hauptmann C, Buehrle C, Maarouf M, Sturm V, Freund H-J, Tass PA. The generation of parkinsonian tremor as revealed by directional coupling analysis. Europhysics Letters. 2008;83(2):20003. DOI: 10.1209/0295-5075/83/20003
  20. Sysoeva MV, Sysoev IV. Mathematical modeling of encephalogram dynamics during epileptic seizure. Technical Physics Letters. 2012;38(2):151-154. DOI 10.1134/S1063785012020137.
  21. Filina EV. Dynamics of local potentials of brain at the absence-epilepsy: empirical modelling. Izvestiya VUZ. Applied Nonlinear Dynamics. 2011;19(4):109-123. DOI: 10.18500/0869-6632-2011-19-4-109-123.
  22. Granger CWJ. Investigating causal relations by econometric models and cross-spectral methods. Econometrica. 1969;37(3):424–438.
  23. Granger CWJ. Testing for causality. A personal viewpoint. J. Economic Dynamics and Control. 1980;2(1):329–352.
  24. Sims CA. Discrete approximations to continuous time distributed lags in econometrics. Econometrica. 1971;39(3):545–563. DOI:10.2307/1913265
  25. Marcellino M. Some consequences of temporal aggregation in empirical analysis. J. Business and Economic Statistics. 1999;17(1):129–136. DOI:10.1080/07350015.1999.10524802
  26. Box J, Jenkins G. Time series analysis. Forecast and management. V. 1,2. Moscow: Mir; 1974. 406 p. (In Russian).
  27. Seber J. Linear regression analysis. Moscow: Mir; 1974. 456 p.
  28. Timmer J, Lauk M, Pfleger W, Deuschl G. Cross-spectral analysis of physiological tremor and muscle activity: I. Theory and application to unsynchronized electromyogram. Biol. Cybern. 1998;78(5):349–357. DOI: 10.1007/s004220050439
  29. Kuznetsov SP. Doubling bifurcations in a simple distributed system model. Radiophysics and Quantum Electronics. 1982;25(11):1364–1368.
  30. Kuznetsov SP. Versatility and similarity in the behavior of related Feigenbaum systems. Radiophysics and Quantum Electronics. 1985;28(8):991–1007.
  31. Ikeda K. Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Commun. 1979;30(2):257–261. DOI:10.1016/0030-4018(79)90090-7
  32. Lang R, Kobayashi K. External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron. 1980;16(3):347–355. DOI: 10.1109/JQE.1980.1070479
  33. Elhadj Z, Sprott JC. A minimal 2-D quadratic map with quasi-periodic route to chaos. Int. J. Bifurcation Chaos. 2008;18(5):1567–1577. DOI:10.1142/S021812740802118X
  34. Ancona N, Marinazzo D, Stramaglia S. Radial basis function approach to nonlinear Granger causality of time series. Phys. Rev. E. 2004;70(5):056221. DOI: 10.1103/PhysRevE.70.056221
  35. Marinazzo D, Pellicoro M, Stramaglia S. Kernel method for nonlinear Granger causality. Phys. Rev. Lett. 2008;100(14):144103. DOI: 10.1103/PhysRevLett.100.144103
  36. Hlavackova-Schindler K, Palus M, Vejmelka M, Bhattacharya J. Causality detection based on information-theoretic approaches in time series analysis. Physics Reports. 2007;441(1):1–46. DOI:10.1016/J.PHYSREP.2006.12.004
  37. Takens F. Detecting strange attractors in turbulence. Lec. Notes in Math. 1981;898:366–381. DOI:10.1007/BFb0091924
  38. Molkov YaA, Mukhin DN, Loskutov EM, Feigin AM, Fidelin GA. Using the minimum description length principle for global reconstruction of dynamic systems from noisy time series. Phys. Rev. E. 2009;80(4):046207. DOI: 10.1103/PhysRevE.80.046207
  39. Yakhno YV, Molkov JI, Muhin DN, Loskutov EM, Feigin AM. Reconstruction of an evolution operator as a technique of analysis of epileptiform electric brain activity. Izvestiya VUZ. Applied Nonlinear Dynamics. 2011;19(6):156-172. DOI: 10.18500/0869-6632-2011-19-6-156-172.
  40. Vlachos I, Kugiumtzis D. Nonuniform state-space reconstruction and coupling detection. Phys. Rev. E. 2010;82(1):016207. DOI: 10.1103/PhysRevE.82.016207
  41. Faes L, Nollo G, Porta A. Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique. Phys. Rev. E. 2011;83(5):051112. DOI: 10.1103/PhysRevE.83.051112
  42. Smirnov DA, Bezruchko BP. Spurious causalities due to low temporal resolution: Towards detection of bidirectional coupling from time series. Europhys. Lett. 2012;100(1):10005-6. DOI:10.1209/0295-5075/100/10005.
Received: 
03.10.2012
Accepted: 
29.04.2013
Published: 
31.07.2013
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