In different fields of physical research, we often meet the problem of distinguishing between bidirectional and unidirectional couplings of oscillatory systems, i.e., mutual influence and one-way influence, on the basis of the observed time series. In this work, it is shown that a widely used approach, based on the calculation of prediction errors of empirical models (Granger causality), may give spurious conclusions on bidirectional coupling if a sampling interval exceeds a certain intrinsic time scale of the studied systems. Taking this effect into account, we propose and illustrate by standard examples a statistical test which allows one to reveal bidirectional coupling with specified confidence probability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Bezruchko, V. Ponomarenko, M. G. Rosenblum, and A. S. Pikovsky, Chaos, 13, No. 1, 179 (2003).
Y. C. Hung and C.K. Hu, Phys. Rev. Lett., 101, No. 24, 244102 (2008).
B. Kralemann, L. Cimponeriu, M. Rosenblum, et al., Phys. Rev. E, 76, No. 5, 055201(R) (2007).
W. Wang, B.T. Anderson, R.K. Kaufmann, and R.B. Myneni, J. Climate, 17, No. 24, 4752 (2004).
I. I. Mokhov and D.A. Smirnov, Izvestiya, Atmos. Ocean. Phys., 44, No. 3, 263 (2008).
I. I. Mokhov and D.A. Smirnov, Doklady Earth Sci., 427, No. 5, 798 (2009).
E. Pereda, R. Quian Quiroga, and J. Bhattacharya, Progr. Neurobiol., 77, No. 10, 1 (2005).
J. Brea, D. F. Russell, and A. B. Neiman, Chaos, 16, No. 2, 026111 (2006).
B.P. Bezruchko, V. I. Ponomarenko, M. D. Prokhorov, et al., Uspekhi—Physics, 51, No. 3, 304 (2008).
D. Smirnov, T. Barnikol, U. Barnikol, et al., Europhys. Lett., 83, No. 2, 20003 (2008).
M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. E, 64, No. 4, 045202(R) (2001).
D. A. Smirnov and B.P. Bezruchko, Phys. Rev. E, 68, No. 4, 046209 (2003).
D. A. Smirnov, J. Commun. Technol. Electron., 51, No. 5, 534 (2006).
D. A. Smirnov, E. V. Sidak, and B. P. Bezruchko, Tech. Phys. Lett., 37, No. 1, 30 (2011).
C. W. J. Granger, Econometrica, 37, No. 3, 424 (1969).
C. W. J. Granger, J. Econ. Dyn. Control, 2, No. 6, 329 (1980).
C. A. Sims, Econometrica, 39, No. 3, 545 (1971).
M. Marcellino, J. Busin. Econom. Stat., 17, No. 1, 129 (1999).
E. Renault, K. Sekkat, and A. Szafarz, J. Emp. Fin., 5, No. 1, 47 (1998).
G. Box and G. Jenkins, Time-Series Analysis: Forecasting and Control, Holden-Day, San Francisco (1970)
G. A. F. Seber and A. J. Lee, Linear Regression Analysis, Wiley, Hoboken, N. J. (2003).
N. N. Nikitin and V.D.Razevig, USSR Comput. Math. Math. Phys., 18, No. 1, 102 (1978).
J. Timmer, M. Lauk, W. Pfleger, and G. Deuschl, Biol. Cybern., 78, No. 1, 349 (1998).
S.P.Kuznetsov, Radiophys. Quantum Electron., 25, No. 12, 996 (1982).
S.P. Kuznetsov, Radiophys. Quantum Electron., 28, No. 8, 681 (1985).
K. Ikeda, Opt. Commun., 30, No. 2, 257 (1979).
R. Lang and K. Kobayashi, IEEE J. Quantum Electron., 16, No. 3, 347 (1980).
D. A. Smirnov and B.P. Bezruchko, Europhys. Lett., 100, No. 1, 10005 (2012).
Ya.A. Molkov, D. N. Mukhin, E.M. Loskutov, et al., Phys. Rev. E, 80, No. 4, 046207 (2009).
Ya. A. Molkov, E. M. Loskutov, D. N. Mukhin, and A.M. Feigin, Phys. Rev. E, 85, No. 3, 036216 (2012).
I. Vlachos and D. Kugiumtzis, Phys. Rev. E, 82, No. 1, 016207 (2010).
L. Faes, G. Nollo, and A. Porta, Phys. Rev. E, 83, No. 5, 051112 (2011).
T. Schreiber and A. Schmitz, Physica D, 142, Nos. 3–4, 346 (2000).
K. Dolan and A. Neiman, Phys. Rev. E, 65, No. 2, 026108 (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 55, Nos. 10–11, pp. 736–750, October–November 2012.
Rights and permissions
About this article
Cite this article
Smirnov, D.A., Bezruchko, B.P. Revealing mutual influence of oscillatory systems from the observation data. Radiophys Quantum El 55, 662–675 (2013). https://doi.org/10.1007/s11141-013-9404-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11141-013-9404-6