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

For citation:

Kornilov M. V., Sysoev I. V. Influence of the choice of the model structure for working capacity of nonlinear Granger causality approach. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 2, pp. 74-87. DOI: 10.18500/0869-6632-2013-21-2-74-87

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 2013no2p074.pdf
(downloads: 147)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
530.182, 51-73
DOI: 
10.18500/0869-6632-2013-21-2-74-87

Influence of the choice of the model structure for working capacity of nonlinear Granger causality approach

Autors: 
Kornilov Maksim Vyacheslavovich, Saratov State University
Sysoev Ilya Vyacheslavovich, Saratov State University
Abstract: 

Currently, the method of nonlinear Granger causality is actively used in many applications in medicine, biology, physics, to identify the coupling between objects from the records of their oscillations (time series) using forecasting models. In this paper the impact of choosing the model structure on the method performance is investigated. The possibility of obtaining reliable estimates of coupling is numerically demonstrated, even if the structure of the constructed forecasting model differs from that of the reference system

Key words: 
The method of nonlinear Granger causality
the reconstruction of the time series
Nonlinear dynamical systems
Reference: 
  1. Granger CWJ. Investigating causal relations by econometric models and cross-spectral methods. Econometrica. 1969;37(3):424–438.
  2. Andrea Brovelli, Mingzhou Ding, Anders Ledberg, Yonghong Chen, Richard Nakamura, Steven L. Bressler. Beta oscillations in a large-scale sensorimotor cortical network: Directional influences revealed by Granger causality. PNAS. 2004;101(26):9849–9854. DOI: 10.1073/pnas.0308538101
  3. Baccala LA, Sameshima K, Ballester G, Do Valle AC, Timo-Laria C. Studing the interactions between brain structures via directed coherence and Granger causality. Applied sig. Processing. 1998;5(1):40–48. DOI:10.1007/s005290050005
  4. Tass P, Smirnov D, Karavaev A, Barnikol U, Barnikol T, Adamchic I, Hauptmann C, Pawelcyzk N, Maarouf M, Sturm V, Freund H-J, Bezruchko B. The causal relationship between subcortical local field potential oscillations and parkinsonian resting tremor. J. Neural Eng. 2010;7(1):016009. DOI: 10.1088/1741-2560/7/1/016009
  5. Mokhov II, Smirnov DA, Tip PI, Kozlenko SS, Kurts Yu. Assessment of the mutual impact of El Niño - the Southern Wobble and the Indian Monsoon. Current problems of ocean and atmospheric dynamics. Moscow: TRIADA LTD. 2010;251–268.
  6. Kozlenko SS, Mokhov II, Smirnov DA. Analysis of the cause and effect relationships between El Niño in the Pacific and its analog in the equatorial Atlantic. Izvestiya. Atmospheric and Oceanic Physics. 2009;45(6):704–713. DOI: 10.1134/S0001433809060036.
  7. Yonghong Chen, Govindan Rangarajan, Jianfeng Feng, Mingzhou Ding. Analyzing Multiple Nonlinear Time Series with Extended Granger Causality. Physics Letters A. 2004;324(1):26–35. DOI:10.1016/j.physleta.2004.02.032
  8. Sysoev IV, Karavaev AS, Nakonechnyj PI. Role of model nonlinearity for granger causality based coupling estimation for pathological tremor. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;18(4):81-90. DOI: 10.18500/0869-6632-2010-18-4-81-90.
  9. Marinazzo D, Pellicoro M, Stramaglia S. Nonlinear parametric model for Granger causality of time series. Phys. Rev. E. 2006;73(6):066216. DOI:10.1103/PhysRevE.73.066216
  10. Smirnov DA. Revealing nonlinear couplings between stochastic oscillators from time series. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;18(2):16-38. DOI: 10.18500/0869-6632-2010-18-2-16-38.
  11. Schreiber T, Schmitz A. Surrogate time series. Physica D. 2000;142(3-4):346–382. DOI:10.1016/S0167-2789(00)00043-9
  12. Dolan T, Neiman A. Surrogate analysis of multichannel data with frequency dependant time lag. Physical review E. 2002;65(2):026108. DOI: 10.1103/PhysRevE.65.026108
  13. Baake E, Baake M, Bock HG, Briggs KM. Fitting ordinary differential equations to chaotic data. Phys. Rev. A. 1992;45(8):5524–5529. DOI: 10.1103/physreva.45.5524.
  14. Bezruchko BP, Smirnov DA, Sysoev IV. Identification of chaotic systems with hidden variables (modified Bock’s algorithm). Chaos, Solitons & Fractals. 2006;29(1):82–90. DOI:10.1016/j.chaos.2005.08.204
  15. Bjork A. Solving Linear Squares Problem by Gram-Schmidt Orthogona lization . Math. Copm. 1976;20:325–328.
  16. Golub G, Van Loan C. Matrix Computations. Baltimore, London: The Johns Hopkins University Press; 1996. 694 p.
  17. Takens F. Detecting strange attractors in turbulence. Lecture Notes in Math. 1981; 898(21):366–381. DOI:10.1007/BFb0091924
  18. Zaslavsky GM, Sagdeev RZ, Usikov DA, Chernikov AA. Weak chaos and quasi-regular structures. Moscow: Nauka; 1991. 236 p. (In Russian).
Received: 
07.11.2011
Accepted: 
28.03.2013
Published: 
31.07.2013
Short text (in English):
PDF icon a2013no2p074.pdf
(downloads: 119)
  • 2024 reads