INFLUENCE OF THE CHOICE OF THE MODEL STRUCTURE FOR WORKING CAPACITY OF NONLINEAR GRANGER CAUSALITY APPROACH
Cite this article as:
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: https://doi.org/10.18500/0869-6632-2013-21-2-74-87
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.
1. Granger C.W.J. Investigating causal relations by econometric models and crossspectral methods // Econometrica. 1969. Vol. 37, No 3. P. 424.
2. Andrea Brovelli, Mingzhou Ding, Anders Ledberg, Yonghong Chen, Richard Nakamura, and Steven L. Bressler. Beta oscillations in a large-scale sensorimotor cortical network: Directional influences revealed by Granger causality // PNAS. 2004. Vol. 101. P. 9849.
3. L.A. Baccala, K. Sameshima, G. Ballester, A.C. Do Valle and C. Timo-Laria. Studing the interactions between brain structures via directed coherence and Granger causality // Applied sig. processing. 1998. Vol. 5. P. 40.
4. P. Tass, D. Smirnov, A. Karavaev, U. Barnikol, T. Barnikol, I. Adamchic, C. Hauptmann, N. Pawelcyzk, M. Maarouf, V. Sturm, H.-J. Freund, and B. Bezruchko. The causal relationship between subcortical local field potential oscillations and parkinsonian resting tremor // J. Neural Eng. 2010. Vol. 7. 016009.
5. И.И. Мохов, Д.А. Смирнов, П.И. Наконечный, С.С. Козленко, Ю. Куртс. Оценка взаимного воздействия Эль-Ниньо – Южного колебания и Индийского муссона // в «Современные проблемы динамики океана и атмосферы» / Ред. А.В. Фролов и Ю.Д. Реснянский. М.: ТРИАДА ЛТД, 2010. С. 251.
6. С.С. Козленко, И.И. Мохов, Д.А. Смирнов. Анализ причинно-следственных связей между Эль-Ниньо в Тихом океане и его аналогом в экваториальной Атлантике // Известия РАН. Физика атмосферы и океана. 2009. Т. 42, No 6. C. 754.
7. Yonghong Chen, Govindan Rangarajan, Jianfeng Feng, Mingzhou Ding. Analyzing Multiple Nonlinear Time Series with Extended Granger Causality // Physics Letters A. Vol. 324, Issue 1. P. 26.
8. И.В. Сысоев, А.С. Караваев, П.И. Наконечный. Роль нелинейности модели в диагностике связей при патологическом треморе методом грейнджеровской причинности // Изв. вузов. Прикладная нелинейная динамика. 2010. Т. 18, No 4. С. 81.
9. Marinazzo Daniele, Pellicoro Mario, and Stramaglia Sebastiano. Nonlinear parametric model for Granger causality of time series// Phys. Rev. E. 2006. Vol. 73. 066216.
10. Смирнов Д.А. Выявление нелинейных связей между стохастическими осцилляторами по временным рядам // Известия вузов. Прикладная нелинейная динамика, 2010. Т. 18, в. 2. С. 16.
11. Schreiber T. and Schmitz A. Surrogate time series // Physica D. 2000. Vol. 142. 346.
12. Kevin T. Dolan and Alexander Neiman. Surrogate analysis of multichannel data with frequency dependant time lag // Physical review E. Vol 65. 026108.
13. Baake E., Baake M., Bock H.G., and Briggs K.M. Fitting ordinary differential equations to chaotic data // Phys. Rev. A. 1992. Vol. 45, No 8. P. 5524.
14. Boris P. Bezruchko, Dmitry A. Smirnov and Ilya V. Sysoev. Identification of chaotic systems with hidden variables (modified Bock’s algorithm) // Chaos, Solitons & Fractals. 2006. Vol. 29. P. 82.
15. Bjork A. Solving Linear Squares Problem by Gram-Schmidt Orthogona lization // Math. Copm. 1976. Vol. 20. P. 325.
16. Дж. Голуб, Ч. Ван Лоун. Матричные вычисления: Пер. с англ. М.: Мир, 1999. 548 с.
17. Takens F. Detecting strange attractors in turbulence // Lecture Notes in Math. 1981. Vol. 898. P. 366.
18. Заславский Г.М., Сагдеев Р.З., Усиков Д.А., Черников А.А. Слабый хаос и квазирегулярные структуры. М.: Наука, 1991. 236 с.
BibTeX
author = {M. V. Kornilov and Ilya Vyacheslavovich Sysoev},
title = {INFLUENCE OF THE CHOICE OF THE MODEL STRUCTURE FOR WORKING CAPACITY OF NONLINEAR GRANGER CAUSALITY APPROACH},
year = {2013},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {21},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/influence-of-the-choice-of-the-model-structure-for-working-capacity-of-nonlinear-granger},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2013-21-2-74-87},pages = {74--87},issn = {0869-6632},
keywords = {The method of nonlinear Granger causality,the reconstruction of the time series,nonlinear dynamical systems.},
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. }}