Algorithm for computing time correlation functions in non-stationary complex dynamic systems
Jiu Zhang(张鹫)1, Lifu Jin(金立孚)2, Bo Zheng(郑波)3,†, Xiongfei Jiang(蒋雄飞)4, Tingting Chen(陈婷婷)5, Cong Xu(徐匆)1,‡, and Yanqing Hu(胡延庆)1
1 Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518055, China; 2 School of Economics and Management, Wenzhou University of Technology, Wenzhou 325035, China; 3 School of Physics and Astronomy, Yunnan University, Kunming 650091, China; 4 College of Finance and Information, Ningbo University of Finance and Economics, Ningbo 315175, China; 5 School of Finance, Zhejiang University of Finance and Economics, Hangzhou 310000, China
Abstract For non-stationary complex dynamic systems, a standardized algorithm is developed to compute time correlation functions, addressing the limitations of traditional methods reliant on the stationary assumption. The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework. Further, it is verified by a practical application in complex financial systems, demonstrating its potential in various complex dynamic systems.
(Computational methods in statistical physics and nonlinear dynamics)
Fund: Project supported by the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation (Grant No. GZC20231050), the National Natural Science Foundation of China (Grant Nos. 12175193 and 11905183), and the 13th Five-year plan for Education Science Funding of Guangdong Province (Grant No. 2021GXJK349).
Corresponding Authors:
Bo Zheng, Cong Xu
E-mail: zhengbo@zju.edu.cn;xuc6@sustech.edu.cn
Cite this article:
Jiu Zhang(张鹫), Lifu Jin(金立孚), Bo Zheng(郑波), Xiongfei Jiang(蒋雄飞), Tingting Chen(陈婷婷), Cong Xu(徐匆), and Yanqing Hu(胡延庆) Algorithm for computing time correlation functions in non-stationary complex dynamic systems 2025 Chin. Phys. B 34 038904
[1] Kwapień J and Drożdż S 2012 Phys. Rep. 515 115 [2] Young J G, St O G, Laurence E, Murphy C, Hébert D L and Desrosiers P 2019 Phys. Rev. X 9 041056 [3] Papaefthymiou E S, Iordanou C and Papadopoulos F 2024 Phys. Rev. Lett. 132 257401 [4] Wang J, Zhang Y J, Xu C, Li J, Sun J, Xie J, Feng L, Zhou T and Hu Y 2024 Nat. Commun. 15 2849 [5] Plerou V, Gopikrishnan P, Rosenow B, Amaral L A N and Stanley H E 1999 Phys. Rev. Lett. 83 1471 [6] Bouchaud J P, Matacz A and Potters M 2001 Phys. Rev. Lett. 87 228701 [7] Wang Y J, Cheng H, Edwards R L, He Y Q, Kong X G, An Z S, Wu J Y, Kelly M J, Dykoski C A and Li X D 2005 Science 308 854 [8] Shen J and Zheng B 2009 Europhys. Lett. 86 48005 [9] Jiang X F and Zheng B 2012 Europhys. Lett. 97 48006 [10] Chen T T, Zheng B, Li Y and Jiang X F 2018 New J. Phys. 20 073005 [11] Zhang J, Jin L F, Zheng B, Li Y and Jiang X F 2022 Physica A 589 126615 [12] Zhang J, Zheng B, Jin L F, Li Y and Jiang X F 2024 Chin. J. Phys. 88 756 [13] Zhang X, Huang T, Wang C P and Zeng C H 2023 Physica A 609 128316 [14] Ivanov P C, Rosenblum M G, Peng C K, Mietus J, Havlin S, Stanley H E and Goldberger A L 1996 Nature 383 323 [15] Amaral L A N, Goldberger A L, Ivanov P C and Stanley H E 1998 Phys. Rev. Lett. 81 2388 [16] Mallika M C, Prabhaa S S, Asokan K, Kumar K S A, Ramamohan T R and Kumar K S 2021 Phys. Rev. E 104 054217 [17] Podobnik B and Stanley H E 2008 Phys. Rev. Lett. 100 084102 [18] Bassler K E, McCauley J L and Gunaratne G H 2007 Proc. Natl Acad. Sci. USA 104 17287 [19] Qiu T, Zheng B and Chen G 2010 New J. Phys. 12 043057 [20] Pan C P, Zheng B, Wu Y Z, Wang Y and Tang X W 2004 Phys. Lett. A 329 130 [21] Cherstvy A G, Vinod D, Aghion E, Chechkin A V and Metzler R 2017 New J. Phys. 19 063045 [22] Breakspear M 2017 Nat. Neurosci. 20 340 [23] Laloux L, Cizeau P, Bouchaud J P and Potters M 1999 Phys. Rev. Lett. 83 1467 [24] Plerou V, Gopikrishnan P, Rosenow B, Amaral L A N, Guhr T and Stanley H E 2002 Phys. Rev. E 65 066126 [25] Qiu T, Zheng B, Ren F and Trimper S 2006 Phys. Rev. E 73 065103 [26] Nagy M, Akos Z, Biro D and Vicsek T 2010 Nature 464 890 [27] Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E and Goldberger A L 1994 Phys. Rev. E 49 1685 [28] Buldyrev S V, Goldberger A L, Havlin S, Mantegna R N, Matsa M E, Peng C K, Simons M and Stanley H E 1995 Phys. Rev. E 51 5084 [29] Hu K, Ivanov P C, Chen Z, Carpena P and Stanley H E 2001 Phys. Rev. E 64 011114 [30] Chen Z, Ivanov P C, Hu K and Stanley H E 2002 Phys. Rev. E 65 041107 [31] Ma Q D Y, Bartsch R P, Bernaola-Galván P, Yoneyama M and Ivanov P C 2010 Phys. Rev. E 81 031101 [32] Zhou W X 2008 Phys. Rev. E 77 066211 [33] Podobnik B, Jiang Z Q, Zhou W X and Stanley H E 2011 Phys. Rev. E 84 066118 [34] Zebende G F 2011 Physica A 390 614 [35] Oświeçimka P, Drożdż S, Forczek M, Jadach S and Kwapień J 2014 Phys. Rev. E 89 023305 [36] Kwapień J, Oświeçimka P and Drożdż S 2015 Phys. Rev. E 92 052815 [37] French K R, Schwert G W and Stambaugh R F 1987 J. Financ. Econ. 19 3 [38] Bekaert G and Wu G J 2000 Rev. Financ. Stud. 13 1 [39] Engle R F 1982 Econometrica 50 987 [40] Challet D and Zhang Y C 1997 Physica A 246 407 [41] Fehr E and Fischbacher U 2003 Nature 425 785 [42] Camerer C F and Fehr E 2006 Science 311 47 [43] Chakraborti A, Toke I M, Patriarca M and Abergel F 2011 Quant. Financ. 11 1013 [44] Chen J J, Tan L and Zheng B 2015 Sci. Rep. 5 8399 [45] Li Y, Zheng B, Chen T T and Jiang X F 2017 Plos One 12 12 [46] The website of the dataset is https://cn.investing.com [47] Liu Y, Gopikrishnan P, Cizeau, Meyer, Peng and Stanley H E 1999 Phys. Rev. E 60 1390 [48] Menkhoff L 2010 J. Bank. Fin. 34 2573
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