Evolution of Complex Systems and 1/f Noise: from Physics to Financial Markets

Abstract:

We introduce the stochastic multiplicative model of time intervals between the events, defining a multiplicative point process and analyze the statistical properties of the signal. Such a model system exhibits power-law spectral density S(f)~1/fβ, scaled as power of frequency for various values of β between 0.5 and 2. We derive explicit expressions for the power spectrum and other statistics and analyze the model system numerically. The specific interest of our analysis is related with the theoretical modeling of the nonlinear complex systems exhibiting fractal behavior and self-organization.

• Periodical: Solid State Phenomena (Volumes 97-98)
• Pages: 65-70
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.97-98.65
• Online since: April 2004
• Authors: V. Gontis, B. Kaulakys, M. Alaburda, J. Ruseckas
• Keywords: 1/f Noise, Complex System, Fractal, Self-Organization

References

[1] D.L. Gilden, T. Thornton and M.W. Mallon: Science Vol. 267 (1995), pp.1837-1839.

[2] H. Wong: Microel. Reliab. Vol. 43 (2003), pp.585-599.

[3] B. Kaulakys and T. Meškauskas: Phys. Rev. E Vol. 58 (1998), pp.7013-7019.

[4] S. Maslov, C. Tang, Y. -C. Zhang: Phys. Rev. Lett. Vol. 83 (1999), pp.2449-2452.

[5] S. Thurner, S.B. Lowen, M.C. Feurstein, C. Heneghan, H.G. Feichtinger, M.C. Teich: Fractals Vol. 5 (1997), pp.565-595. 6 Title of Publication (to be inserted by the publisher).

DOI: 10.1142/s0218348x97000462

[6] B. Kaulakys and T. Meškauskas: Phys. Rev. E Vol. 58 (1998), pp.7013-7019.

[7] B. Kaulakys: Phys. Lett. A Vol. 257 (1999), pp.37-42.

[8] V. Gontis: Lithuanian J. Phys. Vol. 41 (2001), pp.551-555; cond-mat/0201514.

[9] V. Gontis: Nonl. Anal.: Model. Contr. Vol. 7 (2002), pp.43-54; cond-mat/0211317.

[10] V. Gontis and B. Kaulakys: cond-mat/0303089.