Abstract
In an attempt to find parameters of a time series which are absolutely robust with respect to nonlinear distortion, we introduce a function called the entropy profile which measures in some sense the distance between the given process and white noise. This concept combines a clear definition and a simple algorithm, which apply to arbitrary stationary time series, with an informative graphical representation similar to the Fourier spectrum. For sequences derived from one-dimensional maps, the entropy profile indicates periodic and almost periodic behavior and the presence of Markov partitions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Badii and A. Politi,J. Stat. Phys. 40:725–750 (1985).
C. Bandt and B. Pompe, Entropy profiles of speech signals, preprint, Greifswald (1992).
A. M. Blokh and M. Yu. Lyubich,Funct. Anal. Appl. 21:148–150 (1987).
P. Collet and J.-P. Eckmann,Iterated Maps on the Interval as Dynamical Systems (Birkhäuser, Basel, 1980).
P. Collet, J. L. Lebowitz, and A. Porzio,J. Stat. Phys. 47:609–643 (1987).
C. D. Cutler,J. Stat. Phys. 62:651–708 (1991).
J.-P. Eckmann and D. Ruelle,Rev. Mod. Phys. 57:617–656 (1985).
A. M. Fraser,IEEE Trans. Information Theory 35:245–262 (1989); A. M. Fraser and H. L. Swinney,Phys. Rev. A 33:1134–1140 (1986).
P. Grassberger,Z. Naturforsch. 43a:671–680 (1988).
P. Grassberger and I. Procaccia,Phys. Rev. A 28:2591–2593 (1983).
P. Grassberger, T. Schreiber, and C. Schaffrath,Bifurcation Chaos 1:521–548 (1991).
J. Guckenheimer and S. Johnson,Ann. Math. 132:71–130 (1990).
F. Hofbauer and G. Keller,Commun. Math. Phys. 127:319–337 (1990).
S. Isola and A. Politi,J. Stat. Phys. 61:263–291 (1990).
P. Martien, S. C. Pope, P. L. Scott, and R. S. Shaw,Phys. Lett. 110A:399–404 (1985); R. Shaw,The Dripping Faucet as a Model Chaotic System (Aerial Press, Santa Cruz, California, 1984).
J. Milnor,Commun. Math. Phys. 99:177–195 (1985);102:517–519 (1985).
Y. Pomeau and P. Manneville,Commun. Math. Phys. 74:189–197 (1980).
A. Renyi,Probability Theory (North-Holland, Amsterdam, 1970).
S. van Strien, Smooth dynamics on the interval, inNew Directions in Dynamical Systems, T. Bedford and J. Swift, eds. (Cambridge University Press, 1988), pp. 57–119.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bandt, C., Pompe, B. The entropy profile — A function describing statistical dependences. J Stat Phys 70, 967–983 (1993). https://doi.org/10.1007/BF01053603
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01053603