The entropy profile – a function describing statistical dependences. (English) Zbl 0923.58027
Summary: 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.
References:
| [1] | R. Badii and A. Politi,J. Stat. Phys. 40:725-750 (1985). · Zbl 0627.58028 · doi:10.1007/BF01009897 |
| [2] | C. Bandt and B. Pompe, Entropy profiles of speech signals, preprint, Greifswald (1992). |
| [3] | A. M. Blokh and M. Yu. Lyubich,Funct. Anal. Appl. 21:148-150 (1987). · doi:10.1007/BF01078030 |
| [4] | P. Collet and J.-P. Eckmann,Iterated Maps on the Interval as Dynamical Systems (Birkh?user, Basel, 1980). · Zbl 0465.58018 |
| [5] | P. Collet, J. L. Lebowitz, and A. Porzio,J. Stat. Phys. 47:609-643 (1987). · Zbl 0683.58023 · doi:10.1007/BF01206149 |
| [6] | C. D. Cutler,J. Stat. Phys. 62:651-708 (1991). · Zbl 0738.58029 · doi:10.1007/BF01017978 |
| [7] | J.-P. Eckmann and D. Ruelle,Rev. Mod. Phys. 57:617-656 (1985). · Zbl 0989.37516 · doi:10.1103/RevModPhys.57.617 |
| [8] | 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). · Zbl 0712.58038 · doi:10.1109/18.32121 |
| [9] | P. Grassberger,Z. Naturforsch. 43a:671-680 (1988). |
| [10] | P. Grassberger and I. Procaccia,Phys. Rev. A 28:2591-2593 (1983). · doi:10.1103/PhysRevA.28.2591 |
| [11] | P. Grassberger, T. Schreiber, and C. Schaffrath,Bifurcation Chaos 1:521-548 (1991). · Zbl 0874.58029 · doi:10.1142/S0218127491000403 |
| [12] | J. Guckenheimer and S. Johnson,Ann. Math. 132:71-130 (1990). · Zbl 0708.58007 · doi:10.2307/1971501 |
| [13] | F. Hofbauer and G. Keller,Commun. Math. Phys. 127:319-337 (1990). · Zbl 0702.58034 · doi:10.1007/BF02096761 |
| [14] | S. Isola and A. Politi,J. Stat. Phys. 61:263-291 (1990). · doi:10.1007/BF01013965 |
| [15] | 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). · doi:10.1016/0375-9601(85)90065-9 |
| [16] | J. Milnor,Commun. Math. Phys. 99:177-195 (1985);102:517-519 (1985). · Zbl 0595.58028 · doi:10.1007/BF01212280 |
| [17] | Y. Pomeau and P. Manneville,Commun. Math. Phys. 74:189-197 (1980). · doi:10.1007/BF01197757 |
| [18] | A. Renyi,Probability Theory (North-Holland, Amsterdam, 1970). · Zbl 0245.60002 |
| [19] | 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. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
