Estimation of Fractal Dimension of a Noisy Time Series
|
10.5120/6813-9167 |
Muhammad Saleem Khan and Tanveer Ahmed Siddiqui. Article: Estimation of Fractal Dimension of a Noisy Time Series. International Journal of Computer Applications 45(10):1-6, May 2012. Full text available. BibTeX
@article{key:article,
author = {Muhammad Saleem Khan and Tanveer Ahmed Siddiqui},
title = {Article: Estimation of Fractal Dimension of a Noisy Time Series},
journal = {International Journal of Computer Applications},
year = {2012},
volume = {45},
number = {10},
pages = {1-6},
month = {May},
note = {Full text available}
}
Abstract
Estimation of the fractal dimension by using correlation dimension of precipitation time series play a fundamental role in the development of dynamic models of meteorological phenomena. As we know that the fractal dimension provides bounds for the number of independent variables necessary to model the system. We computed the correlation dimensions by Takens algorithm, Grassberger and Procaccia algorithm and by R/S method which gives the lower bound. In this paper, the fractal dimension by the method of correlation dimension of 20-years monsoon daily rainfall time series from June to September of Lahore region is estimated. The simulation of our time series is also considered which is based on wavelet fractional Brownian motion (wfBm) as a model that exhibits the self-similarity.
References
- Takens F. , Detecting strange attractors in turbulence, Dynamical Systems and Turbulence, Warwick 1980 lecture Notes in Math. (1981) 366-381.
- Packard N. H. , Crutchfield J. P. , Farmer J. D. , Shaw R. S. , Geometry from a time series, Phys. Rev. Lett. 45 (1980) 712–716.
- Gibson J. F. , Farmer J. D. , Casdagli M. , Eubank S. , An analytic approach to practical state space reconstruction, Physica D. 57 (1992) 1–30.
- Grassberger P. , Procaccia I. , Measuring the strangeness of strange attractors, Physica D. 9 (1983a) 189–208.
- Grassberger P. , Procaccia I. , Characterization of strange attractors, Phys. Rev. Lett. 50 (1983b) 346–349.
- Kantz, H. , Schreiber, T. , Nonlinear Time Series Analysis, Cambridge University Press Cambridge (1997).
- Sauer T. , Yorke J. , Casdagli M. , Embedology, J, Suitable delay times for continuous systems, Stat. Phys. 65 (1991) 579.
- Fraser A. M. , Swinney H. L. , Independent coordinates for strange attractors from mutual information, Phys. Rev. A 33, 1134 (1986).
- Hegger R. , Kantz H. H. , Schreiber T. , 'Practical implementation of nonlinear time series methods, The TISEAN package Chaos 9 (1999).
- Kennel M. B. , Brown R. , Abarbanel H. D. I. , Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A. 45 (1992) 3403.
- Grassberger P. , Hegger R. , Kantz H. , Schaffrath C. , Schreiber T. , On noise reduction methods for chaotic data, Chaos 3 (1993) 127.
- Provenzale L. A. , Smith R. and Murante G. , Distinguishing between low-dimensional dynamics and randomness in measured time series, access this article Physica D. 58 (1992) 31-49.
- Theiler J. , Lacunarity in a best estimator of fractal dimension, Phys. Lett. A. 135 (1988) 195.
- Takens F. , Braaksma B. L. J. , Broer H. W. , Dynamical Systems and Bifurcations, Lecture Notes in Math. Spring. (1985) 1125.
- Hurst, H. , 1951, "Long Term Storage Capacity of Reservoirs," Transactions of the American Society of Civil Engineers, 116, 770-799.
- Mandelbrot B. ,Van Ness J. W. , Fractional Brownian motions: Fractional noises and applications, SIAM Rev. 10, No. 4 (1968), 422-437.
- Abry, P. ; F. Sellan (1996), "The wavelet-based synthesis for the fractional Brownian motion proposed by F. Sellan and Y. Meyer: Remarks and fast implementation," Appl. and Comp. Harmonic Anal. , 3(4), pp. 377-383.