Publication Abstracts
Dubovikov et al. 2004
, N.V. Starchenko, and , 2004: Dimension of the minimal cover and fractal analysis of time series. Physica A, 339, 591-608, doi:10.1016/j.physa.2004.03.025.
We develop a new approach to the fractal analysis of time series of various natural, technological and social processes. To compute the fractal dimension, we introduce the sequence of the minimal covers associated with a decreasing scale δ. This results in new fractal characteristics: the dimension of minimal covers D-μ, the variation index It related to D, and the new multifractal spectrum ζ(q) defined on the basis of μ. Numerical computations performed for the financial series of companies entering Dow Jones Industrial Index show that the minimal scale τ(μ), which is necessary for determining μ with an acceptable accuracy, is almost two orders smaller than an analogous scale for the Hurst index H. This allows us to consider μ as a local fractal characteristic. The presented fractal analysis of the financial series shows that μ(t) is related to the stability of underlying processes. The results are interpreted in terms of the feedback.
- Get PDF (461 kB)
- PDF documents require the free Adobe Reader or compatible viewing software to be viewed.
- Go to journal article webpage
Export citation: [ BibTeX ] [ RIS ]
BibTeX Citation
@article{du06000k, author={Dubovikov, M. M. and Starchenko, N. V. and Dubovikov, M. S.}, title={Dimension of the minimal cover and fractal analysis of time series}, year={2004}, journal={Physica A}, volume={339}, pages={591--608}, doi={10.1016/j.physa.2004.03.025}, }
[ Close ]
RIS Citation
TY - JOUR ID - du06000k AU - Dubovikov, M. M. AU - Starchenko, N. V. AU - Dubovikov, M. S. PY - 2004 TI - Dimension of the minimal cover and fractal analysis of time series JA - Physica A JO - Physica A VL - 339 SP - 591 EP - 608 DO - 10.1016/j.physa.2004.03.025 ER -
[ Close ]