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Dimension of the minimal cover and fractal analysis of time series

Dimension of the minimal cover and fractal analysis of time series
By JohnLast 3119 days ago

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Dimension of the minimal cover and fractal analysis of time series

by M. M. Dubovikov, N.V. Starchenko, M. S. Dubovikov

This is the article that served as a basis for the iVAR calculation you can download the Variation index iVAR read the original article in Russian too.

Abstract
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 . This results in new fractal characteristics:the dimension of minimal covers D, the variation index related to D, and the new multifractal spectrum (q) de5ned on the basis of . Numerical computations performed for the 5nancial series of companies entering Dow Jones Industrial Index show that the minimal scale , which is necessary for determining with an acceptable accuracy, is almost two orders smaller than an analogous scale for the Hurst index H. This allows us to consider as a local fractal characteristic.The presented fractal analysis of the 5nancial series shows that (t) is related to the stability of underlying processes. The results are interpreted in terms of the feedback.