Multifractal measures, especially for the geophysicist

1989 ◽  
Vol 131 (1-2) ◽  
pp. 5-42 ◽  
Author(s):  
Beno�t B. Mandelbrot
Keyword(s):  
Multifractal Measures

Wavelet series built using multifractal measures

2005 ◽  
Vol 341 (6) ◽  
pp. 353-356 ◽  
Author(s):  
Julien Barral ◽  
Stéphane Seuret
Keyword(s):  
Multifractal Measures ◽  
Wavelet Series

Multifractal measures of earthquakes in west Taiwan

1996 ◽  
Vol 146 (1) ◽  
pp. 131-145 ◽  
Author(s):  
Jeen-Hwa Wang ◽  
Chung-Wein Lee
Keyword(s):  
Multifractal Measures

MULTIFRACTAL MEASURES OF TIME SERIES: f(α) SURFACES

2010 ◽  
Vol 20 (08) ◽  
pp. 2453-2470
Author(s):  
WILLIAM MARTINO ◽  
MICHAEL FRAME
Keyword(s):  
Time Series ◽  
Transition Matrix ◽  
Financial Data ◽  
Contraction Map ◽  
Tent Maps ◽  
Data Points ◽  
Multifractal Measures

Binning the data points of a time series and associating a contraction map with each bin gives rise to a driven IFS representation of the time series. Varying the bins changes the driven IFS, sometimes in complex ways difficult to parse. From the transition matrix for any particular binning we can plot an f(α) curve. Assembling these curves as the bins change gives a surface, which we call the f(α) surface. We use properties of this surface to investigate time series from iterating logistic and tent maps, and also time series of financial data.

From Multifractal Measures to Multifractal Wavelet Series

2005 ◽  
Vol 11 (5) ◽  
pp. 589-614 ◽  
Author(s):  
Julien Barral ◽  
Stéphane Seuret
Keyword(s):  
Multifractal Measures ◽  
Wavelet Series
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