Multifractal measures of time series: curvature surfaces of f(α) curves

Author(s):  
William Martino ◽  
Michael Frame
2010 ◽  
Vol 20 (08) ◽  
pp. 2453-2470
Author(s):  
WILLIAM MARTINO ◽  
MICHAEL FRAME

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.


1997 ◽  
Vol 45 (5) ◽  
pp. 331-345 ◽  
Author(s):  
Jeen-Hwa Wang ◽  
Chung-Wein Lee

Fractals ◽  
2002 ◽  
Vol 10 (03) ◽  
pp. 387-394 ◽  
Author(s):  
NELSON OBREGÓN ◽  
CARLOS E. PUENTE ◽  
BELLIE SIVAKUMAR

Usage of a deterministic fractal-multifractal (FM) procedure to model high-resolution rainfall time series, as derived distributions of multifractal measures via fractal interpolating functions, is reported. Four rainfall storm events having distinct geometries, one gathered in Boston and three others observed in Iowa City, are analyzed. Results show that the FM approach captures the main characteristics of these events, as the fitted storms preserve the records' general trends, their autocorrelations and spectra, and their multifractal character.


1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.


1982 ◽  
Vol 14 (3) ◽  
pp. 156-166 ◽  
Author(s):  
Chin-Sheng Alan Kang ◽  
David D. Bedworth ◽  
Dwayne A. Rollier

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