Multiscaling comparative analysis of time series and geophysical phenomena (original) (raw)
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Chaos Solitons & Fractals, 2004
Understanding the statistical properties of time-occurrence series of seismic sequences is considered one of the most pervasive scientific topics. Investigating into the patterns of seismic sequences reveals evidence of time-scaling features. This is shown in the fractal analysis of the 1986-2001 seismicity of three different seismic zones in Italy. Describing the sequence of earthquakes by means of the series of the interevent times, power-law behaviour has been found applying Hurst analysis and detrended fluctuation analysis (DFA), with consistent values for the scaling exponents. The multifractal analysis has clearly evidenced differences among the earthquake sequences. The multifractal spectrum parameters (maximum a 0 , asymmetry B and width W ), derived from the analysis of the shape of the singularity spectrum, have been used to measure the complexity of seismicity.
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Computing Research Repository, 2009
Current methods for determining whether a time series exhibits fractal structure (FS) rely on subjective assessments on estimators of the Hurst exponent (H). Here, I introduce the Bayesian Assessment of Scaling, an analytical framework for drawing objective and accurate inferences on the FS of time series. The technique exploits the scaling property of the diffusion associated to a time series. The resulting criterion is simple to compute and represents an accurate characterization of the evidence supporting different hypotheses on the scaling regime of a time series. Additionally, a closed-form Maximum Likelihood estimator of H is derived from the criterion, and this estimator outperforms the best available estimators.
Quantitative features of multifractal subtleties in time series
EPL (Europhysics Letters), 2009
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2014
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Scaling detection in time series: diffusion entropy analysis
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where ordinary statistical properties hold true even if strange kinetics are involved. We illustrate a method of statistical analysis based on the Shannon entropy of the diffusion process generated by the time series, called diffusion entropy analysis (DEA). We adopt artificial Gauss and Lévy time series, as prototypes of ordinary and anomalous statistics, respectively, and we analyze them with the DEA and four ordinary methods of analysis, some of which are very popular. We show that the DEA determines the correct scaling exponent even when the statistical properties, as well as the dynamic properties, are anomalous. The other four methods produce correct results in the Gauss case but fail to detect the correct scaling in the case of Lévy statistics.
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Fractal approaches in investigating the time dynamics of self-potential hourly variability
International Journal of Earth Sciences, 2005
Fractal tools have been used to investigate the time dynamics of hourly self-potential data, recorded during the year 2001 by five geoelectrical stations located in one of the most seismic areas of southern Italy. Scaling behaviour has been revealed by means of different statistics: the Lomb Periodogram method, the Detrended Fluctuation Analysis, the Higuchi analysis and the mean distance spanned within the time L. The values of the scaling exponents estimated by means of these methods indicate that the temporal fluctuations of the geoelectrical signals are not typical of purely random stochastic processes (i.e. white noise), but evidence the presence of long-range correlations. Furthermore, it is found that these correlations are linear.
Stochastic Analysis of Scaling Time Series
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Multiscale systems, involving complex interacting processes that occur over a range of temporal and spatial scales, are present in a broad range of disciplines, from financial trading to atmospheric dynamics. Turbulent flows are a classical example of such a complex system. Several methodologies exist to retrieve multiscale information from a given time series obtained from a complex dynamical system; however, each method has its own advantages and limitations. This book presents the mathematical theory behind the stochastic analysis of scaling time series, including a general historical introduction to the problem of intermittency in turbulence, as well as how to implement this analysis for a range of different applications. Covering a variety of statistical methods, such as Fourier analysis, structure-function analysis, wavelet transforms, and Hilbert-Huang transforms, it provides readers with a more thorough understanding of each technique and when they should be applied. New techniques to analyze stochastic processes, including empirical mode decomposition, autocorrelation function of increments, and detrended analysis, are also explored. The final part of the book contains a selection of case studies, on the topics of turbulence and ocean sciences, to demonstrate how these statistical methods can be applied in practice. With MATLAB codes available online, this book is of value to students and researchers in Earth sciences, physics, geophysics, and applied mathematics.
Geophysical Journal International, 1999
We explore the inner dynamics of daily geoelectrical time series measured in a seismic area of the southern Apennine chain (southern Italy). Autoregressive models and the Higuchi fractal method are applied to extract maximum quantitative information about the time dynamics from these geoelectrical signals. First, the predictability of the geoelectrical measurements is investigated using autoregressive models. The procedure is based on two forecasting approaches: the global and the local autoregressive approximations. The first views the data as a realization of a linear stochastic process, whereas the second considers the data points as a realization of a deterministic process, which may be non-linear. Comparison of the predictive skills of the two techniques allows discrimination between low-dimensional chaos and stochastic dynamics. Our findings suggest that the physical systems governing electrical phenomena are characterized by a very large number of degrees of freedom and can be described only with statistical laws. Second, we investigate the stochastic properties of the same geoelectrical signals, searching for scaling laws in the power spectrum. The spectrum fits a power law P( f )∝ f −α, with the scaling exponent α a typical fingerprint of fractional Brownian processes. In this analysis we apply the Higuchi method, which gives a linear relationship between the fractal dimension DΣ and the spectral power law scaling index α: DΣ=(3−α)/2. This analysis highlights the stochastic nature of geoelectrical signals recorded in this seismic area of southern Italy.