Related papers: Multiscaling comparative analysis of time series a…
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…
Time series are characterized by complex memory and/or distribution patterns. In this letter we show that models obeying to different statistics may equally reproduce some pattern of a time series. In particular we discuss the difference…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
We proposed a data-driven approach to dissect multivariate time series in order to discover multiple phases underlying dynamics of complex systems. This computing approach is developed as a multiple-dimension version of Hierarchical Factor…
We present a modification to the diffusion entropy analysis method for detecting temporal scaling. Diffusion entropy analysis detects temporal scaling in a data set by converting a time-series into a diffusion trajectory and using the…
We address the problem of the statistical analysis of a time series generated by complex dynamics with a new method: the Diffusion Entropy Analysis (DEA) (Fractals, {\bf 9}, 193 (2001)). This method is based on the evaluation of the Shannon…
Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both…
We show that different ways of extracting time scales from time-dependent velocity structure functions lead to different dynamic-multiscaling exponents in fluid turbulence. These exponents are related to equal-time multiscaling exponents by…
Multivariate time series classification is a task with increasing importance due to the proliferation of new problems in various fields (economy, health, energy, transport, crops, etc.) where a large number of information sources are…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
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…
We present a systematic way to analyze and model systems having many characteristic time-scales. The method we propose is employed for a test-case of a meandering jet model manifesting chaotic tracer dispersion with long time-correlations.…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…
We introduce a new method for detecting scaling in time series. The method uses the properties of the probability flux for stochastic self-affine processes and is called the probability flux analysis (PFA). The advantages of this method…
Specific aspects of time series analysis are discussed. They are related to the analysis of atmospheric data that are pertinent to clouds. A brief introduction on some of the most interesting topics of current research on climate/weather…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…