Related papers: Self-Excited Multifractal Dynamics
Multifractal processes are a relatively new tool of stock market analysis. Their power lies in the ability to take multiple orders of autocorrelations into account explicitly. In the first part of the paper we discuss the framework of the…
We find that multifractal scaling is a robust property of a large class of continuous stochastic processes, constructed as exponentials of long-memory processes. The long memory is characterized by a power law kernel with tail exponent…
Forecasting multivariate time series remains challenging due to complex cross-variable dependencies and the presence of heterogeneous external influences. This paper presents Spectrogram-Enhanced Multimodal Fusion (SEMF), which combines…
This contribution reports an application of MultiFractal Detrended Fluctuation Analysis, MFDFA based novel feature extraction technique for automated detection of epilepsy. In fractal geometry, Multifractal Detrended Fluctuation Analysis…
In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
Several phenomena are available representing market activity: volumes, number of trades, durations between trades or quotes, volatility - however measured - all share the feature to be represented as positive valued time series. When…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in…
Among the statistical models employed to approximate nonlinear interactions in biological and psychological processes, one prominent framework is that of cascades. Despite decades of empirical work using multifractal formalisms, a…
In this paper, we consider daily financial data of a collection of different stock market indices, exchange rates, and interest rates, and we analyze their multi-scaling properties by estimating a simple specification of the…
We propose a ``multifractal stress activation'' model combining thermally activated rupture and long memory stress relaxation, which predicts that seismic decay rates after mainshocks follow the Omori law $\sim 1/t^p$ with exponents $p$…
Multifractal analysis is a forecasting technique used to study the scaling regularity properties of financial returns, to analyze the long-term memory and predictability of financial markets. In this paper, we propose a novel structural…
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by {\em quenched disorder}. These models exhibit self-organization, with critical…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation…
Integrated models for fluid-driven fracture propagation and general multiphase flow in porous media are valuable to the study and engineering of several systems, including hydraulic fracturing, underground disposal of waste, and geohazard…
While initial approaches to Structure-from-Motion (SfM) revolved around both global and incremental methods, most recent applications rely on incremental systems to estimate camera poses due to their superior robustness. Though there has…
In this paper, we use the generalized Hurst exponent approach to study the multi- scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multiscaling. We…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result…