Related papers: Multifractal cross wavelet analysis
In this paper we propose a new adaptive wavelet denoising methodology using complex wavelets. The method is based on a fully Bayesian hierarchical model in the complex wavelet domain that uses a bivariate mixture prior on the wavelet…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian…
We perform an extensive empirical analysis of scaling properties of equity returns, suggesting that financial data show time varying multifractal properties. This is obtained by comparing empirical observations of the weighted generalised…
It is shown that fractional derivatives of the (integrated) invariant measure of the Feigenbaum map at the onset of chaos have power-law tails in their cumulative distributions, whose exponents can be related to the spectrum of…
One challenge with the analysis of complex systems and the interaction between such systems is that they are composed of different numbers of components, or simply the fact that a different number of observables is available for each…
Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate…
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking…
In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent $\tau(q)$ is related…
Complex systems often involve random fluctuations for which self-similar properties in space and time play an important role. Fractional Brownian motions, characterized by a single scaling exponent, the Hurst exponent $H$, provide a…
A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel…
One of the major reasons for misclassification of multiplex actions during action recognition is the unavailability of complementary features that provide the semantic information about the actions. In different domains these features are…
Source wavelet estimation is the key in seismic signal processing for resolving subsurface structural properties. Homomorphic deconvolution using cepstrum analysis has been an effective method for wavelet estimation for decades. In general,…
When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using classic detrended cross-correlation analysis (DCCA) without considering these common factors will bias…
This paper develops a novel statistical approach to characterize temporally localised cross-oscillatory interactions between channels in a functional brain network. Brain signals are generally nonstationary and the proposed framework uses…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
The crucial aspect of this demonstration is the discovery of renewal events, hidden in the computed dynamics of a multifractal metronome, which enables the replacement of the phenomenon of strong anticipation with a time delayed…
Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into time series representing neurophysiological activity in fixed frequency bands. Using these time series, one can estimate frequency-band specific functional…
With the advancements in technology and monitoring tools, we often encounter multivariate graph signals, which can be seen as the realizations of multivariate graph processes, and revealing the relationship between their constituent…