Related papers: Effect of nonstationarities on detrended fluctuati…
Observability can determine which recorded variables of a given system are optimal for discriminating its different states. Quantifying observability requires knowledge of the equations governing the dynamics. These equations are often…
In this report, a systematic analysis of hourly wind speed data obtained from three potential wind generation sites (in North Dakota) is analyzed. The power spectra of the data exhibited a power-law decay characteristic of $1/f^{\alpha}$…
Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
We use the Detrended Fluctuation Analysis (DFA) and the Grassberger-Proccacia analysis (GP) methods in order to study language characteristics. Despite that we construct our signals using only word lengths or word frequencies, excluding in…
Forced oscillation (FO) is a significant concern threating the power system stability. Its mechanisms are mostly studied via linear models. However, FO amplitude is increasing, e.g., Nordic and Western American FOs, which can stimulate…
A Distortion Contribution Analysis (DCA) obtains the distortion at the output of an analog electronic circuit as a sum of distortion contributions of its sub-circuits. Similar to a noise analysis, a DCA helps a designer to pinpoint the…
Eye movements during fixation of a stationary target prevent the adaptation of the photoreceptors to continuous illumination and inhibit fading of the image. These random, involuntary, small, movements are restricted at long time scales so…
We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…
Correlations in complex systems are often obscured by nonstationarity, long-range memory, and heavy-tailed fluctuations, which limit the usefulness of traditional covariance-based analyses. To address these challenges, we construct scale…
Correlations in multifractal series have been investigated, extensively. Almost all approaches try to find scaling features of a given time series. However, the analysis of such scaling properties has some difficulties such as finding a…
Many real-life signals, such as gravitational wave measurements, biomedical signals, or geophysical data, are strongly non-stationary but can be decomposed into mono-component signals that contain only one active frequency over time. This…
In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first…
Confirmatory factor analysis (CFA) is a statistical method for identifying and confirming the presence of latent factors among observed variables through the analysis of their covariance structure. Compared to alternative factor models, CFA…
This paper extends the existing literature on empirical estimation of the confidence intervals associated to the Detrended Fluctuation Analysis (DFA). We used Montecarlo simulation to evaluate the confidence intervals. Varying the…
Stacked cross-correlation functions have become ubiquitous in the ambient seismic imaging and monitoring community as approximations to the Green's function between two receivers. While theoretical understanding of this approximation to the…
Different variants of MFDFA technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending…
In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…
Detrended fluctuation analysis is used to investigate correlations between the monthly average of the maximum daily temperatures for different locations in the continental US and the different climates these locations have. When we plot the…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…