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The fractional difference operator remains to be the most popular mechanism to generate long memory due to the existence of efficient algorithms for their simulation and forecasting. Nonetheless, there is no theoretical argument linking the…
Direct Feedback Alignment (DFA) is emerging as an efficient and biologically plausible alternative to the ubiquitous backpropagation algorithm for training deep neural networks. Despite relying on random feedback weights for the backward…
It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line…
One of the standardized features of financial data is that log-returns are uncorrelated, but absolute log-returns or their squares namely the fluctuating volatility are correlated and is characterized by heavy tailed in the sense that some…
The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. Many long-term correlated time series in real systems contain various trends. We…
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or…
Motion prediction has been studied in different contexts with models trained on narrow distributions and applied to downstream tasks in human motion prediction and robotics. Simultaneously, recent efforts in scaling video prediction have…
Differences in gait patterns of children with Duchenne muscular dystrophy (DMD) and typically-developing (TD) peers are visible to the eye, but quantifications of those differences outside of the gait laboratory have been elusive. In this…
We extend our previous study of scaling range properties done for detrended fluctuation analysis (DFA) \cite{former_paper} to other techniques of fluctuation analysis (FA). The new technique called Modified Detrended Moving Average Analysis…
Detrended fluctuation analysis (DFA) is a simple but very efficient method for investigating the power-law long-term correlations of non-stationary time series, in which a detrending step is necessary to obtain the local fluctuations at…
Older adults and people suffering from neurodegenerative disease often experience difficulty controlling gait during locomotion, ultimately increasing their risk of falling. To combat these effects, researchers and clinicians have used…
Celestial objects exhibit a wide range of variability in brightness at different wavebands. Surprisingly, the most common methods for characterizing time series in statistics -- parametric autoregressive modeling -- is rarely used to…
Motor activity of humans displays complex temporal fluctuations which can be characterized by scale-invariant statistics, thus documenting that structure and fluctuations of such kinetics remain similar over a broad range of time scales.…
Drift diffusion models (DDMs) have found widespread use in computational neuroscience and other fields. They model evidence accumulation in simple decision tasks as a stochastic process drifting towards a decision barrier. In models where…
Detrended Fluctuation Analysis (DFA) is widely used to assess the presence of long-range temporal correlations in time series. Signals with long-range temporal correlations are typically defined as having a power law decay in their…
Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests…
The linear fractional stable motion (LFSM) extends the fractional Brownian motion (fBm) by considering $\alpha$-stable increments. We propose a method to forecast future increments of the LFSM from past discrete-time observations, using the…
Fundamental knowledge in activity recognition of individuals with motor disorders such as Parkinson's disease (PD) has been primarily limited to detection of steady-state/static tasks (sitting, standing, walking). To date, identification of…
Detrend fluctuation analysis (DFA) has become a choice method for effective analysis of a broad variety of nonstationary signals. We show in the present article that, provided the nonstationary fluctuations occur at a large enough time…
Anomalous temporal fluctuations of helium concentrations in spring emanations have been observed on a number of occasions prior to some major seismic events. Several recent studies have shown that a wide variety of natural systems display…