Search results for "Hurst exponent"
showing 10 items of 12 documents
Benefits of nonlinear analysis indices of walking stride interval in the evaluation of neurodegenerative diseases.
2021
Indices characterising the long-range temporal structure of walking stride interval (SI) variability such as Hurst exponent (H) and fractal dimension (D) may be used in addition to indices measuring the amount of variability like the coefficient of variation (CV). We assess the added value of the former indices in a clinical neurological context. Our aim is to demonstrate that they provide a clinical significance in aging and in frequent neurodegenerative diseases such as Parkinson's disease, Huntington, and amyotrophic lateral sclerosis. Indices assessing the temporal structure of variability are mainly dependent on SI time series length and algorithms used, making quantitative comparisons…
Temporal Structure of Human Gaze Dynamics Is Invariant During Free Viewing.
2015
We investigate the dynamic structure of human gaze and present an experimental study of the frequency components of the change in gaze position over time during free viewing of computer-generated fractal images. We show that changes in gaze position are scale-invariant in time with statistical properties that are characteristic of a random walk process. We quantify and track changes in the temporal structure using a well-defined scaling parameter called the Hurst exponent, H. We find H is robust regardless of the spatial complexity generated by the fractal images. In addition, we find the Hurst exponent is invariant across all participants, including those with distinct changes to higher or…
The effect of round-off error on long memory processes
2011
We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the discretized process is also long memory with the same Hurst exponent as the original process. We consider the properties of two estimators of the Hurst exponent, namely the local Whittle (LW) estimator and the Detrended Fluctuation Analysis (DFA). By using analytical considerations and numerical simulations we show that, in presence of round-off error, both…
Added Value and Clinical Significance of Nonlinear Variability Indices of Walking Stride Interval in Neurodegenerative Diseases
2020
AbstractThough self-paced walking is highly stereotyped, the stride interval fluctuates from one stride to the next around an average value with a measurable statistical variability. In clinical gait analysis, this variability is usually assessed with indices such the standard deviation or the coefficient of variation (CV). The aim of this study is to understand the added value that nonlinear indices of walking stride interval variability, such as Hurst exponent (H) and Minkowski fractal dimension (D), can provide in a clinical context and to suggest a clinical significance of these indices in the most common neurodegenerative diseases: Parkinson, Huntington, and amyotrophic lateral scleros…
Nonlinear Dynamics Techniques for the Detection of the Brain Areas Using MER Signals
2008
A methodology for identifying brain areas from the brain MER signals (microelectrode recordings) is presented, which is based on a nonlinear feature set. We propose nonlinear dynamics measures such as correlation dimension, Hurst exponent and the largest Lyapunov exponent to characterize the dynamic structure. The MER records belong to the Polytechnical University of Valencia, 24 records for each zone (black substance, thalamus, subthalamus nucleus and uncertain area). The detection of each area using characteristics derived from complexity analysis was obtained through a classifier (support vector machine). The joint information between areas is remarkable and the best accuracy result was …
FRACTALITY EVIDENCE AND LONG-RANGE DEPENDENCE ON CAPITAL MARKETS: A HURST EXPONENT EVALUATION
2014
Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is…
Multi-agent-based Order Book Model of financial markets
2006
We introduce a simple model for simulating financial markets, based on an order book, in which several agents trade one asset at a virtual exchange continuously. For a stationary market the structure of the model, the order flow rates of the different kinds of order types and the used price time priority matching algorithm produce only a diffusive price behavior. We show that a market trend, i.e. an asymmetric order flow of any type, leads to a non-trivial Hurst exponent for the price development, but not to "fat-tailed" return distributions. When one additionally couples the order entry depth to the prevailing trend, also the stylized empirical fact of "fat tails" can be reproduced by our …
Statistical analysis of financial returns for a multiagent order book model of asset trading
2007
We recently introduced a realistic order book model [T. Preis, Europhys. Lett. 75, 510 (2006)] which is able to generate the stylized facts of financial markets. We analyze this model in detail, explain the consequences of the use of different groups of traders, and focus on the foundation of a nontrivial Hurst exponent based on the introduction of a market trend. Our order book model supports the theoretical argument that a nontrivial Hurst exponent implies not necessarily long-term correlations. A coupling of the order placement depth to the market trend can produce fat tails, which can be described by a truncated Lévy distribution.
Fractal analyses reveal independent complexity and predictability of gait
2017
Locomotion is a natural task that has been assessed since decades and used as a proxy to highlight impairments of various origins. Most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular…
Fracture Processes Observed with A Cryogenic Detector
2006
In the early stages of running of the CRESST dark matter search using sapphire detectors at very low temperature, an unexpectedly high rate of signal pulses appeared. Their origin was finally traced to fracture events in the sapphire due to the very tight clamping of the detectors. During extensive runs the energy and time of each event was recorded, providing large data sets for such phenomena. We believe this is the first time the energy release in fracture has been directly and accurately measured on a microscopic event-by-event basis. The energy threshold corresponds to the breaking of only a few hundred covalent bonds, a sensitivity some orders of magnitude greater than that of previou…