Local Detrended Fluctuation Analysis Research Articles

Hyperspectral redundancy detection and modeling with local Hurst exponent

Hyperspectral reflectance means a curve in a range of certain wavelength, the complex dynamic structure of which reflects the rich information of an object at different bands, which is often used as various modeling inputs. However, the potential redundancy associating with the information mentioned above will have serious impacts for the accurate extraction of spectral features. Thus, detecting information redundancy is a critical processing for the spectral analysis. By using the local detrended fluctuation analysis, we propose a new method detecting the redundant bands, which focuses on the spectral auto-correlation represented by local Hurst exponent in the moving windows, and the redundant bands can be defined through comparing the auto-correlation between two adjacent windows. Finally, with the fractal feature of the removing redundant bands as the augment, the rapeseed oleic acid prediction model based on the random decision forest is constructed to test our method. For the purpose of comparing, the same feature as the original spectrum is also employed as the augment for the model. The testing result shows that the feature obtained by removing the redundant bands has better performance over the feature of the original spectrum.

Accurate classification of epilepsy seizure types using wavelet packet decomposition and local detrended fluctuation analysis

Electroencephalogram (EEG) signals are widely used in diagnosis of epilepsy. Accurate classification of seizure types based on EEG signals can provide vital information for diagnosis and treatment. Since visual inspection and interpretation of seizure types are time consuming and prone to errors, a novel classification method combining wavelet packet decomposition (WPD) and local detrended fluctuation analysis (L-DFA) is proposed for the computer-aided diagnostic system. The proposed method is able to classify a wide variety of seizures automatically and accurately. As the first step towards this goal, raw EEG signals are decomposed by WPD according to intrinsic frequency bands of human brain. Then L-DFA is applied to characterise the dynamical fractal structure of sub-band signals. Finally, EEG signals are classified by support vector machine based on the combined fractal spectrum features. The experimental results on Temple University Hospital database show that the proposed method achieves a total classification accuracy of 97.80%, outperforming existing methods based on the same database.

Multifractality of Unperturbed and Asymmetric Locomotion

The purpose of this study was to explore the extent of multifractality in unperturbed and constrained locomotion, and to determine if multifractality predicted gait adaptability. Young, healthy participants (n = 15) walked at preferred and slow speeds, as well as asymmetrically (one leg at half speed) on a split-belt treadmill. Stride time multifractality was assessed via local detrended fluctuation analysis, which evaluates the evolution of fluctuations both spatially and temporally. Unperturbed walking exhibited monofractal behavior. Asymmetric walking displayed greater multifractality in the faster moving limb, indicating more intermittent periods of extreme high or low variance. Multifractality was not associated with adaptation to asymmetric walking. These findings further suggest that unperturbed locomotion is monofractal and establish that perturbed walking yields multifractal behavior.

Local detrended fluctuation analysis for spectral red-edge parameters extraction

Nowadays, spectrum technology makes it possible to nondestructively monitor crop and provide real-time diagnostic advice. Spectral red-edge parameters are important detection target for the growth of rapeseed. In this work, we propose a new method to acquire the rapeseed’s spectral red-edge parameters based on local detrended fluctuation analysis (L-DFA). In practice, by using the L-DFA, local Hurst exponent of the spectrum is calculated firstly. And then, six traditional red-edge parameter extraction methods, namely maximum first derivative method, adjusted linear extrapolation method, linear four-point interpolation method, inverted Gaussian method, Lagrangian interpolation method, and polynomial fitting interpolation, are employed to act on the estimated local Hurst exponent, and thus four red-edge parameters, i.e., red-edge position, red-edge amplitude, and left and right red-edge area, are obtained. In our experiments, by using the above four local Hurst exponent-based red-edge parameters as argument, a prediction model is developed to forecast the SPAD values (soil and plant analyzer development, often used as a parameter to indicate the chlorophyll content) for the five rapeseed’s growth periods based on random decision forest method. The results show that the local Hurst exponent-based red-edge feature can produce better model effect than the original spectrum-based one for the all phenological periods. Significance test for the four kinds of plant patterns shows that there is huge difference of the proposed four-dimensional red-edge features between the transplant and direct plant in the whole process of rapeseed’s growth. The differences between the other three groups of plant factors (two planting densities, two fertilizer types, and two weed controls) are not significant in certain specific growth periods of rapeseed. These findings provide a basis for studying difference of rapeseed yield and oil differences between different planting patterns.

The use of copula functions for modeling the risk of investment in shares traded on world stock exchanges

In this paper the two dimensional model of the investment in shares is presented. The shares prices from five different world stock exchanges (New York, London, Frankfurt, Honk Kong, and Sydney) are examined. The copula functions are used to model the risk of investment. The Hurst threshold exponent derived from the local Detrended Fluctuation Analysis is used to determine the safe investment portfolios with no extreme drops in shares prices. The most important result states that the threshold value is not universal for different markets, however, it is influenced by the subsequent level of market freedom. It was shown, that the level, relatively larger in US, UK, and Australia than in Germany and China, affects the Hurst exponent threshold value.

The use of copula functions for modeling the risk of investment in shares traded on the Warsaw Stock Exchange

In our work copula functions and the Hurst exponent calculated using the local Detrended Fluctuation Analysis (DFA) were used to investigate the risk of investment made in shares traded on the Warsaw Stock Exchange. The combination of copula functions and the Hurst exponent calculated using local DFA is a new approach. For copula function analysis bivariate variables composed of shares prices of the PEKAO bank (a big bank with high capitalization) and other banks (PKOBP, BZ WBK, MBANK and HANDLOWY in decreasing capitalization order) and companies from other branches (KGHM—mining industry, PKNORLEN—petrol industry as well as ASSECO—software industry) were used. Hurst exponents were calculated for daily shares prices and used to predict high drops of those prices. It appeared to be a valuable indicator in the copula selection procedure, since Hurst exponent’s low values were pointing on heavily tailed copulas e.g. the Clayton one.

Detection of co-regulation of local structure and magnitude of stride time variability using a new local detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a popular method to numerically define the persistent structure of stride time variability. The conventional DFA assumes that the persistent structure in stride time variability is consistent in time and can be numerically defined by a single DFA scaling exponent. However, stride time regulation has to be adaptive to both environmental and internal perturbations and consequently, the persistent structure of stride time variability will have to be modulated in time. The present article introduces a new local detrended fluctuation analysis (DFAloc) that is able to detect modulation in the structure of stride time variability generated by phase-couplings between temporal scales. DFAloc was used in a reanalysis of the data set of stride time variability of Hausdorff et al. and a data set available at www.physionet.org. The results showed that there were significant phase couplings between temporal scales that generate an inverse correlation (r=−0.54 to −0.83) between the local structure and local magnitude of the stride time variability. Furthermore, the modulation of the local structure was significantly influenced by gait speed, external pace making, and age (all p's<0.05). These results suggest several specific modifications of contemporary theories that have been suggested for the persistent structure of stride time variability found by the conventional DFA.

False Euro (FEUR) exchange rate correlated behaviors and investment strategy

We have searched for correlations and anticorrelations with respect to currencies as CHF, DKK, JPY, and USD in order to understand the EUR behavior. In order to do so we have invented a false euro (FEUR) dating back to 1993 and have derived simulated exchange rates of the FEUR. Within the Detrended Fluctuation Analysis (DFA) statistical method we have obtained the power law behavior describing the rms. deviation of the fluctuations as a function of time. We have compared the time-dependent exponent for these four exchange rates, and observe the role of the DEM, and the other currencies forming the EUR. A simple investment strategy based on the local DFA technique shows one can obtain appreciable gains, even taking into account some modest transaction fee. We compare the time dependent α exponent of the DFA for various exchange rates as in a correlation matrix for estimating respective influences.