scholarly journals GENERALIZED APPROACH TO HURST EXPONENT ESTIMATING BY TIME SERIES

2018 ◽  
Vol 8 (1) ◽  
pp. 28-31 ◽  
Author(s):  
Lyudmyla Kirichenko ◽  
Tamara Radivilova ◽  
Vitalii Bulakh
Keyword(s):  
Time Series ◽  
Fractal Analysis ◽  
Hurst Exponent ◽  
Hypothesis Test ◽  
Interval Estimation ◽  
Stationary Time Series ◽  
Similar Time ◽  
Self Similar ◽  
Short Time

This paper presents a generalized approach to the fractal analysis of self-similar random processes by short time series. Several stages of the fractal analysis are proposed. Preliminary time series analysis includes the removal of short-term dependence, the identification of true long-term dependence and hypothesis test on the existence of a self-similarity property. Methods of unbiased interval estimation of the Hurst exponent in cases of stationary and non-stationary time series are discussed. Methods of estimate refinement are proposed. This approach is applicable to the study of self-similar time series of different nature.

scholarly journals A NOVEL R/S FRACTAL ANALYSIS AND WAVELET ENTROPY CHARACTERIZATION APPROACH FOR ROBUST FORECASTING BASED ON SELF-SIMILAR TIME SERIES MODELING

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040032
Author(s):  
YELIZ KARACA ◽  
DUMITRU BALEANU
Keyword(s):  
Decision Making ◽  
Time Series ◽  
Fractal Analysis ◽  
Back Propagation ◽  
Long Term Memory ◽  
Similar Time ◽  
Wavelet Entropy ◽  
Feed Forward Back Propagation ◽  
Self Similar

It has become vital to effectively characterize the self-similar and regular patterns in time series marked by short-term and long-term memory in various fields in the ever-changing and complex global landscape. Within this framework, attempting to find solutions with adaptive mathematical models emerges as a major endeavor in economics whose complex systems and structures are generally volatile, vulnerable and vague. Thus, analysis of the dynamics of occurrence of time section accurately, efficiently and timely is at the forefront to perform forecasting of volatile states of an economic environment which is a complex system in itself since it includes interrelated elements interacting with one another. To manage data selection effectively and attain robust prediction, characterizing complexity and self-similarity is critical in financial decision-making. Our study aims to obtain analyzes based on two main approaches proposed related to seven recognized indexes belonging to prominent countries (DJI, FCHI, GDAXI, GSPC, GSTPE, N225 and Bitcoin index). The first approach includes the employment of Hurst exponent (HE) as calculated by Rescaled Range ([Formula: see text]) fractal analysis and Wavelet Entropy (WE) in order to enhance the prediction accuracy in the long-term trend in the financial markets. The second approach includes Artificial Neural Network (ANN) algorithms application Feed forward back propagation (FFBP), Cascade Forward Back Propagation (CFBP) and Learning Vector Quantization (LVQ) algorithm for forecasting purposes. The following steps have been administered for the two aforementioned approaches: (i) HE and WE were applied. Consequently, new indicators were calculated for each index. By obtaining the indicators, the new dataset was formed and normalized by min-max normalization method’ (ii) to form the forecasting model, ANN algorithms were applied on the datasets. Based on the experimental results, it has been demonstrated that the new dataset comprised of the HE and WE indicators had a critical and determining direction with a more accurate level of forecasting modeling by the ANN algorithms. Consequently, the proposed novel method with multifarious methodology illustrates a new frontier, which could be employed in the broad field of various applied sciences to analyze pressing real-world problems and propose optimal solutions for critical decision-making processes in nonlinear, complex and dynamic environments.

scholarly journals Analysis of development of raw cow milk prices in the conditions of the Slovak Republic

10.5219/1196 ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 906-914
Author(s):  
Ivana Váryová ◽  
Zuzana Poláková ◽  
Iveta Košovská ◽  
Alexandra Ferenczi Vaňová ◽  
Renáta Krajčírová
Keyword(s):  
Time Series ◽  
Slovak Republic ◽  
Future Trend ◽  
Stationary Time Series ◽  
Cow Milk ◽  
Moderate Increase ◽  
Monthly Data ◽  
Market Report ◽  
Milk And Dairy Products

The paper is focused on the evaluation of the price development of raw cow milk in the Slovak Republic. The aim of the paper is to analyse the development of average prices of the raw Q class cow´s milk in 2006 – 2018 and to forecast the trend of these prices by June 2019. Monthly data from the Market Report of Milk and Dairy Products issued by the Agricultural Information Department – ATIS, as part of the Agricultural Paying Agency, were the base of our information resource. These data were analyzed by using the statistical software called SAS. Box-Jenkins methodology was used to model the future trend of average purchase prices of the raw Q class cow´s milk, designed for modeling stationary and non-stationary time series and time series with seasonal components. During the period of 2006 – 2018 the Slovak dairy market showed significant changes in the prices of raw Q class cow´s milk. Three crisis periods of the dairy sector have been identified, during which the milk price has fallen below 0.30 € per kilogram. Long-term low prices of raw cow milk led to the liquidation of primary milk producers. In the next forecast period, by February 2019 a moderate increase in the average purchase price of raw Q class cow´s milk is expected, followed by a decrease by June 2019.

scholarly journals Use of fractal analysis to evaluate the surface quality of agricultural machinery parts

2020 ◽  
Vol 17 ◽  
pp. 00189
Author(s):  
Oleg Bavykin ◽  
Tatyana Levina ◽  
Vladlena Matrosova ◽  
Anatoly Klochkov ◽  
Vitaliy Enin
Keyword(s):  
Time Series ◽  
Computer Program ◽  
Surface Quality ◽  
Fractal Analysis ◽  
Hurst Exponent ◽  
High Accuracy ◽  
Agricultural Machinery ◽  
Fractal Characteristics

The research of the determination of the fractal characteristics of the surface of a material proposes the use of a stationary profilograph and a computer program for calculating the Hurst exponent. The low accuracy of fractal analysis using the well-known computer program Fractan is revealed. A computer program developed in VBA for the fractal analysis of the time series is described. The high accuracy of the algorithms for calculating the Hurst exponent incorporated in this program is shown.

Scaling behavior of earthquakes’ inter-events time series

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Shahriar Shadkhoo ◽  
Fakhteh Ghanbarnejad ◽  
Gholam Jafari ◽  
Mohammad Tabar
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Hurst Exponent ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Data Set ◽  
Scaling Properties ◽  
Independent Events ◽  
Detrended Fluctuation

AbstractIn this paper, we investigate the statistical and scaling properties of the California earthquakes’ inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0:34 + 1:53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0:50, which is for independent events.

Time-Local Spectral Analysis for Non-Stationary Time Series: The S-Transform for Noisy Signals

2003 ◽  
Vol 03 (03) ◽  
pp. L357-L364 ◽  
Author(s):  
C. R. Pinnegar ◽  
L. Mansinha
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Wavelet Transforms ◽  
Gaussian White Noise ◽  
Stationary Time Series ◽  
Time Frequency ◽  
S Transform ◽  
Undesirable Characteristic ◽  
Noisy Signals ◽  
Short Time

The S-transform is a method of time-local spectral analysis (also known as time-frequency analysis), a modified short-time Fourier Transform, in which the width of the analyzing window scales inversely with frequency, in analogy with continuous wavelet transforms. If the time series is non-stationary and consists of a mix of Gaussian white noise and a deterministic signal, though, this type of scaling leads to larger apparent noise amplitudes at higher frequencies. In this paper, we introduce a modified S-transform window with a different scaling function that addresses this undesirable characteristic.

scholarly journals Fractal analysis of muscle activity patterns during locomotion: pitfalls and how to avoid them

2020 ◽  
Author(s):  
Alessandro Santuz ◽  
Turgay Akay
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Hurst Exponent ◽  
Activity Patterns ◽  
Surrogate Data ◽  
Time Dependent ◽  
Physiological Data ◽  
Adult Mice

AbstractTime-dependent physiological data, such as electromyogram (EMG) recordings from multiple muscles, is often difficult to interpret objectively. Here, we used EMG data gathered during mouse locomotion to investigate the effects of calculation parameters and data quality on two metrics for fractal analysis: the Higuchi’s fractal dimension (HFD) and the Hurst exponent (H). A curve is fractal if it repeats itself at every scale or, in other words, if its shape remains unchanged when zooming in the curve at every zoom level. Many linear and nonlinear analysis methods are available, each of them aiming at the explanation of different data features. In recent years, fractal analysis has become a powerful nonlinear tool to extract information from physiological data not visible to the naked eye. It can present, however, some dangerous pitfalls that can lead to misleading interpretations. To calculate the HFD and the H, we have extracted muscle synergies from normal and mechanically perturbed treadmill locomotion from the hindlimb of adult mice. Then, we used one set per condition (normal and perturbed walking) of the obtained time-dependent coefficients to create surrogate data with different fluctuations over the original mean signal. Our analysis shows that HFD and H are exceptionally sensitive to the presence or absence of perturbations to locomotion. However, both metrics suffer from variations in their value depending on the parameters used for calculations and the presence of quasi-periodic elements in the time series. We discuss those issues giving some simple suggestions to reduce the chance of misinterpreting the outcomes.New & NoteworthyDespite the lack of consensus on how to perform fractal analysis of physiological time series, many studies rely on this technique. Here, we shed light on the potential pitfalls of using the Higuchi’s fractal dimension and the Hurst exponent. We expose and suggest how to solve the drawbacks of such methods when applied to data from normal and perturbed locomotion by combining in vivo recordings and computational approaches.

Correlation structure of end-expiratory lung volume in anesthetized rats with intact upper airway

2000 ◽  
Vol 278 (6) ◽  
pp. R1446-R1452 ◽  
Author(s):  
Xiaobin Zhang ◽  
Eugene N. Bruce
Keyword(s):  
Time Series ◽  
Lung Volume ◽  
Hurst Exponent ◽  
Upper Airway ◽  
Correlation Structure ◽  
Original Time Series ◽  
Dispersional Analysis ◽  
Anesthetized Rats ◽  
Original Time

The correlation structure of breath-to-breath fluctuations of end-expiratory lung volume (EEV) was studied in anesthetized rats with intact airways subjected to positive and negative transrespiratory pressure (i.e., PTRP and NTRP, correspondingly). The Hurst exponent, H, was estimated from EEV fluctuations using modified dispersional analysis. We found that H for EEV was 0.5362 ± 0.0763 and 0.6403 ± 0.0561 with PTRP and NTRP, respectively (mean ± SD). Both H were significantly different from those obtained after random shuffling of the original time series. Also, H with NTRP was significantly greater than that with PTRP ( P = 0.029). We conclude that in rats breathing through the upper airway, a positive long-term correlation is present in EEV that is different between PTRP and NTRP.

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