Oscillations in the evaluation of fractal dimension of RR intervals time series

2010 ◽  
Author(s):  
A M Diosdado ◽  
G G Coyt ◽  
B M P Uribe
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Rr Intervals

Runoff Fractal Dimension of Songhua River Basin in Harbin Station Based on Db4 Wavelet

2012 ◽  
Vol 550-553 ◽  
pp. 2537-2540
Author(s):  
Hai Yan Gu ◽  
Yong Wang ◽  
Lei Yu
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
River Basin ◽  
Fractal Theory ◽  
Measurement Methods ◽  
Self Similarity ◽  
Songhua River ◽  
Songhua River Basin ◽  
The Songhua River Basin ◽  
The Songhua River

The wavelet analysis and fractal theory into the analysis of hydrological time series, fluctuations in hydrological runoff sequence given the complexity of the measurement methods--- fractal dimension. The real monthly runoffs of 28 years from Songhua River basin in Harbin station are selected as research target. Wavelet transform combined with spectrum method is used to calculate the fractal dimension of runoff. Moreover, the result demonstrates that the runoff in Songhua River basin has the characteristic of self-similarity, and the complexity of runoff in the Songhua River basin in Harbin station is described quantificationally.

scholarly journals Fractal dimension algorithms and their application to time series associated with natural phenomena

2013 ◽  
Vol 475 ◽  
pp. 012002 ◽  
Author(s):  
F Cervantes-De la Torre ◽  
J I González-Trejo ◽  
C A Real-Ramírez ◽  
L F Hoyos-Reyes
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Natural Phenomena

Time Evolution of the Fractal Dimension of Electric Self-Potential Time Series

2007 ◽  
pp. 407-418 ◽  
Author(s):  
F. Cervantes-De la Torre ◽  
C. G. Pavía‐Miller ◽  
A. Ramirez-Rojas ◽  
F. Angulo-Brown
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Time Evolution ◽  
Self Potential

Soft Computing Based Statistical Time Series Analysis, Characterization of Chaos Theory, and Theory of Fractals

2013 ◽  
pp. 30-61 ◽  
Author(s):  
Mofazzal H. Khondekar ◽  
Dipendra N. Ghosh ◽  
Koushik Ghosh ◽  
Anup Kumar Bhattacharya
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Time Series Analysis ◽  
Soft Computing ◽  
Chaos Theory ◽  
Filter Design ◽  
Theoretical Perspective ◽  
Series Analysis ◽  
Statistical Time

The present work is an attempt to analyze the various researches already carried out from the theoretical perspective in the field of soft computing based time series analysis, characterization of chaos, and theory of fractals. Emphasis has been given in the analysis on soft computing based study in prediction, data compression, explanatory analysis, signal processing, filter design, tracing chaotic behaviour, and estimation of fractal dimension of time series. The present work is a study as a whole revealing the effectiveness as well as the shortcomings of the various techniques adapted in this regard.

scholarly journals Multiscale Entropy Analysis: Application to Cardio-Respiratory Coupling

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1042 ◽  
Author(s):  
Mirjana M. Platiša ◽  
Nikola N. Radovanović ◽  
Aleksandar Kalauzi ◽  
Goran Milašinović ◽  
Siniša U. Pavlović
Keyword(s):  
Heart Failure ◽  
Time Series ◽  
Sinus Rhythm ◽  
Healthy Subjects ◽  
Coupled Systems ◽  
Multiscale Entropy ◽  
Rr Intervals ◽  
Control Subjects ◽  
Respiratory Signal ◽  
Physiological Systems

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrillation (HFAF), sinus rhythm (HFSin), and sinus rhythm with ventricular extrasystoles (HFVES)). Compared with healthy control subjects, alterations in respiratory signal properties were observed in patients from the HFSin and HFVES groups. Further, mean MSE curves of RR intervals and respiratory signal were not statistically different only in the HFSin group (p = 0.43). The level of synchrony between these time series was significantly higher in HFSin and HFVES patients than in control subjects and HFAF patients (p < 0.01). In conclusion, depending on the specific pathologies, primary alterations in the regularity of cardiac rhythm resulted in changes in the regularity of the respiratory rhythm, as well as in the level of their asynchrony.

scholarly journals Coercively Adjusted Auto Regression Model for Forecasting in Epilepsy EEG

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Sun-Hee Kim ◽  
Christos Faloutsos ◽  
Hyung-Jeong Yang
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Regression Model ◽  
Random Coefficients ◽  
Experimental Results ◽  
Ar Model ◽  
Forecasting Method ◽  
Eeg Data ◽  
Future Value ◽  
Auto Regression

Recently, data with complex characteristics such as epilepsy electroencephalography (EEG) time series has emerged. Epilepsy EEG data has special characteristics including nonlinearity, nonnormality, and nonperiodicity. Therefore, it is important to find a suitable forecasting method that covers these special characteristics. In this paper, we propose a coercively adjusted autoregression (CA-AR) method that forecasts future values from a multivariable epilepsy EEG time series. We use the technique of random coefficients, which forcefully adjusts the coefficients with−1and 1. The fractal dimension is used to determine the order of the CA-AR model. We applied the CA-AR method reflecting special characteristics of data to forecast the future value of epilepsy EEG data. Experimental results show that when compared to previous methods, the proposed method can forecast faster and accurately.

scholarly journals F-Ratio Test and Hypothesis Weighting: A Methodology to Optimize Feature Vector Size

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
R. M. Dünki ◽  
M. Dressel
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Signal Analysis ◽  
Feature Vector ◽  
Spectral Power ◽  
Ratio Test ◽  
Test Statistics ◽  
Biomedical Signal ◽  
Statistical Assessment ◽  
Biomedical Signal Analysis

Reducing a feature vector to an optimized dimensionality is a common problem in biomedical signal analysis. This analysis retrieves the characteristics of the time series and its associated measures with an adequate methodology followed by an appropriate statistical assessment of these measures (e.g., spectral power or fractal dimension). As a step towards such a statistical assessment, we present a data resampling approach. The techniques allow estimating σ2(F), that is, the variance of an F-value from variance analysis. Three test statistics are derived from the so-called F-ratio σ2(F)/F2. A Bayesian formalism assigns weights to hypotheses and their corresponding measures considered (hypothesis weighting). This leads to complete, partial, or noninclusion of these measures into an optimized feature vector. We thus distinguished the EEG of healthy probands from the EEG of patients diagnosed as schizophrenic. A reliable discriminance performance of 81% based on Taken's χ, α-, and δ-power was found.

Fractal dimension of time series estimated by the surface division method

2019 ◽  
Vol 64 (9) ◽  
pp. 7-24
Author(s):  
Grzegorz Przekota
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Standard Deviation ◽  
Growth Rates ◽  
Classical Approach ◽  
Degree Of Stability ◽  
Analysis Of Time Series

One of the most important issues to be settled in the analysis of time series is determining their variability andidentifying the process of shaping their values. In the classical approach, volatility is most often identified with the variance of growth rates.However, risk can be characterisednot only by the variability, but also by the predictability of the changes which can be evaluatedusing thefractal dimension. The aim of this paper is to presentthe applicability of the fractal dimension estimated by the surface division method tothe assessment ofthe properties of time series. The paper presents a method for determining the fractal dimension, its interpretation, significance tables and an example of its application. Fractal dimension has been used here to describe the properties of the time series of the WIG stockexchange index in 2014–2018 and the time series of the growth rates of the largest listed Polish companiesin 2015–2018. The applied methodmakesit possible toclassify a time series into one of three classesof series: persistent, random or antipersistent. Specific cases showthe differences between the use of standard deviation and fractal dimension for riskassessment. Fractal dimension appears here to be a method for assessing the degree of stability of variations.

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