Time series irreversibility analysis using Jensen–Shannon divergence calculated by permutation pattern

In this paper, we propose Jensen–Shannon divergence (JSD) based on horizontal visibility graph (HVG) to measure the time series irreversibility for both stationary and non-stationary series efficiently. Numerical simulations are first conducted to show the validity of the proposed method and then empirical applications to the financial time series and traffic time series are investigated. It can be found that JSD shows better robustness than Kullback–Leibler divergence (KLD) on quantifying time series irreversibility and correctly distinguishes the different type of simulated series. For the empirical analysis, JSD based on HVG is able to detect the significant time irreversibility of stock indices and reveal the relationship between different stock indices. JSD results show the time irreversibility of speed time series for different detectors and present better accuracy and robustness than KLD. The hierarchical clustering based on their behavior of time irreversibility obtained by JSD classifies the detectors into four groups.

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A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

Engineering Proceedings ◽

10.3390/engproc2021005010 ◽

2021 ◽

Vol 5 (1) ◽

pp. 10

Author(s):

Mark Levene

Keyword(s):

Time Series ◽

Goodness Of Fit ◽

Marginal Distribution ◽

Hypothesis Test ◽

Data Sets ◽

Test Statistic ◽

Sample Test ◽

Kolmogorov Smirnov ◽

Heavy Tailed ◽

Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

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Research on Attention EEG Based on the Multiscale Jensen-Shannon Divergence

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.529.675 ◽

2014 ◽

Vol 529 ◽

pp. 675-678

Author(s):

Zheng Xia Zhang ◽

Si Qiu Xu ◽

Er Ning Zhou ◽

Xiao Lin Huang ◽

Jun Wang

Keyword(s):

Time Series ◽

Brain Function ◽

Complexity Analysis ◽

Function Parameter ◽

Function Evaluation ◽

Analysis Method ◽

Eeg Signals ◽

Eyes Closed ◽

Statistical Complexity ◽

Jensen Shannon Divergence

The article adopted the multiscale Jensen-Shannon Divergence analysis method for EEG complexity analysis. Then the study found that this method can distinguish between three different status (Eyes closed, count, in a daze) acquisition of EEG time series. It showed that three different states of EEG time series have significant differences. In each state of the three different states (Eyes closed, count, in a daze), we aimed at comparing and analyzing the statistical complexity of EEG time series itself and the statistical complexity of EEG time series shuffled data. It was found that there are large amounts of nonlinear time series in the EEG signals. This method is also fully proved that the multiscale JSD algorithm can be used to analyze attention EEG signals. The multiscale Jensen-Shannon Divergence statistical complexity can be used as a measure of brain function parameter, which can be applied to the auxiliary clinical brain function evaluation in the future.

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Testing time series irreversibility using complex network methods

EPL (Europhysics Letters) ◽

10.1209/0295-5075/102/29902 ◽

2013 ◽

Vol 102 (2) ◽

pp. 29902 ◽

Cited By ~ 6

Author(s):

Jonathan F. Donges ◽

Reik V. Donner ◽

Jürgen Kurths

Keyword(s):

Time Series ◽

Complex Network ◽

Testing Time ◽

Network Methods ◽

Time Series Irreversibility

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Relative asynchronous index: a new measure for time series irreversibility

Nonlinear Dynamics ◽

10.1007/s11071-018-4275-1 ◽

2018 ◽

Vol 93 (3) ◽

pp. 1545-1557 ◽

Cited By ~ 3

Author(s):

Pengbo Yang ◽

Pengjian Shang

Keyword(s):

Time Series ◽

Time Series Irreversibility

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An Entropy Formulation Based on the Generalized Liouville Fractional Derivative

Entropy ◽

10.3390/e21070638 ◽

2019 ◽

Vol 21 (7) ◽

pp. 638 ◽

Cited By ~ 2

Author(s):

Rui A. C. Ferreira ◽

J. Tenreiro Machado

Keyword(s):

Time Series ◽

Fractional Derivative ◽

Fractional Order ◽

Dow Jones Industrial Average ◽

Liouville Fractional Derivative ◽

Entropy Formulation ◽

New Formula ◽

Jensen Shannon Divergence

This paper presents a new formula for the entropy of a distribution, that is conceived having in mind the Liouville fractional derivative. For illustrating the new concept, the proposed definition is applied to the Dow Jones Industrial Average. Moreover, the Jensen-Shannon divergence is also generalized and its variation with the fractional order is tested for the time series.

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Research on Attention EEG Based on Jensen-Shannon Divergence

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.884-885.512 ◽

2014 ◽

Vol 884-885 ◽

pp. 512-515

Author(s):

Zheng Xia Zhang ◽

Si Qiu Xu ◽

Er Ning Zhou ◽

Xiao Lin Huang ◽

Jun Wang

Keyword(s):

Time Series ◽

Brain Function ◽

Complexity Analysis ◽

The State ◽

Function Evaluation ◽

Eeg Signals ◽

Alpha Wave ◽

Eyes Closed ◽

Statistical Complexity ◽

Jensen Shannon Divergence

The article adopted the Jensen - Shannon Divergence analysis method for alpha wave EEG complexity analysis, used to quantify the three different status (Eyes closed, count, idle) degree of coupling between acquisition of EEG time series. The algorithm are used to calculate the statistical complexity of alpha wave EEG signals then T test, the results show that the state of eyes closed and idle under the coupling degree between EEG time series, and the state of eyes closed and counting, counting and daze cases EEG time series have significant differences. Thus JSD algorithm can be used to analyze EEG signals attention, statistical complexity can be used as a measure of brain function parameters and would be applied to the auxiliary clinical brain function evaluation in the future.

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Multiscale Jensen-Shannon Divergence Based Analysis of Beta Wave Attention EEG

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.574.723 ◽

2014 ◽

Vol 574 ◽

pp. 723-727

Author(s):

Zheng Xia Zhang ◽

Si Qiu Xu ◽

Er Ning Zhou ◽

Xiao Lin Huang ◽

Jun Wang

Keyword(s):

Time Series ◽

Brain Function ◽

Complexity Analysis ◽

Function Parameter ◽

Function Evaluation ◽

Eeg Signals ◽

Multi Scale ◽

Eyes Closed ◽

Statistical Complexity ◽

Jensen Shannon Divergence

The article adopted the multiscale Jensen - Shannon Divergence analysis method for EEG complexity analysis, then the study found that this method can distinguish between three different status (Eyes closed, count, in a daze) acquisition of Beta EEG time series, shows three different states of Beta EEG time series have significant differences. In each state of the three different states (Eyes closed, count, in a daze),we are aimed at comparing and analyzing the statistical complexity of EEG time series itself and the statistical complexity of EEG time series shuffled data, finding that there are large amounts of nonlinear time series in the Beta EEG signals. This method is also fully proved that the multi-scale JSD algorithm can be used to analyze EEG signals, attention statistical complexity can be used as a measure of brain function parameter, which can be applied to the auxiliary clinical brain function evaluation in the future.

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