Multiscale Fractional Cumulative Residual Entropy of Higher-Order Moments for Estimating Uncertainty

2020 ◽  
Vol 19 (04) ◽  
pp. 2050038
Author(s):  
Keqiang Dong ◽  
Xiaofang Zhang
Keyword(s):  
Time Series ◽  
Logistic Map ◽  
Higher Order ◽  
Stationary Time Series ◽  
Residual Entropy ◽  
Third Order ◽  
Cumulative Residual Entropy ◽  
Cumulative Residual ◽  
Simulated Time ◽  
Analyze Time Series

The fractional cumulative residual entropy is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. In this paper, we present an approach to measure the uncertainty of non-stationary time series named higher-order multiscale fractional cumulative residual entropy. We describe how fractional cumulative residual entropy may be calculated based on second-order, third-order, fourth-order statistical moments and multiscale method. The implementation of higher-order multiscale fractional cumulative residual entropy is illustrated with simulated time series generated by uniform distribution on [0, 1]. Finally, we present the application of higher-order multiscale fractional cumulative residual entropy in logistic map time series and stock markets time series, respectively.

Generalized Cumulative Residual Entropy of Time Series Based on Permutation Patterns

2021 ◽  
pp. 2150055
Author(s):  
Qin Zhou ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Stock Markets ◽  
Multiple Scales ◽  
Permutation Entropy ◽  
Residual Entropy ◽  
Permutation Patterns ◽  
Cumulative Residual Entropy ◽  
The Us ◽  
Cumulative Residual ◽  
Different Characteristics

Cumulative residual entropy (CRE) has been suggested as a new measure to quantify uncertainty of nonlinear time series signals. Combined with permutation entropy and Rényi entropy, we introduce a generalized measure of CRE at multiple scales, namely generalized cumulative residual entropy (GCRE), and further propose a modification of GCRE procedure by the weighting scheme — weighted generalized cumulative residual entropy (WGCRE). The GCRE and WGCRE methods are performed on the synthetic series to study properties of parameters and verify the validity of measuring complexity of the series. After that, the GCRE and WGCRE methods are applied to the US, European and Chinese stock markets. Through data analysis and statistics comparison, the proposed methods can effectively distinguish stock markets with different characteristics.

scholarly journals Higher-Order Information Measures from Cumulative Densities in Continuous Variable Quantum Systems

2020 ◽  
Vol 2 (4) ◽  
pp. 560-578
Author(s):  
Saúl J. C. Salazar ◽  
Humberto G. Laguna ◽  
Robin P. Sagar
Keyword(s):  
Continuous Variable ◽  
Quantum Systems ◽  
Higher Order ◽  
Residual Entropy ◽  
Information Measures ◽  
Cumulative Residual Entropy ◽  
Interacting Systems ◽  
Correlation Measures ◽  
Cumulative Residual ◽  
Definition Of

A definition of three-variable cumulative residual entropy is introduced, and then used to obtain expressions for higher order or triple-wise correlation measures, that are based on cumulative residual densities. These information measures are calculated in continuous variable quantum systems comprised of three oscillators, and their behaviour compared to the analogous measures from Shannon information theory. There is an overall consistency in the behaviour of the newly introduced measures as compared to the Shannon ones. There are, however, differences in interpretation, in the case of three uncoupled oscillators, where the correlation is due to wave function symmetry. In interacting systems, the cumulative based measures are shown in order to detect salient features, which are also present in the Shannon based ones.

HIGHER ORDER COMPLEXITY OF TIME SERIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2979-2990 ◽  
Author(s):  
FANJI GU ◽  
ENHUA SHEN ◽  
XIN MENG ◽  
YANG CAO ◽  
ZHIJIE CAI
Keyword(s):  
Time Series ◽  
Mental Arithmetic ◽  
Higher Order ◽  
Second Order ◽  
Stationary Time Series ◽  
Eeg Signals ◽  
Eyes Closed ◽  
Logistic Mapping ◽  
Original Time ◽  
Different Order

A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second-order complexity of these time series shows that the second-order complexities do reflect the degree of nonstationarity and thus can be considered as its indicator. It is also shown that the second-order complexities of the EEG signals from subjects doing mental arithmetic are significantly higher than those from subjects in deep sleep or resting with eyes closed.

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