Wavelet entropy of BOLD time series: An application to Rolandic epilepsy

<p>Model-free gradation of predictability of a geophysical system is essential to quantify how much inherent information is contained within the system and evaluate different forecasting methods' performance to get the best possible prediction. We conjecture that Multiscale Information enclosed in a given geophysical time series is the only input source for any forecast model. In the literature, established entropic measures dealing with grading the predictability of a time series at multiple time scales are limited. Therefore, we need an additional measure to quantify the information at multiple time scales, thereby grading the predictability level. This study introduces a novel measure, Wavelet Entropy Energy Measure (WEEM), based on Wavelet entropy to investigate a time series's energy distribution. From the WEEM analysis, predictability can be graded low to high. The difference between the entropy of a wavelet energy distribution of a time series and entropy of wavelet energy of white noise is the basis for gradation. The metric quantifies the proportion of the deterministic component of a time series in terms of energy concentration, and its range varies from zero to one. One corresponds to high predictable due to its high energy concentration and zero representing a process similar to the white noise process having scattered energy distribution. The proposed metric is normalized, handles non-stationarity, independent of the length of the data. Therefore, it can explain the evolution of predictability for any geophysical time series (ex: precipitation, streamflow, paleoclimate series) from past to the present. WEEM metric's performance can guide the forecasting models in getting the best possible prediction of a geophysical system by comparing different methods.&#160;</p>

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Wavelet entropy and fractional Brownian motion time series

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2005.09.060 ◽

2006 ◽

Vol 365 (2) ◽

pp. 282-288 ◽

Cited By ~ 24

Author(s):

D.G. Pérez ◽

L. Zunino ◽

M. Garavaglia ◽

O.A. Rosso

Keyword(s):

Time Series ◽

Brownian Motion ◽

Fractional Brownian Motion ◽

Wavelet Entropy ◽

Motion Time

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Recognizing factors affecting decline in groundwater level using wavelet-entropy measure (case study: Silakhor plain aquifer)

Journal of Hydroinformatics ◽

10.2166/hydro.2019.111 ◽

2019 ◽

Vol 21 (3) ◽

pp. 510-522 ◽

Cited By ~ 2

Author(s):

Mehdi Komasi ◽

Soroush Sharghi

Keyword(s):

Time Series ◽

Groundwater Level ◽

Temperature Time Series ◽

Entropy Measure ◽

Wavelet Entropy ◽

Factors Affecting ◽

Change Factors ◽

Natural Time ◽

Important Approach ◽

Temperature Time

Abstract The most important approach to identify the behavior of hydrological processes is time series analysis of this process. Wavelet-entropy measure has been considered as a criterion for the degree of time series fluctuations and consequently uncertainty. Wavelet-entropy measure reduction indicates the reduction in natural time series fluctuations and thus, the occurrence of an unfavorable trend in time series. In this way, to identify the main cause of declining aquifer water level in the Silakhor plain, monthly time series of rainfall, temperature and output discharge were divided into three different time periods. Then, these time series were decomposed to multiple frequent time series by wavelet transform and then, the wavelet energies were computed for these decomposed time series. Finally, wavelet-entropy measure was computed for each different time period. Given the entropy reduction of about 71, 13 and 10.5% for discharge, rainfall and temperature time series respectively, it can be concluded that fluctuation decrease of discharge time series has relatively more effect on groundwater level oscillation patterns with respect to the rainfall and temperature time series. In this regard, it could be concluded that the climate change factors are not facing significant changes; thus, human activities can be regarded as the main reason for the declining groundwater level in this plain.

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

Fractals ◽

10.1142/s0218348x20400320 ◽

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.

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Wavelet entropy-based evaluation of intrinsic predictability of time series

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.5145005 ◽

2020 ◽

Vol 30 (3) ◽

pp. 033117 ◽

Cited By ~ 10

Author(s):

Ravi Kumar Guntu ◽

Pavan Kumar Yeditha ◽

Maheswaran Rathinasamy ◽

Matjaž Perc ◽

Norbert Marwan ◽

...

Keyword(s):

Time Series ◽

Wavelet Entropy

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The LDE-Type Flare Occurrence (1969-1993)

International Astronomical Union Colloquium ◽

10.1017/s0252921100025458 ◽

1994 ◽

Vol 144 ◽

pp. 279-282

Author(s):

A. Antalová

Keyword(s):

Time Series ◽

Fourier Analysis ◽

Sunspot Cycle ◽

List Type ◽

Type Number ◽

Solar Cycles ◽

Type Iv ◽

Long Duration ◽

Cycle Maximum ◽

Flare Index

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.

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