scholarly journals Stochastic and Self-Organisation Patterns in a 17-Year PM10 Time Series in Athens, Greece

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 307
Author(s):  
Dimitrios Nikolopoulos ◽  
Aftab Alam ◽  
Ermioni Petraki ◽  
Michail Papoutsidakis ◽  
Panayiotis Yannakopoulos ◽  
...  
Keyword(s):  
Time Series ◽  
Symbolic Dynamics ◽  
Long Memory ◽  
Tsallis Entropy ◽  
Entropy Analysis ◽  
Boltzmann Entropy ◽  
Analysis Techniques ◽  
Block Entropy ◽  
Self Organisation ◽  
First Time

This paper utilises statistical and entropy methods for the investigation of a 17-year PM10 time series recorded from five stations in Athens, Greece, in order to delineate existing stochastic and self-organisation trends. Stochastic patterns are analysed via lumping and sliding, in windows of various lengths. Decreasing trends are found between Windows 1 and 3500–4000, for all stations. Self-organisation is studied through Boltzmann and Tsallis entropy via sliding and symbolic dynamics in selected parts. Several values are below −2 (Boltzmann entropy) and 1.18 (Tsallis entropy) over the Boltzmann constant. A published method is utilised to locate areas for which the PM10 system is out of stochastic behaviour and, simultaneously, exhibits critical self-organised tendencies. Sixty-six two-month windows are found for various dates. From these, nine are common to at least three different stations. Combining previous publications, two areas are non-stochastic and exhibit, simultaneously, fractal, long-memory and self-organisation patterns through a combination of 15 different fractal and SOC analysis techniques. In these areas, block-entropy (range 0.650–2.924) is significantly lower compared to the remaining areas of non-stochastic but self-organisation trends. It is the first time to utilise entropy analysis for PM10 series and, importantly, in combination with results from previously published fractal methods.

scholarly journals Fractal and Long-Memory Traces in PM10 Time Series in Athens, Greece

Environments ◽  
2019 ◽  
Vol 6 (3) ◽  
pp. 29 ◽  
Author(s):  
Dimitrios Nikolopoulos ◽  
Konstantinos Moustris ◽  
Ermioni Petraki ◽  
Dionysios Koulougliotis ◽  
Demetrios Cantzos
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Meta Analysis ◽  
Fractal Dimensions ◽  
Threshold Values ◽  
Rescaled Range ◽  
Computational Calculations ◽  
Fractal Time ◽  
First Time ◽  
Memory Techniques

This work examines if chaos and long memory exist in PM10 concentrations recorded in Athens, Greece. The algorithms of Katz, Higuchi, and Sevcik were employed for the calculation of fractal dimensions and Rescaled Range (R/S) analysis for the calculation of the Hurst exponent. Windows of approximately two months’ duration were employed, sliding one sample forward until the end of each utilized signal. Analysis was applied to three long PM10 time series recorded by three different stations located around Athens. Analysis identified numerous dynamical complex fractal time-series segments with patterns of long memory. All these windows exhibited Hurst exponents above 0.8 and fractal dimensions below 1.5 for the Katz and Higuchi algorithms, and 1.2 for the Sevcik algorithm. The paper discusses the importance of threshold values for the postanalysis of the discrimination of fractal and long-memory windows. After setting thresholds, computational calculations were performed on all possible combinations of two or more techniques for the data of all or two stations under study. When all techniques were combined, several common dates were found for the data of the two combinations of two stations. When the three techniques were combined, more common dates were found if the Katz algorithm was not included in the meta-analysis. Excluding Katz’s algorithm, 12 common dates were found for the data from all stations. This is the first time that the results from sliding-window chaos and long-memory techniques in PM10 time series were combined in this manner.

scholarly journals Symbolic time series characterization and block entropy analysis of DC-DC converters

2008 ◽  
Vol 57 (10) ◽  
pp. 6112
Author(s):  
Wang Xue-Mei ◽  
Zhang Bo ◽  
Qiu Dong-Yuan ◽  
Chen Liang-Gang
Keyword(s):  
Time Series ◽  
Entropy Analysis ◽  
Block Entropy

scholarly journals On nonparametric regression for bivariate circular long-memory time series

2021 ◽  
Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Long Range ◽  
Long Memory ◽  
Regression Function ◽  
Confidence Bands ◽  
Long Range Dependence ◽  
Asymptotic Results ◽  
Memory Time ◽  
Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

scholarly journals Multiscale Sample Entropy of Two-Dimensional Decaying Turbulence

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 245
Author(s):  
Ildoo Kim
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Soap Film ◽  
Sample Entropy ◽  
Series Data ◽  
Entropy Analysis ◽  
Measured Time ◽  
Energetic Analysis ◽  
Turbulence Data ◽  
Decaying Turbulence

Multiscale sample entropy analysis has been developed to quantify the complexity and the predictability of a time series, originally developed for physiological time series. In this study, the analysis was applied to the turbulence data. We measured time series data for the velocity fluctuation, in either the longitudinal or transverse direction, of turbulent soap film flows at various locations. The research was to assess the feasibility of using the entropy analysis to qualitatively characterize turbulence, without using any conventional energetic analysis of turbulence. The study showed that the application of the entropy analysis to the turbulence data is promising. From the analysis, we successfully captured two important features of the turbulent soap films. It is indicated that the turbulence is anisotropic from the directional disparity. In addition, we observed that the most unpredictable time scale increases with the downstream distance, which is an indication of the decaying turbulence.

scholarly journals The CSS and The Two-Staged Methods for Parameter Estimation in SARFIMA Models

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Erol Egrioglu ◽  
Cagdas Hakan Aladag ◽  
Cem Kadilar
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Simulation Study ◽  
Long Memory ◽  
Moving Average ◽  
Mean Square ◽  
Sample Sizes ◽  
Advantages And Disadvantages

Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) models are used in the analysis of seasonal long memory-dependent time series. Two methods, which are conditional sum of squares (CSS) and two-staged methods introduced by Hosking (1984), are proposed to estimate the parameters of SARFIMA models. However, no simulation study has been conducted in the literature. Therefore, it is not known how these methods behave under different parameter settings and sample sizes in SARFIMA models. The aim of this study is to show the behavior of these methods by a simulation study. According to results of the simulation, advantages and disadvantages of both methods under different parameter settings and sample sizes are discussed by comparing the root mean square error (RMSE) obtained by the CSS and two-staged methods. As a result of the comparison, it is seen that CSS method produces better results than those obtained from the two-staged method.

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