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 Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods

1997 ◽  
Vol 246 (3-4) ◽  
pp. 609-632 ◽  
Author(s):  
David C. Caccia ◽  
Donald Percival ◽  
Michael J. Cannon ◽  
Gary Raymond ◽  
James B. Bassingthwaighte
Keyword(s):  
Time Series ◽  
Dispersional Analysis ◽  
Rescaled Range ◽  
Fractal Time

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 Conjugate fluctuation analysis for a set of 41 magnetic clouds measured by the ACE spacecraft

2014 ◽  
Vol 1 (1) ◽  
pp. 583-613 ◽  
Author(s):  
A. Ojeda González ◽  
W. D. Gonzalez ◽  
O. Mendes ◽  
M. O. Domingues ◽  
R. R. Rosa
Keyword(s):  
Time Series ◽  
Plasma Sheath ◽  
Magnetic Clouds ◽  
Fluctuation Analysis ◽  
Threshold Values ◽  
Time Intervals ◽  
Rescaled Range ◽  
Distribution Of Values ◽  
Detrended Fluctuation

Abstract. The statistical distribution of values in the signal and the autocorrelations (interpreted as the memory or persistence) between values are attributes of a time series. The autocorrelation function values are positive in a~time series with persistence, while it are negative in a time series with anti persistence. The persistence of values with respect to each other can be strong, weak, or nonexistent. A strong correlation implies a "memory" of previous values in the time series. The long-range persistence in time series could be studied using semivariograms, rescaled-range, detrended fluctuation analysis and Fourier spectral analysis, respectively. In this work the persistence analysis has been used to study IMF time series. We use data from the IMF GSM-components with time resolution of 16 s. Time intervals corresponding to distinct processes around 41 MCs in the period between March 1998 and December 2003 were selected. In this exploratory study the purpose with this selection is to deal with the cases presenting the three periods: plasma sheath, MC and post-MC. We calculated one exponent of persistence (e.g., α, β, Hu, Ha) over the previous three time intervals. The persistence exponent values increased inside cloud regions, and it was possible select the following threshold values: 〈α(j)〉 =1.392; 〈Ha(j)〉 = 0.327; 〈Hu(j)〉 =0.875. These values are useful as another test to evaluate the quality of the identification. If the cloud is well-structured, then the persistence exponents values exceed thresholds. In 80.5% of the cases studied, these tools were able to separate the region of the cloud from neighboring regions. The Hausdorff exponent (Ha) provides the best results.

SUNSPOTS DATA ANALYSIS USING TIME SERIES

Fractals ◽  
2008 ◽  
Vol 16 (03) ◽  
pp. 259-265 ◽  
Author(s):  
YUSUF H. SHAIKH ◽  
A. R. KHAN ◽  
M. I. IQBAL ◽  
S. H. BEHERE ◽  
S. P. BAGARE
Keyword(s):  
Time Series ◽  
Hurst Exponent ◽  
Sunspot Cycle ◽  
Fractal Dimensions ◽  
Data Sets ◽  
Range Analysis ◽  
Data Set ◽  
Rescaled Range ◽  
Rescaled Range Analysis ◽  
Sunspot Data

The record of the sunspot number visible on the sun is regularly collected over the centuries by various observatories for studying the different factors influencing the sunspot cycle and solar activity. Sunspots appear in cycles, and last several years. These cycles follow a certain pattern which is well known. We analyzed monthly and yearly averages of sunspot data observed from year 1818 to 2002 using rescaled range analysis. The Hurst exponent calculated for monthly data sets are 0.8899, 0.8800 and 0.8597 and for yearly data set is 0.7187. Fractal dimensions1 calculated are 1.1100, 1.1200, 1.1403 and 1.2813. From the study of Hurst exponent and fractal dimension, we conclude that time series of sunspots show persistent behavior. The fundamental tool of signal processing is the fast Fourier transform technique (FFT). The sunspot data is also analyzed using FFT. The power spectrum of monthly and yearly averages of sunspot shows distinct peaks at 11 years confirming the well known 11-year cycle. The monthly sunspot data is also analyzed using FFT to filter the noise in the data.

CHAOS, NOISE AND COMPLEX FRACTAL DIMENSIONS

Fractals ◽  
1993 ◽  
Vol 01 (01) ◽  
pp. 21-28 ◽  
Author(s):  
BRUCE J. WEST ◽  
X. FAN
Keyword(s):  
Time Series ◽  
Power Law ◽  
Colored Noise ◽  
Fractal Dimensions ◽  
Chaotic Time Series ◽  
Range Analysis ◽  
Rescaled Range ◽  
Rescaled Range Analysis ◽  
Power Law Index ◽  
Two Degree Of Freedom

Herein we propose a measure to distinguish a chaotic time series from one which is colored noise. We apply rescaled range analysis to the chaotic time series generated by a two-degree-of-freedom, nonintegrable Hamiltonian system, and find a modulated power-law for R/S. The combination of the power-law index and the period of modulation suggests a complex fractal dimension, which may be the signature of chaos. Some residual questions are collected.

Canadian REITs and Stock Prices: Fractional Cointegration and Long Memory

2006 ◽  
Vol 09 (03) ◽  
pp. 441-462 ◽  
Author(s):  
Ata Assaf
Keyword(s):  
Stock Prices ◽  
Long Memory ◽  
Fractional Cointegration ◽  
Long Run ◽  
Rescaled Range ◽  
Residual Series ◽  
Short Run ◽  
Memory Techniques ◽  
Property Markets

The literature is not clear on whether there are co-dependencies domestically across real estate and stock markets, despite the importance of this question for portfolio diversification strategies. In this article, we use fractional cointegration and long memory techniques to search for co-dependence in the Canadian markets. The measures of long-term persistence employed are the modified rescaled range statistic (R/S) proposed by Lo (1991), and the rescaled variance (V/S) statistic proposed by Giraitis et al. (2003). We find evidence to suggest long co-memories between stock and securitized property markets in the long term, but some evidence is also found in some sub-samples. The implication of our results is that securitized property and stocks are not considered to be substitutable assets over the short run and these assets may be held together in a portfolio for diversification purposes. However, over the long run, there is less benefit of holding both assets in a portfolio, since a fractional cointegration is found in the residual series.

Return Intervals Analysis of the Sunspot Time Series

2010 ◽  
Vol 29-32 ◽  
pp. 1144-1149
Author(s):  
Jie Fan ◽  
Wan Qing Li ◽  
Hong Zhang ◽  
Ke Qiang Dong
Keyword(s):  
Time Series ◽  
Long Range ◽  
Threshold Values ◽  
Range Analysis ◽  
Scaling Method ◽  
Long Range Correlations ◽  
Rescaled Range ◽  
Rescaled Range Analysis

Rescaled range analysis (R/S) method is a scaling method commonly used for detecting the long-range correlations in many time series. The aim of this paper is to show that, using the rescaled range analysis on sunspot time series, how the threshold values q affects the correlations of the return intervals for events above a certain threshold q. We find that both the original records and the return intervals are long-range correlated.

An Epistemological Criticism of Social Entrepreneurship: Is Social Entrepreneurship a Sound Scientific Field of Research

2018 ◽  
Author(s):  
Amir Forouharfar
Keyword(s):  
Social Entrepreneurship ◽  
Social Constructivism ◽  
Social Epistemology ◽  
American English ◽  
Meta Analysis ◽  
Research Question ◽  
Knowledge Structure ◽  
Scientific Field ◽  
The Other ◽  
First Time

The paper was shaped around the pivotal question: Is SE a sound and scientific field of research? The question has given a critical tone to the paper and has also helped to bring out some of the controversial debates in the realm of SE. The paper was organized under five main discussions to be able to provide a scientific answer to the research question: (1)<b> </b>is “social entrepreneurship” an oxymoron?, (2) the characteristics of SE knowledge, (3) sources of social entrepreneurship knowledge, (4) SE knowledge: structure and limitations and (5) contributing epistemology-making concepts for SE.<b> </b>Based on the sections,<b> </b>the study relied on the relevant philosophical schools of thought in <i>Epistemology </i>(e.g. <i>Empiricism</i>, <i>Rationalism</i>, <i>Skepticism</i>, <i>Internalism</i> vs. <i>Externalism</i>,<i> Essentialism, Social Constructivism</i>, <i>Social Epistemology, etc.</i>) to discuss these controversies around SE and proposes some solutions by reviewing SE literature. Also, to determine the governing linguistic discourse in the realm of SE, which was necessary for our discussion,<i> Corpus of Contemporary American English (COCA)</i> for the first time in SE studies was used. Further, through the study, SE buzzwords which constitute SE terminology were derived and introduced to help us narrowing down and converging the thoughts in this field and demarking the epistemological boundaries of SE. The originality of the paper on one hand lies in its pioneering discussions on SE epistemology and on the other hand in paving the way for a construction of sound epistemology for SE; therefore in many cases after preparing the philosophical ground for the discussions, it went beyond the prevalent SE literature through meta-analysis to discuss the cases which were raised. The results of the study verified previously claimed embryonic pre-paradigmatic phase in SE which was far from a sound and scientific knowledge, although the scholarly endeavors are the harbingers of such a possibility in the future which calls for further mature academic discussion and development of SE knowledge by the SE academia.

Sign in / Sign up

Export Citation Format

Share Document