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

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Department of Informatics and Computer Engineering, University of West Attica, Agiou Spyridonos, GR-12243 Aigaleo, Greece
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Department of Mechanical Engineering, University of West Attica, Petrou Ralli & Thivon 250, GR-12244 Aigaleo, Greece
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Department of Environment, Ionian University, M. Minotou-Giannopoulou 26, GR-29100 Zakynthos, Greece
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Department of Industrial Design and Production Engineering, University of West Attica, Petrou Ralli & Thivon 250, GR-12244 Aigaleo, Greece
*
Author to whom correspondence should be addressed.
Environments 2019, 6(3), 29; https://doi.org/10.3390/environments6030029
Received: 11 January 2019 / Revised: 15 February 2019 / Accepted: 19 February 2019 / Published: 26 February 2019
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. View Full-Text
Keywords: fractal dimension; katz; higuchi; sevcik; R/S analysis; Hurst exponent; air pollution; PM10 fractal dimension; katz; higuchi; sevcik; R/S analysis; Hurst exponent; air pollution; PM10
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Nikolopoulos, D.; Moustris, K.; Petraki, E.; Koulougliotis, D.; Cantzos, D. Fractal and Long-Memory Traces in PM10 Time Series in Athens, Greece. Environments 2019, 6, 29.

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