Long-memory traces in $$\hbox {PM}_{10}$$ time series in Athens, Greece: investigation through DFA and R/S analysis

Abstract

This paper investigates the existence of chaos in concentration dynamics of particulate matter with an aerodynamic diameter less than or equal to $$10\,\upmu \hbox {m}$$ ( $$\hbox {PM}_{10}$$ ) in the greater Athens area (GAA), Greece. It reports findings on three 16-year $$\hbox {PM}_{10}$$ time series recorded by three different air pollution monitoring stations located in GAA and examines if critical fractal epochs with long memory exist. Detrended Fluctuation Analysis (DFA) and Rescaled Range (R/S) Analysis were used via sliding windows of approximately 1-month duration. In all $$\hbox {PM}_{10}$$ time series, several segments were found with critical fractal behaviour and hidden long-memory patterns. All these segments exhibited Hurst exponents above 0.75 and DFA exponents above 1.75. Twelve $$\hbox {PM}_{10}$$ segments with fractality and long memory were commonly identified by both techniques. In one case, long memory was identified concurrently across all three air pollution monitoring stations and in another case, across two stations. The importance of the agreement between two different and independent chaos-analysis techniques is discussed in association with the proper selection of threshold values. This is the second time to address chaos in $$\hbox {PM}_{10}$$ data series in GAA, and the first time to combine two widely accepted techniques, DFA and R/S analysis.