An analysis of multifractal characteristics of API time series in Nanjing, China

• Multifractal characteristic of API time series is studied based on MF-DFA and singularity spectrum.
• Strength of distribution multifractality is stronger than that of correlation multifractality.
• Temporal variation in structure of API time series is mainly related to long-range correlations.

This paper describes multifractal characteristics of daily air pollution index (API) records in Nanjing from 2001 to 2012. The entire daily API time series is first divided into 12 parts that serve as research objects, and the generalized Hurst exponent is calculated for each series. And then, the multifractal sources are analyzed and singularity spectra are shown. Next, based on a singularity spectrum, the multifractal-characteristics parameters (maximum exponent αα00, spectrum width ΔΔαα, and asymmetry ΔΔααas) are introduced. The results show that the fractality of daily API for each year is multifractal. The multifractal sources originate from both a broad probability density function and different long-range correlations with small and large fluctuations. The strength of the distribution multifractality is stronger than that of the correlation multifractality. The variation in the structure of API time series with increasing years is mainly related to long-range correlations. The structure of API time series in some years is richer. These findings can provide a scientific basis for further probing into the complexity of API.