Modified DFA for a robust discrimination between short-term and long-range correlations in short time series

Since the standard detrended fluctuation analysis (s-DFA) method depends on asymptotic power-law scaling assumption, it has been questioned on its ability in characterizing the correlation structure at the small scales, let alone discriminating the correlation structures of short time series. A modified DFA (m-DFA) with a novel defined fluctuation function is employed in this study to discriminate and characterize the distinct (short-termed or long-ranged) correlation structures in short time series. Detailed results show that the m-DFA is able not only to distinguish the short-termed, or long-ranged correlation, but also to well quantify the correlation strengths in both output from classical models and real-world series (for example, DTR variability over China) of data length as short as 2000. Moreover, m-DFA can work effectively in time series with strong correlation of even shorter length as 500. The correlation structures inferred by m-DFA in short intervals contribute greatly to better understanding of local and evolutionary correlation features of an underlying process, not limited to only global one from s-DFA.