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Superfamily classification of nonstationary time series based on DFA scaling exponents

The superfamily phenomenon of time series with different dynamics can be characterized by the motif rank patterns observed in the nearest-neighbor networks of the time series in phase space. However, the determinants of superfamily classification are unclear. We attack this problem by studying the influence of linear temporal correlations and multifractality using fractional Brownian motions (FBMs) and multifractal random walks (MRWs). Numerical investigations unveil that the classification of superfamily phenomenon is uniquely determined by the detrended fluctuation analysis (DFA) scaling exponent $α$ of the time series. Only four motif patterns are observed in the simulated data, which are delimited by three DFA scaling exponents $α\simeq 0.25$, $α\simeq 0.35$ and $α\simeq 0.45$. The validity of the result is confirmed by stock market indexes and turbulence velocity signals.