Magnitude and sign scaling in power-law correlated time series
Yosef Ashkenazy, Shlomo Havlin, Plamen Ch. Ivanova,
C-K. Peng, Verena Schulte-Frohlinde and H. Eugene Stanley
Abstract
A time series can be decomposed into two sub-series: a magnitude
series and a sign series. Here we analyze separately the scaling
properties of the magnitude series and the sign series using the
increment time series of cardiac interbeat intervals as an example. We
find that time series having identical distributions and long-range
correlation properties can exhibit quite different temporal
organizations of the magnitude and sign sub-series. From the cases we
study, it follows that the long-range correlations in the magnitude
series indicate nonlinear behavior. Specifically, our results suggest
that the correlation exponent of the magnitude series is a
monotonically increasing function of the multifractal spectrum width
of the original series. On the other hand, the sign series mainly
relates to linear properties of the original series. We also show that
the magnitude and sign series of the heart interbeat interval series
can be used for diagnosis purposes.