## 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.

Original language | English |
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Pages (from-to) | 19-41 |

Number of pages | 23 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 323 |

DOIs | |

State | Published - 15 May 2003 |

### Bibliographical note

Funding Information:Partial support was provided by the NIH/National Center for Research Resources (P41 RR13622), the Israel-USA Binational Science Foundation, and the German Academic Exchange Service (DAAD). We thank L.A.N. Amaral, D. Baker, S.V. Buldyrev, A. Bunde, J.M. Hausdorff, R. Karasik, J.W. Kantelhardt, G. Paul, Y. Yamamoto, and especially to A.L. Goldberger for helpful discussions.

## Keywords

- Magnitude correlations
- Multifractal spectrum
- Nonlinearity
- Scaling
- Volatility