Journal of Statistical Physics

, Volume 106, Issue 1–2, pp 125–145

Degrees of Freedom of a Time Series

  • M. Eugenia Mera
  • Manuel Morán

DOI: 10.1023/A:1013172129075

Cite this article as:
Mera, M.E. & Morán, M. Journal of Statistical Physics (2002) 106: 125. doi:10.1023/A:1013172129075


We give a formal proof that if f is a smooth dynamics on a d-dimensional smooth manifold and μ is an ergodic and exact dimensional measure with Hausdorff dimension dim μ>d−1, then the number d of degrees of freedom of the dynamics can be recovered from the observation of an orbit. We implement, with this purpose, an algorithm based on the analysis of the microstructure of μ. We show how a correct estimation of d permits the computation of the Liapunov spectrum with a high accuracy avoiding the issue of the spurious exponents.

degrees of freedom dimension embedology singular value decomposition Liapunov exponents 

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • M. Eugenia Mera
    • 1
  • Manuel Morán
    • 1
  1. 1.Departamento de Análisis Económico IUniversidad ComplutenseMadridSpain

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