Universidad Complutense de Madrid
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Degrees of freedom of a time series

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Mera Rivas, Maria Eugenia and Morán Cabré, Manuel (2002) Degrees of freedom of a time series. Journal of Statistical Physics, 106 (1-2). pp. 125-145. ISSN 0022-4715

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Official URL: https://doi.org/10.1023/A:1013172129075



Abstract

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 dimμ>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.


Item Type:Article
Uncontrolled Keywords:Degrees of freedom; Dimension; Embedology; Singular value decomposition; Liapunov exponents.
Subjects:Sciences > Mathematics
ID Code:58885
Deposited On:17 Feb 2020 13:29
Last Modified:17 Feb 2020 13:29

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