Orthogonal projection, embedding dimension and sample size in chaotic time series from a statistical perspective

15 September 1994

journal article
Published by The Royal Society in Philosophical Transactions A

Vol. 348 (1688) , 325-341
https://doi.org/10.1098/rsta.1994.0094

Abstract

By studying systematically the orthogonal projections, in a particular sense associated with a (random) time series admitting a possibly chaotic skeleton and in a sequence of suitably defined L ₂ -spaces, we describe a geometric characterisation of the notion of embedding dimension within a statistical framework. The question of sample size requirement in the statistical estimation of the said dimension is addressed heuristically, ending with a pleasant surprise: the curse of dimensionality may be lifted except in the excessively stringent cases.

Keywords

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