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Orthogonal projection, embedding dimension and sample size in chaotic time series from a statistical perspective. (English) Zbl 0859.62077

Summary: 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 \({\mathcal L}_2\)-spaces, we describe a geometric characterization 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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