Cheng, B.; Tong, H. Orthogonal projection, embedding dimension and sample size in chaotic time series from a statistical perspective. (English) Zbl 0859.62077 Philos. Trans. R. Soc. Lond., Ser. A 348, No. 1688, 325-341 (1994). 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. Cited in 4 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:estimation of embedding dimension; sequence of L2-spaces; distance functions; nonlinear autoregression; orthogonal projections; time series; chaotic skeleton; embedding dimension; sample size requirement; curse of dimensionality PDFBibTeX XMLCite \textit{B. Cheng} and \textit{H. Tong}, Philos. Trans. R. Soc. Lond., Ser. A 348, No. 1688, 325--341 (1994; Zbl 0859.62077) Full Text: DOI