2003/05/20 by Ilya Zaliapin, I. Zaliapin, Andrei Gabrielov +3
Computer Science · Mathematics · Physics and Astronomy · #Image and Signal Denoising Methods #NMR spectroscopy and applications #Statistical and numerical algorithms #physics.data-an
paper · pdf · doi:10.1142/s0218348x04002604
published as Fractals, 12, No. 3, 275-292 (2004) · 37 pages, 19 figures
arxiv created 2003/05/20 · openalex publication_date 2004/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated, and on its base, a computationally effective algorithm is constructed for decomposition of a time series into a hierarchy of trends (local linear approximations) at different scales. The top of the hierarchy is the global linear approximation over the whole observational interval, the bottom is the original time series. Each internal level of the hierarchy corresponds to a piecewise linear approximation of analyzed series. Possible applications of the introduced Multiscale Trend Analysis (MTA) go far beyond the linear interpolation problem: This paper develops and illustrates methods of self-affine, hierarchical, and correlation analyses of time series.