Abstract:
The paper proposes a new method to forecast time series. We assume that a time series is a sequence of eigenvalues of a discrete self-adjoint operator acting in a Hilbert space. In order to construct such an operator, we use the theory of solving inverse problems of spectral analysis. The paper gives a theoretical justification for the proposed method. An algorithm for solving the inverse problem is given. Also, we give an example of constructing a differential operator whose eigenvalues practically coincide with a given time series.
Keywords:inverse spectral problem, perturbation theory, time series.
\Bibitem{Sed19}
\by A.~I.~Sedov
\paper The use of the inverse problem of spectral analysis to forecast time series
\jour J. Comp. Eng. Math.
\yr 2019
\vol 6
\issue 1
\pages 74--78
\mathnet{http://mi.mathnet.ru/jcem142}
\crossref{https://doi.org/10.14529/jcem190108}
\elib{https://elibrary.ru/item.asp?id=37294997}
Linking options:
https://www.mathnet.ru/eng/jcem142
https://www.mathnet.ru/eng/jcem/v6/i1/p74
This publication is cited in the following 2 articles:
A. I. Sedov, “Prognozirovanie mnogomernogo vremennogo ryada metodom obratnoi zadachi spektralnogo analiza”, J. Comp. Eng. Math., 9:1 (2022), 35–42
A. I. Sedov, G. A. Kameneva, T. A. Bondarenko, Lecture Notes in Electrical Engineering, 729, Advances in Automation II, 2021, 306
Citation in format AMSBIB
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