Sedov, A. I. The use of the inverse problem of spectral analysis to forecast time series. (English) Zbl 1499.35721 J. Comput. Eng. Math. 6, No. 1, 74-78 (2019). Summary: 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. MSC: 35R30 Inverse problems for PDEs 35A01 Existence problems for PDEs: global existence, local existence, non-existence 47A52 Linear operators and ill-posed problems, regularization Keywords:inverse spectral problem; perturbation theory; time series × Cite Format Result Cite Review PDF Full Text: DOI MNR References: [1] “Joint Sessions of the Petrovskii Seminar on Differential Equations and Mathematical Problems of Physics and the Moscow Mathematical Society (Thirteenth session, 2-5 February 1990)“, V. V. Dubrovskiy, V. A. Sadovnichiy, “To the Substantiation of the Method of Calculating the Eigenvalues of a Discrete Operator using Regularized Traces”, pp. 137, Russian Math. Surveys, 45:4 (1990), 127-155 · doi:10.1070/RM1990v045n04ABEH002368 [2] A. I. Sedov, “O suschestvovanii i edinstvennosti resheniya obratnoi zadachi spektralnogo analiza dlya samosopryazhennogo diskretnogo operatora”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2008, no. 2, 100-103 · Zbl 1291.47010 [3] A. I. Sedov, “O priblizhennom reshenii obratnoi zadachi spektralnogo analiza dlya stepeni operatora Laplasa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2010, no. 5, 73-78 · Zbl 1227.35246 [4] A. I. Sedov, “Ob obratnoi zadache spektralnogo analiza”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 7, 91-99 · Zbl 1244.47015 [5] G. A. Zakirova, E. V. Kirillov, “The Existence of Solution of the Inverse Spectral Problem for Discrete Self- Adjoint Semi-Bounded from Below Operator”, J. Comp. Eng. Math., 2:4 (2015), 95-99 · Zbl 1359.35004 · doi:10.14529/jcem150410 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.