Geodesic
The use of the inverse problem of spectral analysis to forecast time series
Journal of computational and engineering mathematics, Tome 6 (2019) no. 1, pp. 74-78 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{JCEM_2019_6_1_a7,
     author = {A. I. Sedov},
     title = {The use of the inverse problem of spectral analysis to forecast time series},
     journal = {Journal of computational and engineering mathematics},
     pages = {74--78},
     year = {2019},
     volume = {6},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2019_6_1_a7/}
}
TY  - JOUR
AU  - A. I. Sedov
TI  - The use of the inverse problem of spectral analysis to forecast time series
JO  - Journal of computational and engineering mathematics
PY  - 2019
SP  - 74
EP  - 78
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JCEM_2019_6_1_a7/
LA  - en
ID  - JCEM_2019_6_1_a7
ER  - 
%0 Journal Article
%A A. I. Sedov
%T The use of the inverse problem of spectral analysis to forecast time series
%J Journal of computational and engineering mathematics
%D 2019
%P 74-78
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/JCEM_2019_6_1_a7/
%G en
%F JCEM_2019_6_1_a7
A. I. Sedov. The use of the inverse problem of spectral analysis to forecast time series. Journal of computational and engineering mathematics, Tome 6 (2019) no. 1, pp. 74-78. http://geodesic.mathdoc.fr/item/JCEM_2019_6_1_a7/

[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 | MR

[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

[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

[4] A. I. Sedov, “Ob obratnoi zadache spektralnogo analiza”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 7, 91–99 | Zbl

[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 | DOI | Zbl