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

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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. 
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     author = {A. I. Sedov},
     title = {The use of the inverse problem of spectral analysis to forecast time series},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2019_6_1_a7/}
}
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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/